TALKS

Relativistic irreversible thermodynamics: Where do we stand?
L.S. García-Colín

Universidad Autonoma Metropolitana and El Colegio Nacional Mexico

Abstract: Relativistic Irreversible Thermodynamics is still in the process of being developed. In spite of the many efforts that have been advanced in the past seventy years to accomplish a complete, unquestionable formalism, the existing ones have still many subtle debatable drawbacks. Two of the most important ones are the way of introducing heat -dissipation- in the theory of relativity and the derivation of the correct extension of the classical Navier-Stokes equations in this framework.
In this lecture I will discuss the basic features of the main representative theories together with their weak points.I will also include a recent version drawn from kinetic theory as well as a possible experimental test which, if realizable in the laboratory, could shed light on the most suitable of all these versions.

Nonlinear extension of Onsager's theory and dynamic arrest in colloidal suspensions
M. Medina-Noyola

Instituto de Fisica Manuel Sandoval Vallarta, Universidad Autonoma de San Luis Potosi

Abstract: In this work we propose an extension of Onsager's theory of time-dependent thermal fluctuations of equilibrium systems, to the case in which the system relaxes irreversibly along a non-equilibrium trajectory that can be approximated as a sequence of stationary states. The resulting canonical theory is applied to the description of the irreversible diffusive relaxation of the local concentration of a colloidal dispersion that proceeds toward its stable thermodynamic equilibrium state. The central assumption of this theory is that the irreversible relaxation of the macroscopically-observed mean value of the local concentration profile of colloidal particles is described by a diffusion equation involving a local mobility that depends not only on the mean profile but also on the time-evolving pair distribution function (t-PDF) for which we also derive the corresponding relaxation equation. The resulting theory considers, for example, the possibility that these relaxation processes occur under the influence of external fields, such as gravitational forces acting in the process of sedimentation, but which may in the process be trapped in meta-stable or dynamically arrested states

Time evolution of thermodynamic temperature in the early stage of universe
F. Márkus [1], F. Vázquez [2], K. Gambár [3]

[1] Department of Physics, Budapest University of Technology and Economics, Budafoki 8, H-1521 Budapest, Hungary, [2] Department of Physics, Universidad Autonoma de Morelos, Cuernavaca, Mor., Mexico, [3] Dennis Gabor Applied University, Etele ut 68, H-1115 Budapest Hungary

Abstract: We show a possible way to introduce naturally the concept of a Lorentz invariant dynamical temperature which may be a thermodynamic parameter in cosmological models. This is done within the framework of classical field theory. A scalar field $\varphi$ is introduced which acts as a potential function to generate the (thermo)dynamic temperature. Such a potential allows us to describe the time evolution of this fundamental thermal property in the framework of inflationary models of the early universe. The dynamics contains a phase transition dividing the energy propagation into a dissipative and a non-dissipative process involving a spontaneous symmetry breaking mechanism. We find that the time evolution of the inflation field $\phi$ involves two main stages: first it decreases in the inflation period and later, after a long time, it starts to oscillate with a decreasing amplitude. It is shown that the general behavior of the thermal field $\varphi$ differs from that of the inflation field. It decreases reaching its minimal value and then, at about the beginning of the oscillating stage, it increases monotonically converting the energy of the inflation field into heat in the post-inflationary reheating process. This description is in line with cosmological inflationary models.

The Rayleigh-Brillouin spectrum as a test for non-equilibrium special relativistic irreversible thermodynamics
A. Sandoval-Villalbazo [1], A.L. García-Perciante [2], L.S. García-Colín [3]

[1] Departamento de Fisica y Matematicas, Universidad Iberoamericana, [2] Departamento de Matematicas Aplicadas y Sistemas, UAM-Cuajimalpa, [3] Departamento de Fisica, UAM-Iztapalapa

Abstract: This work shows the calculation of the Rayleigh-Brillouin spectrum in three different versions of relativistic non-equilibrium thermodynamics. We analyze the outcomes in each case and question the validity of the three aproaches. We finally address the question concerning which of the theories is a better candidate for properly describing relativistic hydrodynamics.

Dissipative relativistic hydrodynamics: kinetic foundations
A.L. García-Perciante [1], A. Sandoval-Villalbazo [2], L.S. García-Colín [3]

[1] Depto. de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, [2] Depto. de Fisica y Matematicas, Universidad Iberoamericana, [3] Depto. de Fisica, Universidad Autonoma Metropolitana-Iztapalapa

Abstract: Following the classical approach to linear irreversible thermodynamics as provided by Boltzmann's kinetic equation, we discuss the analogous situation for the case of relativistic irreversible thermodynamics. In particular the long debated question regarding the existence of a physically sound first order dissipative theory can be addressed within this framework. We show explicitly that a relativistic Navier-Stokes regime follows from this approach.

Fluctuation relations for a classical harmonic oscillator in an electromagnetic field
J.I. Jiménez-Aquino , R.M. Velasco , F.J. Uribe

Universidad Autonoma Metropolitana-Iztapalapa

Abstract: In this work, we establish some fluctuation relations for a classical two-dimensional system of independent charged harmonic oscillators in the presence of an electromagnetic field. The main fluctuation relation quantifies irreversible behavior by comparing probabilities of observing particular trajectories during forward and backward processes and is expressed in terms of the work performed by the externally time-dependent electric field when the system is driven away from equilibrium. In the absence of a harmonic force and assuming a constant electric field, our theoretical results reduce to the fluctuation relations for a classical two-dimensional system of noninteracting electrons under the influence of externally crossed electric and magnetic fields, recently studied by D. Roy and N. Kumar, Phys. Rev. E 78, 052102 (2008).

Fluctuations in nonequilibrium thermodynamics
J.V. Sengers

Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742 USA

Abstract: The lecture will deal with thermal fluctuations on hydrodynamic scales in fluids and fluid mixtures that are out of thermal or mechanical equilibrium, but in the absence of convection or turbulence. The principle of local thermodynamic equilibrium is known to be valid for the thermodynamic properties, however, it is never valid for the fluctuations of these properties. While thermal fluctuations in equilibrium fluids are spatially short ranged except at states near a critical point, fluctuations in nonequilibrium fluids are always long ranged, even far away from any hydrodynamic instability. These physical features will be demonstrated for temperature fluctuations in nonisothermal fluids, for concentration fluctuation in mixtures in the presence of a concentration gradient and for velocity fluctuations in laminar flows.

Kinetic theory for binary granular mixtures: Some applications
V. Garzo

Departamento de Fisica, Universidad de Extremadura, E-06071, Badajoz Spain

Abstract: Many features of granular media can be modeled by a fluid of hard spheres with inelastic collisions. Under rapid flow conditions, the sample of grains resembles a granular gas so that binary collisions prevail and kinetic theory tools can be a quite useful tool to analyze granular flows. In the rapid flow regime, the macroscopic behavior of grains can be described through hydrodynamic balance equations for the densities of mass, momentum and energy. At low density, a fundamental basis for the derivation of hydrodynamic equations and explicit expressions for the transport coefficients appearing in them is provided by the Boltzmann equation conveniently modified to account for inelastic binary collisions. The goal of this talk is to give an overview of some recent advances made for binary granular gases by using the Boltzmann kinetic theory. Some of the results will cover aspects such as energy nonequipartition, transport properties, instabilities, violations of the Onsager reciprocal relations and of the Einstein relation, segregation or mixing, non-Newtonian properties,... In some cases, the analytical results will be compared with Monte Carlo and molecular dynamics simulations, showing the reliability of kinetic theory to describe granular flows even for strong dissipation.

Contact Structure Preserving Dynamics in Boltzmann, Enskog and n-point Kinetic Theories
M. Grmela

Ecole Polytechnique de Montreal, Montreal, Canada H3C 3A7

Abstract: The time evolution governed by the Boltzmann equation can be seen as a continuous sequence of Legendre transformations (i.e. contact structure preserving transformations) bringing the Boltzmann entropy to the entropy characterizing the ideal gas in classical equilibrium thermodynamics. In the same framework we discuss time evolutions resulting in non-ideal gas fundamental thermodynamic relations.

Nonequilibrium Monte Carlo simulation of flow-induced crystallization of a short-chain polyethylene liquid in uniaxial elongational flow
C. Baig [1], B.J. Edwards [2]

[1] Institute of Chemical Engineering and High Temperature Chemical Processes, University of Patras, Greece, [2] Department of Chemical and Biomolecular Engineering, University of Tennessee, USA

Abstract: Nonequilibrium Monte Carlo simulations were performed for an atomistic model of a dense liquid composed of linear polyethylene chains undergoing uniaxial elongational flow. The simulations were conducted at four temperatures ranging from 300 K to 450 K. At the higher temperatures of 400 K and 450 K, simulation results revealed that the polyethylene chains were stretched significantly as a function of flow strength, but that the systems remained in the liquid phase. At the lower two temperatures of 300 K and 350 K, clear evidence was obtained of a flow-induced phase transition to a crystalline solid phase. This evidence included a structure factor for the multi-chain system that compared favorably with an experimental x-ray diffraction measurement of a crystalline linear polyethylene at all relevant length scales, including Bragg peaks at the correct k values. Simulated values of the internal energy (and the configurational temperature) revealed a flow-induced jump in absolute value, reminiscent of a first-order phase transition. The heat capacity of both phases could be calculated based on the configurational temperature. A distinct flow-induced enthalpy change was also evident between the liquid and crystalline states. Monitoring the configurational temperature of the system revealed a strong flow decrease with increasing flow strength, providing a plausible microscopic physical origin (i.e., related to the local conformation environment of the chains) for the flow-induced enhancement of the crystalline (or melting) temperature that has been reported in experiments.

Entropy and Chaos of a nonlinear chain of particles
F. Bagnoli [1], R. Rechtman [2]

[1] Dipartimento di Energetica, Universita di Firenze, Firenze, Italy, [2] Centro de Investigacion en Energia, UNAM, Temixco, Morelos, Mexico

Abstract: We study the thermodynamic and chaotic properties of the Fermi, Pasta, Ulam model, a set of particles with simple nonlinear interactions and show that the thermodynamic entropy and the largest Lyapunov exponent or the Kolmogorov-Sinai entropy present the same behavior as the energy of the model changes. In other words, we find that dynamical quantities such as the largest Lyapunov exponent or the KS entropy are really thermodynamic quantities. We justify this relation using a Markov model. We consider a simple irreversible process and show that the relation between dynamic and hydrodynamic quantities holds.

Dynamic renormalization
H.C. Öttinger

Department of Materials, ETH Zurich, Switzerland

Abstract: We show how the dynamic renormalization of nonequilibrium systems can be carried out within the general framework of nonequilibrium thermodynamics. Whereas the renormalization of Hamiltonians is well-known from equilibrium thermodynamics, the renormalization of dissipative brackets, or friction matrices, is the main new feature for nonequilibrium systems. Renormalization turns out to be a reduction rather than a coarse-graining technique, that is, no new dissipative processes arise in the dynamic renormalization procedure. The general ideas are illustrated for dilute polymer solutions where, in renormalizing bead-spring chain models, dissipative hydrodynamic interactions between different smaller beads contribute to the friction coefficient of a single larger bead. An outlook on the dynamic renormalization of gelation dynamics is given.

A functional relationship for Newton´s endoreversible wngine
J.L. del Río-Correa

Physics Department, Universidad Autonoma Metropolitana-Iztapalapa

Abstract: We define a Newton´s endoreversible engine, as an engine where the heat flux from the engine to the cold bath obeys the Newton´s law, but the heat flux from the heat bath to the engine is arbitrary. We find a functional relationship between the engine power and the engine ecological function. We use this relationship for to establish a general relation between two forms of the engine operation mode, i.e. the maximum power (MP) criterion and the maximum ecological function (MEF) criterion. In particular, we find the relation between the operation temperatures of the endoreversible engine and the efficiency engine in both operation modes. We show that under very general conditions the efficiency in the MEF criteria is greater than the efficiency in the MP criteria. We illustrate our results in several special cases and compare them with the numerical results of other authors.

The faint young sun paradox: A finite-time thermodynamic approach
F. Angulo-Brown

Escuela Superior de Fisica y Matematicas - IPN Mexico

Abstract: According to models of stellar evolution, the Sun at the early stages of its main-sequence lifetime had only 70 percent the energy output that it has today. This change in solar luminosity has affected the earth´s radiation balance, in such a manner that two Gyr ago the earth's mean surface temperature would have been below the freezing point of water. However, geological evidence for liquid water as early as 3.8 Gyr has been reported. Thus, radiative balance between Sun and earth along is not sufficient to explain the early presence of liquid water temperatures on earth´s surface. This problem is known as the faint young Sun paradox. Many proposals have been published to solve this paradox. In the present work we propose a finite-time thermodynamic (FTT) approach to obtain liquid water temperature at the early stages of the earth based on a FTT model for air convective cells in the atmosphere. This model uses two modes of atmospheric operation: A maximum power output regime and the so-called ecological regime. Several scenarios of albedo and greenhouse effect are considered.

Complex Systems Approach to Sea Urchin Sperm Navigation
M. Aldana [1], J. Espinal [1], G. Martinez [1], A. Darszon [2], A. Guerrero [2], C. Wood [2]

[1] Instituto de Ciencias Fisicas, Universidad Nacional Autonoma de Mexico, Cuernavaca, Morelos, [2] Instituto de Biotecnologia, Universidad Nacional Atuonoma de Mexico, Cuernavaca Mexico

Abstract: Fertilization is one of the fundamental processes of living systems. Here we study how sea urchin sperms swim towards the egg. As is usual in complex systems, several levels of description are involved in this process. In this presentation we focus, at the biochemical level, on how polypeptides secreted by the egg trigger signaling pathways for calcium oscillations in the flagellum, which modify sperm navigation, producing on occasions chemotaxis. Our theoretical analysis is based on experimental determinations performed within our group. Our modeling incorporates discrete and semi-continuous dynamical formalisms developed for the study of complex networks. Several experimental observations are recovered and some predictions have been corroborated by new experiments. The finding that the chemical network operates at criticality, as in critical phenomena, is a matter for future reflection. Finally, as an overview, we comment on some aspects of sperm navigation related to other levels of description, such as molecular machines present in the flagellum, hydrodynamic considerations and space exploration strategies. A proper understanding and integration of these levels of description is an open challenge.

Non-equilibrium Thermodynamics of Gene Expression and Transcriptional Regulation
E. Hernández-Lemus [1+2]

[1] Departamento de Genomica Computacional, Instituto Nacional de Medicina Genomica, Mexico, D.F., Mexico, [2] Centro de Ciencias de la Complejidad, Universidad Nacional Autonoma de Mexico, Mexico, D.F., Mexico

Abstract: In recent times whole-genome gene expression analysis has turned out to be a highly important tool to study the coordinated function of a very large number of genes within their corresponding cellular environment, especially in relation to phenotypic diversity and disease. A wide variety of methods of quantitative analysis have been developed to cope with high throughput data sets generated by gene expression profiling experiments. Due to the complexity associated with transcriptomics, especially in the case of gene regulation phenomena, most of these methods are of a probabilistic or statistical nature. Even if these methods have reached a central status in the development of an integrative, systematic understanding of the associated biological processes, they very rarely constitute a concrete guide to the actual physicochemical mechanisms behind biological function and the role of these methods is more on a hypotheses generating line. An important improvement could be done with the development of a thermodynamic theory for gene expression and transcriptional regulation that will build the foundations for a proper integration of the vast amount of molecular biophysical data and could lead, in the future, to a systemic view of genetic transcription and regulation. Applications of the thermodynamic formalism are outlined with regards to dynamic response in cancer cell-lines.

Scaling laws and the critical phenomenon analysis in polymer-like micellar solutions
M. Munoz [1], J.E. Puig [1], O. Manero [2], F. Bautista [3]

[1] Universidad de Guadalajara, Chemical Engineering, [2] Universidad Nacional Autonoma de Mexico, Instituto de Investigacion en Materiales, [3] Universidad de Guadalajara, Physics, Centro de Ensenanza Tecnica Industrial

Abstract: The shear-banding flow phenomenon in polymer-like micellar solutions is examined here with the reduced Bautista-Manero-Puig (BMP) model. The model predicts a master flow diagram, in which all data collapse at low shear rates, and exhibits a critical point. Moreover, the model predicts that a non-equilibrium critical line is reached upon decreasing the shear banding intensity parameter, which corresponds to increasing temperature, increasing surfactant concentration or varying salt-to-surfactant concentration. By using non-equilibrium critical theory, the generalized dissipated energy and the scaling laws, a set of symmetrical reduced stress versus reduced shear rate curves is obtained, similar to gas-liquid transitions around the critical point. In addition, we have derived the properties near the critical point, the non-equilibrium critical exponents and found that they are non classical. The model has only two independent dimensionless constants.

Pattern formation and morphology evolution in Langmuir monolayers
A. Gutierrez , R. Castillo

Instituto de Fisica, UNAM. P. O. Box 20-364, D. F., Mexico 01000

Abstract: We present a study of how patterns formed by Langmuir monolayer domains of a stable phase, usually solid or liquid condensed, propagate into a metastable one, usually liquid expanded. During this propagation, the interface between the two phases moves as the metastable phase is transformed into the more stable one. The interface becomes unstable and forms patterns as a result of the competition between a chemical potential gradient that destabilizes the interface on one hand, and line tension that stabilizes the interface on the other. Heat is not playing a role. During domain growth, we found a morphology transition from tip splitting to side branching, doublons were also found. The fractal dimension was also measured. These morphological features were observed with Brewster angle microscopy in three different monolayers at the water/air interface: Nervonic acid, dioctadecylamine, ethyl palmitate, and ethyl stearatem etc. We observed the onset of the instability in round domains when an abrupt lateral pressure jump is made on the monolayer. Frequency histograms of unstable wavelengths are consistent with the linear-instability dispersion relation of classical free-boundary models. Evolution of the fractal dimension as growth evolves has been measured. In addition, we developed a technique for measuring the expanded phase approach velocity in the neighborhood of the growing solid domain, using silica microspheres. Our experiments show evidence of a density profile around the growing domain. A model explaining why Langmuir monolayers present this kind of non-equilibrium growth patterns is presented. At the steady state, the growth behavior is determined by Laplace.s equation in the chemical potential with specific boundary conditions. These equations are equivalent to those used in the theory of morphology diagrams for two-dimensional diffusional growth, where morphological transitions of the kind observed here have been predicted.

Non-equilibrium Thermodynamics Modeling of Concentrated Polymer Blends
M. Dressler [1], B.J. Edwards [2]

[1] ETH Zurich, Switzerland, [2] Department of Chemical Engineering, UT Knoxville, U.S.A.

Abstract: In the third workshop of non-equilibrium Thermodynamics we proposed a non--equilibrium Thermodynamics model for dilute polymer blends (disperse phase volume fraction φ < 0.1) with a droplet morphology [1]. In the fourth workshop we applied this model to analyze microstructure--rheology relationships in simple viscometric flows [2]. Our contribution in the fifth workshop is about non--equilibrium Thermodynamics of more concentrated polymer blends (disperse phase volume fraction φ > 0.1) with a droplet morphology. In these systems we expect significant droplet--droplet interactions, lyotropic isotropic--nematic phase transitions of oriented droplets, distortion elasticity, and a pronounced effect of droplet inertia on the flow behavior. To give a physically satisfactory description of these phenomena, we chose as the thermodynamic variables a second rank conformation tensor for the matrix phase, a droplet shape tensor for the disperse phase, and a droplet orientation tensor. For these thermodynamic variables we derive Poisson and dissipation brackets. We use the bracket formalism of non--equilibrium Thermodynamics to derive a thermodynamically consistent conformation tensor theory for concentrated polymer blends. We discuss this set of flow equations and we compare it with our earlier theories for dilute polymer blends with a droplet morphology.

[1] M. Dressler and B. J. Edwards, Rheology of polymer blends with matrix-phase viscoelasticity and a narrow droplet size distribution, J. Non-Newtonian Fluid Mech. 120 (2004) 189-205.
[2] M. Dressler, B. J. Edwards, E. J. Windhab, An examination of droplet deformation and break-up between concentrically rotating cylinders, J. Non-Newtonian Fluid Mech. 152 (2008) 86-100.

Low frequency vibrational modes and thermal relaxation in glasses
G.G. Naumis [1], F. Salazar [1], R. Romero-Arias [2]

[1] Instituto de Fisica, UNAM, Mexico D.F., Mexico

Abstract: We present a non-linear model that allows us to explore the relationship between energy relaxation, thermal conductivity and the excess of low frequency vibrational modes (LFVM) that are present in glasses. The model is a chain of the Fermi-Pasta-Ulam type, with non-linear second neighbor springs added at random. We show that the time for relaxation is increased as LFVM are removed, while the thermal conductivity diminishes. These results are important in order to understand the role of the cooling speed and thermal conductivity during a glass transition. Also, the model provides evidence for the fundamental importance of LFVM in the Fermi-Pasta-Ulam problem.

Non-Equilibrium Thermodynamics Modeling of Coupled Biochemical Cycles in Living Cells
Y. Demirel

Department of Chemical and Biomolecular Engineering, University of Nebraska Lincoln United States

Abstract: Every developed and adapted biological system extracts useful energy from outside, converts to the adenosine triphosphate (ATP), and uses for the coupled biochemical cycles and transport processes, protein synthesis, and other energy utilizing processes. The coupling refers that a flow occurs without or against its primary thermodynamic driving force, which may be a gradient of temperature, or chemical potential, or reaction affinity. The principles of thermodynamics allow the progress of a process without or against its primary driving force only if it is coupled with another spontaneous process. This is consistent with the statement of second law, which states that a finite amount of organization may be obtained at the expense of a greater amount of disorganization in a series of coupled spontaneous processes. A living cell has to maintain nonvanishing thermodynamic forces, such as electrochemical potential gradient, and hence is an open, nonequilibrium system. This study presents the modeling equations for thermodynamically and mathematically coupled system of an elementary reaction with heat and mass flows and external resistances. The modeling is based on the linear nonequilibrium thermodynamics (LNET) formulations by assuming that the system is in the vicinity of global equilibrium (GE). Experimental investigations revealed that LNET is capable of describing thermodynamically coupled processes of oxidative phosphorylation, mitochondrial H+ pumps, and (Na+ and K+)]-ATPase, because mainly due to enzymatic feedback. Moreover, the LNET formulation does not require the detailed mechanism of the coupling. Kinetic descriptions and considerations may lead to a loss of the generality characteristics of thermodynamic formulations, since the kinetics is based on specific models. The modeling equations have produced some unique cross coefficients between scalar process of chemical reaction and vectorial processes of heat and mass flows. These coefficients relate the cross interactions to measurable kinetic parameters, transport coefficients, and degrees of thermodynamic couplings. Some representative solutions of thermodynamically coupled reaction]transport systems are presented and discussed.

Thermodynamics-guided NEMD on interface
Y. Ding , H.C. Öttinger

Department of Materials, Polymer Physics, ETH Zurich, Switzerland

Abstract: Heat and mass transfer processes through liquid-gas interfaces are of great interest from the perspective of both theoretical physics and engineering applications. We present a thermodynamics-guided Non-Equilibrium Molecular Dynamics (NEMD) study, the goal of which is to expand our understanding of these out-of-equilibrium processes from a theoretical point of view. Rather than result-oriented numerical experiments, thermodynamics-guided simulations are carried out to help defining appropriate thermodynamic variables. Described by well-defined thermodynamic variables, new physics for interfacial phenomena is expected. State-of-art simulation techniques, which aim to overcome the main challenges for NEMD (NE-ensemble control and sampling), will be discussed in detail : Hybrid Monte Carlo and MD simulations for large particle systems (up to million particles) have been designed utilizing the modern multi-CPU and multi-GPU computer architectures. 40 to 100 times hardware speed-up can be achieved with GPU optimized computing. This makes sophisticated NE-sampling of large system achievable in a reasonable time.

Viscoplasticity of metals: comments on dislocation density models
M. Hütter

Department of Materials, Polymer Physics, ETH Zurich, Switzerland

Abstract: The evolution of mobile and immobile (forest) dislocations strongly affects the viscoplastic behavior of crystalline metals. In this contribution, a class of coarse-grained dynamic models for the dislocation densities is examined from the perspective of nonequilibrium thermodynamics. Particularly, analogies and differences to chemical reactions are discussed, and the thermodynamic driving forces for the different kinetic processes are identified. Finally, we address some points that are critical for linking such a description to the atomistic and the macroscopic levels.

Hydrodynamic interactions in confined colloidal suspensions
J.L. Arauz

Instituto de Fisica, Universidad Autonoma de San Luis Potosi Mexico

Abstract: The effect of the hydrodynamic interactions on the motion of confined colloidal particles is studied by optical microscopy. We consider three cases: colloidal particles close to a single wall, confined in a spherical drop, or confined between two walls. In all cases, we track the particles motion using a CCD camera operating at 30 frames per second. From the particles trajectories, different quantities describing the hydrodynamic interactions particle-particle and particle-confining boundaries are obtained. Here, results for quantities such as the mean squared displacement, step distribution functions, hydrodynamic diffusion coefficients and the hydrodynamic function are presented.

Control and structure formation in internally driven colloidal suspensions
I. Pagonabarraga

Dpt. Fisica Fonamental, Universitat de Barcelona, Carrer Marti i Franques, 08028-Barcelona Spain

Abstract: I will discuss the kinetics of suspensions in which their motion and emergent collective behavior is a result of internal mechanisms. I will in particular address the kinetics and collective mechanical properties of colloidal suspensions which can propel as a result of internal processes. I will analyze how they can interact through basic physical processes, such as the ones induced by the embedding solvent in which they move, and will describe how emergent mesostructures can develop spontaneously, and how they are affected by external fields. I will also analyze the effect of such structures on the mechanical properties of these materials.

Heat transfer and entropy production in the parallel plate flow of a power-law fluid with asymmetric convective cooling
M. López de Haro [1], S. Cuevas [2], A. Beltrán [3]

[1] Departamento de Fisica, Universidad de Extremadura, Av. de Elvas s/n, Badajoz 06071, Spain, on sabbatical leave from Centro de Investigacion en Energa, Universidad Nacional Autonoma de Mexico, A.P. 34, Temixco, Mor. 62580, Mexico [2] Centro de Investigacion en Energia, Universidad Nacional Autonoma de Mexico, A.P. 34, Temixco, Mor. 62580, Mexico, [3] Universidad Politecnica de Cataluna, Barcelona, Spain

Abstract: The heat transfer and entropy production in the parallel plate flow of a power-law fluid are analyzed. Asymmetric convective cooling is included in the analysis by considering thermal boundary conditions of the third kind. Peculiarities related to the temperature field for certain values of the power-law index, to our knowledge not reported so far, are pointed out. In cases where physical solutions of the temperature field are obtained, conditions for minimum entropy generation are determined. (*) M.L.H.: The work of MLH has been supported by the Ministerio de Educacion y Ciencia (Spain) through Grant No. FIS2007.60977 (partially financed by FEDER funds) and by the Junta de Extremadura through Grant No. GRU09038.

Thermodynamically consistent coarse graining the non-equilibrium dynamics of unentangled polymer melts
P. Ilg , H.C. Öttinger , M. Kröger

Department of Materials, Polymer Physics, ETH Zurich, Switzerland

Abstract: We present a novel, thermodynamically guided strategy for the dynamic simulation of microscopic models for complex fluids that is able to efficiently bridge the time- and length scale gap between the microscopic level and macroscopic dynamics. The systematic coarse-graining method is exemplified for low-molecular polymeric systems subjected to homogeneous flow fields. We use established concepts of nonequilibrium thermodynamics and an alternating Monte-Carlo-molecular dynamics iteration scheme in order to obtain the model equations for the slow variables [1]. For chosen flow situations of interest, the established model predicts structural as well as material functions beyond the regime of linear response. The results are in quantitative agreement with those obtaind via standard nonequilibrium molecular dynamics simulations. As a by-product, we present the first steady state equibiaxial simulation results for polymer melts. The method is simple to implement and allows for the calculation of time-dependent behavior through quantities readily available from the nonequilibrium steady states. The proposed method is very efficient and particularly powerful for weak up to moderate external forcings, and therefore complements standard nonequilibrium methods which are better suited in the regime of strong external forcings.

[1] P. Ilg, H.C. Öttinger, M. Kröger, Phys. Rev. E, 2009, 79, 011802.

Non-Equilibrium Thermodynamics for surfaces and Local Equilibrium for the Liquid-Vapor Interface
D. Bedeaux

Department of Chemistry, Norwegian University of Science and Technology, Trondheim Norway

Abstract: Experiments done in the last ten years have found temperature differences across the liquid-vapour interface of the order of 10 degrees Celsius during evaporation in one- component systems. These temperature differences are much larger than expected on the basis of kinetic theory. The challenge is to describe these results in a clear macroscopic context, on the one hand, and to understand them on a microscopic level, on the other hand. We will show how non-equilibrium thermodynamics for surfaces provides the needed macroscopic description for multi-component systems. Catalytic surfaces are considered. The description uses, as Gibbs did for equilibrium interfaces, excess densities. This implies that the surface is a separate thermodynamic system. When the system is not in equilibrium the surface will even have a temperature and chemical potentials different from the temperatures and chemical potentials in the adjacent phases. Using balance equations and the Gibbs relation one obtains the excess entropy production of the surface and are thereby able to give force-flux relations (boundary conditions) for transport into and through the surface. An important assumption in this analysis is that the surface is in local equilibrium. We have simulated such transports using molecular dynamics [1-5]. On the basis of these simulations we were then able to verify that the description using non-equilibrium thermodynamics is correct. In order to investigate the validity of local equilibrium in more detail we have used the square gradient model for the surface in one- component systems [6] and for binary mixtures [7,8]. The square gradient contribution to the free energy density shows that there is no local equilibrium in the interfacial region in the continuous description. On the basis of numerical results we have been able to show that in the description using excess densities, obtained by integration over the continuous profiles, the assumption of local equilibrium is valid. We conclude that the use of non-equilibrium thermodynamics for surfaces, using excess densities, is appropriate for many systems.

1. A. Rosjorde, D.W. Fossmo, D. Bedeaux, S. Kjelstrup and B. Hafskjold, J. of Colloid and Int. Science 232 (2000) 178-185, 240 (2001) 355-364
2. J-M. Simon, S. Kjelstrup, D. Bedeaux, and B. Hafskjold, J. Phys. Chem. B108 (2004) 7186
3. J. Xu, S. Kjelstrup and D. Bedeaux, Phys. Chem. Chem. Phys. 8 (2006) 2017-2027
4. J. Ge, S. Kjelstrup, D. Bedeaux, J-M. Simon, B. Rousseaux, Phys. Rev. E75 (2007) 061604
5. S. Kjelstrup, D. Bedeaux, I. Inzoli and J-M. Simon, Energy 33 (2008) 1185-1196
6. E. Johannessen and D. Bedeaux, Physica A 330 (2003) 354-372
7. K.S. Glavatskiy and D. Bedeaux, Phys. Rev. E 77 (2008) 061101, 1-15.
8. K.S. Glavatskiy and D. Bedeaux, Phys. Rev. E 79 (2009) 021608, 1-19.

POSTERS

Conjugate heat transfer and entropy generation optimization of MHD flow in a microchannel
G. Ibánez [1], S. Cuevas [2]

Universidad Politecnica de Chiapas, Eduardo J. Selvas S/N. Col. Magisterial. Tuxla Gutierrez, Chiapas 29010, Mexico, [2] Centro de Investigatcion en Energia, UNAM, A.P. 34, Temixco, Morelos 62580, Mexico

Abstract: Entropy generation due to steady-state conjugate heat transfer of a magnetohydrodynamic flow in a microchannel between two parallel electrically conducting walls of finite thickness is investigated. The heat transfer equations in the solid walls and in the fluid are solved simultaneously using thermal boundary conditions of the third kind at the outer surfaces of the walls and continuity of temperature and heat flux across the fluid-wall interfaces. We assume that a nonzero constant, longitudinal pressure gradient is applied in the x direction of the microchannel. The analytic solutions for the velocity, temperature and electric current density fields of the system are used to calculate the global entropy generation rate explicitly. In dimensionless terms, this function depends on the convective heat transfer coefficients (Biot numbers) of each surface, Bi, Peclet number, Pe, constant axial temperature gradient, dθ/dx, thermal conductivity ratio wall to fluid, γ, dimensionless wall thickness ratio, δ, Hartmann number, M, dimensionless wall conductance ratio, c, and dimensionless ambient temperature, θa. We have taken into account irreversibilities caused by viscous dissipation, heat flow and electric conduction in the fluid and due to heat flow and electric conduction in the walls. It is found that there is an optimum Biot number for both the lower and upper surfaces where the global entropy generation rate displays a minimum for specific operation conditions of the system. Also, we observe that the rate of global entropy reaches minimum values for specific values of dθ/dx, M and c, respectively, when the other parameters are fixed. Moreover, the effects of the externally applied magnetic field on the heat transfer within the MHD microchannel are studied. It is found that there is a magnetic field strength that minimizes the heat transfer.

Numerical study of diffusion in a conical tube
M.V. Vázquez , L. Dagdug

Depto. de Fisica, Universidad Autonoma Metropolitana - Iztapalapa, Mexico, 09340, Distrito Federal

Abstract: Monte Carlo computational simulations were ran to calculate the mean-survival time (MST) of a brownian particle in a conical tube, varying geometrical parameters such as the tube's wall slope and axial length. Theoretically the MST satisfies a backward equation whose solution relates our experimentally determined MST to an effective diffusion, so we can compare this value against several models. Some findings are that both directions of transport are not equivalent and the existing models do not satisfactorily explain the observed behavior.

Kinetic Theory Methods in Traffic Flow
A.R. Méndez [1], R.M. Velasco [2]

[1] Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana - Cuajimalpa, [2] Departamento de Fisica, Universidad Autonoma Metropolitana - Iztapalapa

Abstract: Similarly to the treatment of dilute gases, kinetic methods are formulated to study unidirectional freeway traffic. From these it is possible to construct fluid-dynamic equations which not only have the advantage of having fewer adjustable parameters than the heuristic models, but also allow for a more formal inclusion of finer effects. In this work we compare the two principal approaches within the microscopic formalisms and present advances in the modeling of the synchronization phenomena, the phase transition between free flow and traffic jams.

Hydrodynamic correlation functions of nematic liquid crystals under shear and flexoelectric deformation
H. Híjar [1], R.F. Rodríguez [2]

[1] Facultad de Ciencias, Universidad Nacional Autonoma de Mexico, Circuito Exterior de Ciudad Universitaria, 04510, Mexico D.F., Mexico, [2] Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Apartado Postal 20-364, 01000 Mexico, D.F., Mexico

Abstract: We use a fluctuating hydrodynamic description in order to calculate the velocity and orientation (director) correlation functions of hydrodynamic fluctuations for a nematic liquid crystals in a non-equilibrium steady state produced by both, a planar shear flow and an external uniform electric field, which induces an elastic deformation through the so called flexoelectric effect. We fully analyze the effects of these external gradients to estimate the changes on the light scattering spectrum produced by both gradients with respect to its equilibrium shape. We find that these non-equilibrium effects give rise to an asymmetry of the spectrum, which consists on an increment of its maximum and a displacement in the frequency shift space. These changes are proportional to the magnitude of the external gradients and depend also on the relative orientation of the gradients with respect to the wave vector. We find that shear flow can produce significant changes on dynamic correlations. Specifically, it can induce a maximum degree of change of the dynamic structure factor of 5%, for normalized velocity gradients of the order 0.1 << 1. On the other hand, the flexoelectric effect produces only small changes on the structure factor, which are about two orders of magnitude smaller with respect to those due to the presence of the shear flow. Our analysis suggests that the effects produced on dynamic correlations by the flexoelectric effect would be hard to observe in experiments, while those due to the shear flow could be detected.

Relativistic Brownian motion in econophysics: a proposal
A. Aragonés-Munoz , A. Sandoval-Villalbazo

Departamento de Fisica y Matematicas, Universidad Iberoamericana

Abstract: Relativistic Brownian motion theory is applied to the study of a simple economic system, using well-known results regarding physical situations. The work emphasizes cases in which Gaussian distributions are not valid while describing price behavior. We also study the possibility of applying Juttner distributions functions to the general theory of Levy processes. As far as we know, the application of the Jü distribution to the study of economic systems is an interesting idea that deserves further consideration.

A dynamical phase transition between the dissipative and the non-dissipative solutions of a thermal process and its consequences
K. Gambár

Dennis Gabor Applied University, Etele ut 68, H-1115 Budapest, Hungary

Abstract: Dynamic phase transitions between non-dissipative and dissipative processes are discussed from different viewpoints. Thermal and mechanical examples are shown to illustrate the transition pointing out their realistic behavior. In the thermal case, an abstract scalar field has been introduced to generate a dynamical temperature and a covariant field equation to describe the heat propagation with finite speed.less than the speed of light.of action. It has been shown how this scalar field can be connected to the usual temperature (local equilibrium temperature) and the Fourier.s heat conduction. The dynamical phase transition is in between these two kinds of . wave and non-wave . propagation. In the mechanical example the phase transition is shown on a .stretched string on a rotating wheel. system. In both cases similar Klein-Gordon equations with a .negative mass. term describe the spinodal instability. It seems interesting that the thermal case may have an important role in the definition of a really dynamical temperature in cosmology.

Excess of low frequency vibrational modes and glass transition: a molecular dynamics study in Lennard-Jones systems at constant pressure
H.M. Flores-Ruiz , G.G. Naumis

Instituto de Fisica, UNAM, Mexico D.F., Mexico

Abstract: Using molecular dynamics at constant pressure, the relationship between the excess of low frequency vibrational modes (known as the boson peak) and glass transition is investigated for Lennard-Jones systems. It is observed that the quadratic mean displacement is enhanced by such modes, as predicted using a harmonic Hamiltonian for metastable states. As a result, glasses loose mechanical stability at lower temperatures than the corresponding crystal, since the Lindemann criterion is observed. Finally, we found that the average force and elastic constant is reduced in the glass due to such excess of modes. The ratio between average elastic constants can be approximated using the 2/3 rule between melting and glass transition temperature.

Adiabatic linear response and Einstein relation in non-equilibrium steady states for tilted periodic potentials
R. Salgado-García

Centre de Physique Theorique, UMR 7644 CNRS-Ecole Polytechnique, 91128 Palaiseau Cedex, France

Abstract: The adiabatic linear response for the steady state probability density function is calculated for tilted periodic potentials subject to an arbitrary probing force field. I show that for a suitable choice of the probing force field, the usual form of the Einstein relation holds in the non-equilibrium steady state regime. A violation function of the Einstein relation can be given analytically in terms of quadratures involving the probing force and the 'adjoint probability density'. The latter is given by the probability density function associated to the adjoint current operator of the non perturbed Fokker-Planck equation. All these findings are in good agreement with numerical Langevin simulations.

Entropy Generation in a Semiconductor Thermoelectric Device
M.A. Olivares Robles , M. Lindero Hernández

ESIME-Culhuacan - Instituto Politecnico Nacional, Mexico

Abstract: In this work we make use of the Entropy Minimization method to analyze a basic two-stage semiconductor thermoelectric device, which contains one thermocouple in the second stage and several thermocouples in the first stage. Our study focuses on the influence of current of the first stage indicating changes in entropy depending on the number of thermocouples in the second one.

Optimization of two-stage Peltier module with the method of Yamanashi and exergy analysis of the system
C. Ramírez-López , M.A. Olivares-Robles

ESIME-Culhuacan - Instituto Politecnico Nacional, Mexico

Abstract: In this work we present a theoretical analysis of a two-stage thermoelectric system. The aim is to establish the important parameters for the design of the modules and, with the help of a computer program, to simulate the system.s performance for variations of COP and the cooling capacity (β).
The system comprises a pyramidal arrangement consisting of a first Peltier module with a varying number of thermocouples and a second module with a single thermocouple. To analyze the thermodynamic performance of the system, the parameters for the second module are kept constant but changes of those of the first module are allowed. In this way optimal performance values are determined as well as corresponding values for the COP and .. We also present a small exergy analysis of the cooling system, with the aim of observing its exergetic efficiency.

Properties of Polyelectrolyte Solutions Using Electrostatic Dissipative Particle Dynamics in the Grand Canonical Ensemble
F. Alarcón Oseguera [1+2], A. Gama Goicochea [2], E. Pérez [1]

[1] Instituto de Fisica, Universidad Autonoma de San Luis Potosi, Alvaro Obregon 64, San Luis Potosi, Mexico, [2] Centro de Investigacion en Polimeros, COMEX Group, Marcos Achar Lobaton 2, 55885 Tepexpan, Edo. de Mexico, Mexico

Abstract: We have studied a bulk electrolyte, and polyelectrolyte.surfactant solutions by means of the mesoscopic dissipative particle dynamics (DPD) method, in the grand canonical ensemble. The electrostatic interactions are calculated using the Ewald sum method and the structure of the fluid is analyzed through the radial distribution function between charged particles. The results are in very good agreement with those reported in the literature using a different method for the calculation of the electrostatic forces, and with those obtained using DPD in the canonical ensemble. We also studied solutions confined by walls and analyzed the salt.dependent conformation of dilute flexible polyelectrolytes in solution. For the complex systems mentioned above, the electrostatic interactions play a key role in understanding phenomena that do not occur in noncharged systems. Therefore, the inclusion of these interactions is essential to capture phenomena such as polyelectrolyte.surfactants aggregates. The implications and further applications of this work are presented too.

Some new Thomson's second relations for a thermoelectric device
L.A. Arias-Hernández [1], R.T. Páez-Hernández [2], F. Angulo [1]

[1] Dpto. de Fisica, Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, U.P. Zacatenco, Edif. #9, 2o Piso, Ciudad de Mexico, 07738, Mexico, [2] Area de Fisica de Procesos Irreversibles, Dpto. de Ciencias Basicas, Universidad Autonoma Metropolitana-A, Av. San Pablo #180, Ciudad de Mexico, 02200, Mexico.

Abstract: Within the linear irreversible thermodynamics context, in recent years energy converter models have been proposed. The results show that it is possible to obtain stationary states with nonzero power output for these converters. One of the first irreversible energy converter studied was the thermocouple. Thomson derived two important relationships for the relevant effects that describe the energetic behavior of this converter.
These relations were justified under the theory proposed by Onsager. In this work we show that if the thermocouple is operated in a different regime to that of minimum entropy production, we can derive new relations between the Peltier heat and the Seebeck power.

Cross effects in the electrical resistivity variation of carbon black-polymer composites with the temperature
D. Reyes-Contreras [1], E. Vigueras-Santiago [2], S. Hernández-López [2], M. Mayorga-Rojas [1]

[1] Facultad de Ciencias, Universidad Autonoma del Estado de Mexico, UAEMex, [2] Facultad de Quimica, Universidad Autonoma del Estado de Mexico, UAEMex.

Abstract: We report the experimental observation of non-linear changes of electrical resistivity with respect to the temperature of thin-films of carbon black-filled polymer composites. After, applying the methods of irreversible thermodynamics, we identify the cross effects related to the heat flux, electrical transport and stress. In particular, we analyze and quantify the Onsager coefficients associated to the above mentioned cross effects.

Finite-time thermoeconomic optimization for a solar-driven heat engine model
M.A. Barranco-Jiménez [1], N. Sanchez-Salas [2]

[1] Departamento de Ciencias Basicas, Escuela Superior de Computo del IPN, Av. Miguel Bernard Esq. Juan de Dios Batiz, U.P. Zacatenco CP 07738, D.F., Mexico, [2] Departamento de Fisica, Escuela Superior de Fisica y Matematicas del IPN, Edif. 9 U.P. Zacatenco, CP 07738, D.F., Mexico

Abstract: In the present paper, the thermoeconomic optimization of an endoreversible solar-driven heat engine has been carried out by using finite-time/finite-size thermodynamic theory. In the considered heat engine model, the heat transfer from the hot reservoir to the working fluid is assumed to be Dulong-Petit type and the heat transfer to the cold reservoir is assumed of the conduction type. In this work, the optimum performance and two design parameters have been investigated under three objective functions: the power output per unit total cost, the efficient power per unit total cost and the ecological function per unit total cost. The effects of the technical and economical parameters on the thermoeconomic performance have been also discussed under the aforementioned three criteria of performance.

Mesoscopic approach for linear polymers melts and solutions: nonlinear effects in viscometric flows and unidimensional approximation for nonisothermal flows
A. Rybakov , A. Gusev , G. Pyshnograi

Altai State Technical University

Abstract: Rheological equations of state of linear polymer solutions and melts are obtained using methods of statistical mechanics and thermodynamics for the description and interpretation of nonlinear effects. These equations have been formulated on the basis of Brownian dynamics with entered non Markovian anisotropic noise and it has been shown that introduction of a certain kind of non Markovian fluctuations leads to the occurrence at a macrolevel of intermediate scales of length which may be interpreted as the radius of a tube as in theory by De Gennes, or as the length of a chain between entanglements as in the theory by Graessley. For the description of the process of formation of a polymeric film it is necessary to account for the fact that the received film is cooled and exposed to a stretching. As these processes occur simultaneously their mathematical modeling requires the joint solution of the equations for pressure and heat conduction. In this work in order to find the established pressure at a stretching a rheological model has been used in which the parameters are functions of temperature. For the thermal calculation it was assumed that the thickness of a film is small. Also the non-uniform current of a nonlinear viscoelastic liquid between parallel plates under the action of a constant pressure gradient is calculated. A comparison of the results of the calculation of the velocity with experimental data is performed. This allows us to draw the conclusion, that in the considered case of Poiseuille flow, the rheological model does not lead to a parabolic profile of velocity between parallel plates a result that does not contradict experimental data.

Efficiency at maximum omega function: An analytically solvable model for stochastic heat engines
L. López-Palacios , N. Sanchez-Salas

Depto. de Fisica, Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, UP Zacatenco, Edif. #9, 2o Piso, Ciudad de Mexico 07738, Mexico

Abstract: We study a class of cyclic Brownian heat engines in the context of finite-time thermodynamics. For infinitely long cycle time, the engine works at the Carnot efficiency limit, producing, however, zero power. We find an expression for the efficiency at maximum omega function, and we compare this with the efficiency at maximum power. Our results are illustrated with a simple one-dimensional engine working in and with a time-dependent harmonic potential.

Colloids in narrow channels: evidence of freezing in one-dimension?
S. Herrera-Velarde , R. Castaneda-Priego

Division de Ciencias e Ingenierias, Campus Leon, de la Universidad de Guanajuato. Loma del Bosque 103, Col. Lomas del Campestre, 37150 Leon, Guanajuato, Mexico

Abstract: We study both the structural and dynamic properties of colloidal particles confined in narrow channels by means of Brownian dynamics and Monte Carlo simulations. We here consider different types of particle interactions, namely screened Coulomb, superparamagnetic and WCA interactions. In each case, we find that at low densities the system exhibits a typical fluid-like structure. However, at higher densities the system undergoes a freezing-like transition. We observe that such transition is reached when the main peak of the static structure factor takes a value of about 7. We also observed that the mean-square displacement, W(t), shows the well-known crossover from normal diffusion at short-times to sub-diffusion at long-times in which W(t) = 2Ft^1/2, However, when the freezing-like transition is achieved the reduced mobility factor F, decreases dramatically taking values approximately of 0.05. Those features allow us to establish both static and dynamic criteria for determining the solid-like transition.

Memory and Multipolar Effects on Dielectric Relaxation
H. Híjar , I. Santamaría-Holek

Facultad de Ciencias, Universidad Nacional Autonoma de Mexico, Circuito Exterior de Ciudad Universitaria, 04510, D.F. Mexico

Abstract: A mesoscopic entropy production approach is used in order to obtain the Fokker-Planck equation governing the evolution of the probability distribution function of a system of polar molecules in an external time-dependent electric field and in contact with a heat reservoir. A non-Markovian description is considered through the presence of memory functions entering into the linear relations coupling generalized fluxes and forces. This Fokker-Planck equation allows us to construct a coupled hierarchy of macroscopic evolution equations for the polarization vector, the quadrupolar moment tensor, i.e. the order parameter tensor, etc. This hierarchy is approximated up to the octupolar moment and the coupling between the quadrupolar and dipole moments is considered explicitly. Under this approximation the effects of order parameter relaxation on the complex susceptibility of the system are derived. Non-Markovian effects are taken into account by introducing different memory functions and the way in which they affect both the real and imaginary part of the complex susceptibility is studied in detail.

Effecitve heat transfer in oscillating flows
S.R. Perez-Becker , S. Celis , S. Cuevas , J.A. del Río

Centro de Investigacion en Energia, Universidad Nacional Autonoma de Mexico

Abstract: Previous studies of axial heat transport in a laminary oscillatory flow, with no net mass flow, have shown that an effective thermal diffusivity could be achieved, and it was several orders of magnitude larger than the molecular thermal diffusivity. These studies were mostly theoretical and an experimental corroboration was needed. In this poster we analyze the effective thermal diffusivity in a series of experiments. We study the axial heat transfer in a circular tube with a constant cross section using an oscillating Newtonian fluid under thermal conducting and insulating tubes. The experiments show that, in spite of complying with almost all of the theoretical assumptions, no substantial increase of the effective thermal diffusivity could be observed when compared to the molecular thermal diffusivity present in another reference tube. An explanation of these results is proposed via the introduction of the concept of tidal displacement. Calculations for a group of Newtonian and Maxwellian Fluids were made with the purpose of finding suitable parameters for which an actual improvement on the axial heat transport could be observed.

Diffusion in complex geometries: an approach with biological applications
I. Pineda , L. Dagdug

Universidad Autonoma Metropolitana Unidad Iztapalapa, Av. San Rafael Atlixco No. 186, Col Vicentina C.P. 09340, Mexico, D.F.

Abstract: The diffusion equation has universal validity and satisfactorily describes the features of the mass transport in any geometry. However, actually this equation can not be analytically solved for a set of boundary conditions describing complex geometries, like interconnected spatial regions that are very common in the shapes of life. In this work we solved the diffusion equation in a geometry inspired by an ionic channel, and which consist of two chambers connected by a conical capillary. We used the Fick-Jacobs.s equation to model the diffusion inside the channel and a pair of propagators to describe the translocation and return fluxes across the capillary. Finally we joined the solutions in each chamber with the capillary using radiative boundary conditions.

Maximum entropy formalism to describe transcriptional regulation in cancer
K. Baca-López [1+2], E. Hernández-Lemus [2+3], M. Mayorga [1]

[1] Facultad de Ciencias, Universidad Autonoma del Estado de Mexico, Toluca, Mexico, [2] Departamento de Genomica Computacional, Instituto Nacional de Medicina Genomica, Mexico, D.F., Mexico, [3] Centro de Ciencias de la Complejidad, Universidad Nacional Autonoma de Mexico, Mexico, D.F., Mexico

Abstract: The vast majority of human diseases is related with the dynamic interaction of many genes and their products as well as environmental constraints. That fact makes them complex phenomena. Cancer (and breast cancer in particular) is a paradigmatic example of such complex behavior. Due to this fact, the analysis of the biochemical interactions involved often is based on the consideration of the related gene regulatory relationships. Since gene regulation is a non-equilibrium process, the inference and analysis of such phenomena could be done following the tenets of non-equilibrium statistical mechanics and irreversible thermodynamics. The traditional program in statistical mechanics consists in inferring the joint probability distribution for either microscopic states (equilibrium) or mesoscopic-states (non-equilibrium) given a model for the particle interactions (e.g. intermolecular potentials).
On the other hand, an inverse problem in statistical mechanics, is based on considering a realization of the probability distribution of micro- or meso-states and using it to infer the interaction potentials between particles. Following this protocol, we analyzed more than 200 whole-genome gene expression experiments in breast cancer patients, and by means of a nonlinear analysis based on an information-theoretical measure, we deconvolute the associated set of transcriptional interactions, i.e. we discover a set of fundamental biochemical reactions related to this pathology. By doing this, we showed how to apply the tools of non-linear statistical physics to generate hypothesis to be tested on clinical and biochemical settings in relation to cancer phenomenology.

Hysteresis in Pressure-Driven DNA denaturation
L.A. Nicasio-Collazo [1], E. Hernández-Lemus [2+3], R. Castaneda-Priego [1]

[1] Departamento de Fisica, Universidad de Guanajuato, Leon, [2] Departamento de Genomica Computacional, Instituto Nacional de Medicina Genomica, Mexico, D.F., Mexico, [3] Centro de Ciencias de la Complejidad, Universidad Nacional Autonomca de Mexico, Mexico, D.F., Mexico

Abstract: A theory that accounts for the observation of hysteresis in pressure-driven DNA denaturation is proposed, combining an irreversible thermodynamic approach with an equation of state based on the Poisson-Boltzmann cell model. The theory predicts hysteresis curves for a DNA sequence in terms of the system parameters, i.e., salt concentration, density of DNA molecules and temperature. A great deal of attention has been drawn to thermal driven denaturation processes in the past. In recent times, the discovery of stress-induced denaturation, observed at the one-molecule level has revealed new insights into the complex phenomena involved in the thermo-mechanics of DNA function. Understanding the effect of local pressure variations in DNA stability is thus an appealing topic. Such processes as cellular stress, dehydration, and changes in the ionic strenght of the medium could account for such local pressure changes that will affect the molecular mechanics of DNA and hence its stability. Moreover, since this study incorporates the effect of pressure through a thermodynamic analysis, much of what is known from temperature-driven experiments will shed light on the pressure-induced melting issue.

Single Droplet Dynamics in the Framework of Non-equilibrium Thermodynamics
M. Dressler [1], B.J. Edwards [2]

[1] ETH Zurich, Switzerland, [2] Department of Chemical Engineering, UT Knoxville, U.S.A.

Abstract: During the past few years, models to describe the shape and orientation of a single droplet in a flowing liquid phase have become very popular, e.g. the Maffettone--Minale Model and its various generalizations which take into account the elasticity of either one or both phases. In this talk we discuss dynamic models for single droplet deformation in the framework of non--equilibrium Thermodynamics. We introduce a set of thermodynamic variables for this dynamic problem and we use the bracket formalism of non--equilibrium Thermodynamics to derive thermodynamically consistent flow equations for a single deforming droplet in a deforming matrix fluid.
We take into account droplet shape, coverage of droplets by surfactants, and inertia of the droplet phase. We propose new models for single droplet deformation, we discuss their thermodynamic consistency, their predictive power, and we compare with existing models in the literature.