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We study a model of a lipid bilayer membrane described by two order parameters: the chemical composition described using the Gaussian model and the spatial configuration described with the elastic deformation model of a membrane with a finite thickness or, equivalently, for an adherent membrane. We assume and explain on physical grounds the linear coupling between the two order parameters. Using the exact solution, we calculate the correlation functions and order parameter profiles. We also study the domains that form around inclusions on the membrane. We propose and compare six distinct ways to quantify the size of such domains. Despite its simplicity, the model has many interesting features like the Fisher-Widom line and two distinct critical regions.

There is a long-standing question as to whether and to what extent it is possible to describe nonequilibrium systems in stationary states in terms of global thermodynamic functions. The positive answers have been obtained only for isothermal systems or systems with small temperature differences. We formulate thermodynamics of the stationary states of the ideal gas subjected to heat flow in the form of the zeroth, first, and second law. Surprisingly, the formal structure of steady state thermodynamics is the same as in equilibrium thermodynamics. We rigorously show that U satisfies the following equation dU = T* dS* − pdV for a constant number of particles, irrespective of the shape of the container, boundary conditions, the size of the system, or the mode of heat transfer into the system. We calculate S* and T* explicitly. The theory selects stable nonequilibrium steady states in a multistable system of ideal gas subjected to volumetric heating. It reduces to equilibrium thermodynamics when heat flux goes to zero.

We investigate the thermal relaxation of an ideal gas from a nonequilibrium stationary state. The gas is enclosed between two walls, which initially have different temperatures. After making one of the walls adiabatic, the system returns to equilibrium. We notice two distinct modes of heat transport and associated timescales: one connected with a traveling heat front and the other with internal energy diffusion. At the heat front, which moves at the speed of sound, pressure, temperature, and density change abruptly, leaving lower values behind. This is unlike a shock wave, a sound wave, or a thermal wave. The front moves multiple times between the walls and is the dominant heat transport mode until surpassed by diffusion. We found that it can constitute an order 1 factor in shaping the dynamics of the outflow of internal energy. We found that cooling such a system is quicker than heating, and that hotter bodies cool down quicker than colder ones. The latter is known as the Mpemba effect.

We analyse a compressible Poiseuille flow of ideal gas in a plane channel. We provide the form of internal energy U for a non-equilibrium stationary state (NESS) that includes viscous dissipation and pressure work. We demonstrate that U depends strongly on the ratio {\Delta}p/p_0, where {\Delta}p is the pressure difference between inlet and outlet and p_0 is the outlet's pressure. In addition, U depends on two other variables: the channel aspect ratio and the parameter equivalent to Reynolds number. The stored internal energy, {\Delta}U=U-U0, is small compared to the internal energy U0 of the equilibrium state (ES) for a moderate range of values of {\Delta}p/p_0. However, {\Delta}U can become large for big {\Delta}p or close to vacuum conditions at the outlet (p_0~0 Pa)., Comment: 17 pages, 9 figures

Specific lipid environments are necessary for the establishment of protein signalling platforms in membranes, yet their origin has been highly debated. We present a continuum, exactly solvable model of protein induced local demixing of lipid membranes. The coupling between a local composition and a local thickness of the membrane induces lipid domains around inclusions with hydrophobic mismatch, even for temperatures above the miscibility critical point of the membrane. The model qualitatively explains the experimentally observed formation of lipid domains induced by anchoring of reconstituted actin in flat supported lipid bilayers.

We discovered an out-of-equilibrium transition in the ideal gas between two walls, divided by an inner, adiabatic, movable wall. The system is driven out-of-equilibrium by supplying energy directly into the volume of the gas. At critical heat flux, we have found a continuous transition to the state with a low-density, hot gas on one side of the movable wall and a dense, cold gas on the other side. Molecular dynamic simulations of the soft-sphere fluid confirm the existence of the transition in the interacting system. We introduce a stationary state Helmholtz-like function whose minimum determines the stable positions of the internal wall. This transition can be used as a paradigm of transitions in stationary states and the Helmholtz-like function as a paradigm of the thermodynamic description of these states., Comment: 8 pages, 6 figures; paragraph one rewritten; comments added regarding maxEP, and figures 4, 5 and 6 are added; references added and typos corrected

A gold-capped Janus particle suspended in a near-critical binary liquid mixture can self-propel under illumination. We have immobilized such a particle in a narrow channel and studied the nonequilibrium dynamics of a binary solvent around it, using experiment and numerical simulations. For the latter we consider both a purely diffusive and a hydrodynamic model. All approaches indicate that the early time dynamics is purely diffusive and characterized by composition layers traveling with a constant speed from the surface of the colloid into the bulk. Subsequently, hydrodynamic effects set in and the transient state is destroyed by strong nonequilibrium concentration fluctuations, which arise as a result of the temperature gradient and the vicinity of the critical point of the binary liquid mixture. They give rise to a complex, permanently changing coarsening patterns. For a mobile particle, the transient dynamics results in propulsion in the direction opposite to that observed after the steady state is attained., Comment: 39 pages, 20 figures

We consider the situation in which a colloidal particle modifies locally the solvent leading to a spatially dependent viscosity. This situation is typical for colloidal particles in crowded environment, for example DNA-grafted particles in a polymer solution, or a hot particle which implies a temperature gradient to a viscous liquid. By means of suitable approximations we calculate the dependence of the friction force on the profile of the local viscosity. Our results show that in the case of axially symmetric viscosity profile the friction force is sensitive to the anisotropy of the viscous profile whereas it is not sensitive to for-ahead asymmetries. Our results are crucial for active microrheology measurements where tracer particles are pulled through complex fluids.

We study colloidal particles with chemically inhomogeneous surfaces suspended in a critical binary liquid mixture. The inhomogeneous particle surface is composed of patches with alternating adsorption preferences for the two components of the binary solvent. By describing the binary liquid mixture \emph{at} its consolute point in terms of the critical Ising model we exploit its conformal invariance in two spatial dimension. This allows us to determine exactly the universal profiles of the order parameter, the energy density, and the stress tensor as well as some of their correlation functions around a single particle for various shapes and configurations of the surface patches. The formalism encompasses several interesting configurations, including Janus particles of circular and needle shapes with dipolar symmetry and a circular particle with quadrupolar symmetry. From these single-particle properties we construct the so-called small particle operator expansion (SPOE), which enables us to obtain asymptotically exact expressions for the position- and orientation-dependent critical Casimir interactions of the particles with distant objects, such as another particle or the confining walls of a half plane, strip, or wedge, with various boundary conditions for the order parameter. In several cases we compare the interactions at large distances with the ones at close distance (but still large on the molecular scale). We also compare our analytical results for two Janus particles with recent simulation data., 81 pages, 25 figures

Using a fluid particle dynamics method we numerically investigate the motion of a spherical Janus particle suspended in a binary liquid mixture, which emerges under heating of one-half of a colloid surface. The method treats simultaneously the flow of the solvent and the motion of the particle, hence, the velocity of the particle can be computed directly. Our approach accounts for a phenomenon of critical adsorption, therefore, a particle that is adsorptionwise nonneutral is always completely covered by an adsorption layer (droplet). In order to establish the mechanism of self-propulsion, we study systematically various combinations of adsorption preference on both hemispheres of the Janus colloid as function of the heating power for symmetric and nonsymmetric binary solvents and for various particle sizes in three spatial dimensions. Only for a particle for which the heated hemisphere is neutral whereas the other hemisphere prefers one of the two components of the mixture does the reversal of the direction of motion occur. The particle self-propels much faster in nonsymmetric binary solvents. Self-propulsion originates from a gradient of mechanical stress, in a way similar to the Marangoni effect. This stress is not localized at the edge but distributed within the whole droplet. We compare our findings with the experimental observations and other theoretical results.

Systems kept out of equilibrium in stationary states by an external source of energy store an energy $\Delta U=U-U_0$. $U_0$ is the internal energy at equilibrium state, obtained after the shutdown of energy input. We determine $\Delta U$ for two model systems: ideal gas and Lennard-Jones fluid. $\Delta U$ depends not only on the total energy flux, $J_U$, but also on the mode of energy transfer into the system. We use three different modes of energy transfer where: the energy flux per unit volume is (i) constant; (ii) proportional to the local temperature (iii) proportional to the local density. We show that $\Delta U /J_U=\tau$ is minimized in the stationary states formed in these systems, irrespective of the mode of energy transfer. $\tau$ is the characteristic time scale of energy outflow from the system immediately after the shutdown of energy flux. We prove that $\tau$ is minimized in stable states of the Rayleigh-Benard cell.

Spatial correlations play an important role in characterizing material properties related to non-local effects. Inter alia, they can give rise to fluctuation-induced forces. Equilibrium correlations in fluids provide an extensively studied paradigmatic case, in which their range is typically bounded by the correlation length. Out of equilibrium, conservation laws have been found to extend correlations beyond this length, leading, instead, to algebraic decays. In this context, here we present a systematic study of the correlations and forces in fluids driven out of equilibrium simultaneously by quenching and shearing, both for non-conserved as well as for conserved Langevin-type dynamics. We identify which aspects of the correlations are due to shear, due to quenching, and due to simultaneously applying both, and how these properties depend on the correlation length of the system and its compressibility. Both shearing and quenching lead to long-ranged correlations, which, however, differ in their nature as well as in their prefactors, and which are mixed up by applying both perturbations. These correlations are employed to compute non-equilibrium fluctuation-induced forces in the presence of shear, with or without quenching, thereby generalizing the framework set out by Dean and Gopinathan. These forces can be stronger or weaker compared to their counterparts in unsheared systems. In general, they do not point along the axis connecting the centers of the small inclusions considered to be embedded in the fluctuating medium. Since quenches or shearing appear to be realizable in a variety of systems with conserved particle number, including active matter, we expect these findings to be relevant for experimental investigations., 19 pgs (15 main text + 4 appendices); 7 figures

The basic phenomenology of experimentally observed synchronization (i.e., a stochastic phase locking) of identical, beating flagella of a biflagellate alga is known to be captured well by a minimal model describing the dynamics of coupled, limit-cycle, noisy oscillators (known as the noisy Kuramoto model). As demonstrated experimentally, the amplitudes of the noise terms therein, which stem from fluctuations of the rotary motors, depend on the flagella length. Here we address the conceptually important question which kind of synchrony occurs if the two flagella have different lengths such that the noises acting on each of them have different amplitudes. On the basis of a minimal model, too, we show that a different kind of synchrony emerges, and here it is mediated by a current carrying, steady-state; it manifests itself via correlated "drifts" of phases. We quantify such a synchronization mechanism in terms of appropriate order parameters $Q$ and $Q_{\cal S}$ - for an ensemble of trajectories and for a single realization of noises of duration ${\cal S}$, respectively. Via numerical simulations we show that both approaches become identical for long observation times ${\cal S}$. This reveals an ergodic behavior and implies that a single-realization order parameter $Q_{\cal S}$ is suitable for experimental analysis for which ensemble averaging is not always possible., Comment: 10 pages, 2 figures

Correction for ‘Transient coarsening and the motility of optically heated Janus colloids in a binary liquid mixture’ by Juan Ruben Gomez-Solano et al., Soft Matter, 2020, DOI: 10.1039/d0sm00964d.

We study the non-equilibrium coarsening dynamics of a binary liquid solvent around a colloidal particle in a presence of a time-dependent temperature gradient that emerges after temperature quench of a suitably coated colloid surface. The solvent is maintained at its critical concentration and the colloid is fixed in space. The coarsening patterns near the surface are shown to be strongly dependent on the colloid surface adsorption properties and on the temperature evolution. The temperature gradient alters the morphology of a binary solvent near the surface of a colloid as compared to the coarsening proceeding at constant temperature everywhere. We also present results for the evolution of coarsening in thin films with confining surfaces preferring one species of the binary liquid mixture over the other. Confinement leads to a faster phase segregation process and formation of a bridge connecting the colloid and both the confining walls., Comment: 9 pages, 12 figures

We consider a cube placed between two planar surfaces bounding a three-dimensional Ising slab. This system can be viewed as the magnetic analog of a colloidal particle immersed in a fluid, which is confined by two parallel walls. Near the bulk critical point of the Ising ferromagnet the cube gets exposed to the potential of the fluctuation that induces the critical Casimir force. Using Monte Carlo simulations we study the dependence of this potential on the relative boundary conditions at the two surfaces and at the cube within a wide range of temperatures above and below the bulk critical temperature. In order to calculate the critical Casimir force and its potential, we adopt an approach based on an integration scheme of free energy differences. The scaling functions of the corresponding critical Casimir forces are also determined.

Critical Casimir interactions between colloidal particles arise from the confinement of fluctuations of a near-critical solvent in the liquid gap between closely-spaced particles. So far, the comparison of theoretical predictions and experimental measurements of critical Casimir forces (CCFs) has focused on the critical solvent composition, while it has been lacking for off-critical compositions. We address this issue by investigating CCFs between spherical colloidal particles around the critical point of a binary solvent through a combination of experiments, previous Ising Monte Carlo simulation results and field-theoretical methods. By measuring the correlation length of the near-critical solvent and the pair potentials of the particles in terms of radial distribution functions and by determining the second virial coefficient, we test in detail theoretical predictions. Our results indicate that the critical Casimir theory gives quantitative correct predictions for the interaction potential between particles in a near critical binary mixture if weak preferential adsorption of the particle surface is taken into account.

Using mesoscopic numerical simulations and analytical theory we investigate the coarsening of the solvent structure around a colloidal particle emerging after a temperature quench of the colloid surface. Qualitative differences in the coarsening mechanisms are found, depending on the composition of the binary liquid mixture forming the solvent and on the adsorption preferences of the colloid. For an adsorptionwise neutral colloid, as function of time the phase being next to its surface alternates. This behavior sets in on the scale of the relaxation time of the solvent and is absent for colloids with strong adsorption preferences. A Janus colloid, with a small temperature difference between its two hemispheres, reveals an asymmetric structure formation and surface enrichment around it, even if the solvent is within its one-phase region and if the temperature of the colloid is above the critical demixing temperature $T_c$ of the solvent. Our phenomenological model turns out to capture recent experimental findings according to which, upon laser illumination of a Janus colloid and due to the ensuing temperature gradient between its two hemispheres, the surrounding binary liquid mixture develops a concentration gradient., 8 pages, 4 figures

Tricritical Casimir forces in ^{3}He-^{4}He wetting films are studied, within mean field theory, in terms of a suitable lattice gas model for binary liquid mixtures with short-ranged surface fields. The proposed model takes into account the continuous rotational symmetry O(2) of the superfluid degrees of freedom associated with ^{4}He and it allows, inter alia, for the occurrence of a vapor phase. As a result, the model facilitates the formation of wetting films, which provides a strengthened theoretical framework to describe available experimental data for tricritical Casimir forces acting in ^{3}He-^{4}He wetting films.

We investigate the effect of quenched surface disorder on effective interactions between two planar surfaces immersed in fluids which are near criticality and belong to the Ising bulk universality class. We consider the case that, in the absence of random surface fields, the surfaces of the film belong to the surface universality class of the so-called ordinary transition. We find analytically that in the linear weak-coupling regime, i.e., upon including the mean-field contribution and Gaussian fluctuations, the presence of random surface fields with zero mean leads to an attractive, disorder-induced contribution to the critical Casimir interactions between the two confining surfaces. Our analytical, field-theoretic results are compared with corresponding Monte Carlo simulation data., 25 pages, 3 figures

We show that hydrophilic ions present in a confined, near-critical aqueous mixture can lead to an attraction between like charge surfaces with opposing preferential adsorption of the two species of the mixture, even though the corresponding Casimir potential in uncharged systems is repulsive. This prediction agrees with a recent experiment [Nellen et al., Soft Matter, 2011, 7, 5360]. We also show that oppositely charged hydrophobic surfaces can repel each other, although the Casimir potential between uncharged surfaces with like preferential adsorption (selectivity) is attractive. This behavior is expected when the electrostatic screening length is larger than the correlation length, and one of the confining surfaces is strongly selective and weakly charged, whereas the other confining surface is weakly selective and strongly charged. The Casimir potential can change sign because the hydrophilic ions near the weakly hydrophobic surface can overcompensate the effect of hydrophobicity, and this surface can act as a hydrophilic one. We also predict a more attractive interaction between charged, hydrophilic surfaces and a more repulsive interaction between charged, hydrophobic surfaces than given by the sum of the Casimir and Debye-Hückel potentials. Our theory is derived systematically from a microscopic approach, and combines the Landau-type and Debye-Hückel theories with an additional contribution of an entropic origin.

Spatial confinement of a near-critical medium changes its fluctuation spectrum and modifies the corresponding order parameter distribution, resulting in effective, so-called critical Casimir forces (CCFs) acting on the confining surfaces. These forces are attractive for like boundary conditions of the order parameter at the opposing surfaces of the confinement. For colloidal particles dissolved in a binary liquid mixture acting as a solvent close to its critical point of demixing, one thus expects the emergence of phase segregation into equilibrium colloidal liquid and gas phases. We analyze how such phenomena occur asymmetrically in the whole thermodynamic neighborhood of the consolute point of the binary solvent. By applying field-theoretical methods within mean-field approximation and the semi-empirical de Gennes-Fisher functional, we study the CCFs acting between planar parallel walls as well as between two spherical colloids and their dependence on temperature and on the composition of the near-critical binary mixture. We find that for compositions slightly poor in the molecules preferentially adsorbed at the surfaces, the CCFs are significantly stronger than at the critical composition, thus leading to pronounced colloidal segregation. The segregation phase diagram of the colloid solution following from the calculated effective pair potential between the colloids agrees surprisingly well with experiments and simulations.

If colloidal solute particles are suspended in a solvent close to its critical point, they act as cavities in a fluctuating medium and thereby restrict and modify the fluctuation spectrum in a way which depends on their relative configuration. As a result effective, so-called critical Casimir forces (CCFs) emerge between the colloids. The range and the amplitude of CCFs depend sensitively on the temperature and the composition of the solvent as well as on the boundary conditions of the order parameter of the solvent at the particle surfaces. These remarkable, moreover universal features of the CCFs provide the possibility for an active control over the assembly of colloids. This has triggered a recent surge of experimental and theoretical interest in these phenomena. We present an overview of current research activities in this area. Various experiments demonstrate the occurrence of thermally reversible self-assembly or aggregation or even equilibrium phase transitions of colloids in the mixed phase below the lower consolute points of binary solvents. We discuss the status of the theoretical description of these phenomena, in particular the validity of a description in terms of effective, one-component colloidal systems and the necessity of a full treatment of a ternary solvent-colloid mixture. We suggest perspectives on the directions towards which future research in this field might develop., Comment: review, 88 pages, 19 figures

We present exact derivations of the effective capillary wave fluctuation induced forces resulting from pinning of an interface between two coexisting phases at two points separated by a distance r. In two dimensions the Ising ferromagnet calculations based on the transfer matrix approach give an attractive force decaying as 1/r for large distances. In three dimensions mapping of the body-centered solid-on-solid model onto the 6-vertex model allows for exact solution using the bosonization analysis of the equivalent XXZ Heisenberg quantum chain. The exact result gives the attractive force which decays asymptotically as 1/(r\log r)., Comment: 4 pages, 2 figures, accepted for publication in Phys. Rev. Lett

An exact statistical mechanical derivation is given of the critical Casimir interactions between two defects in a planar lattice-gas Ising model. Each defect is a finite group of nearest-neighbor spins with modified coupling constants. Such a system can be regarded as a model of a binary liquid mixture with the molecules confined to a membrane and the defects mimicking protein inclusions embedded into the membrane. As suggested by recent experiments, certain cellular membranes appear to be tuned to the proximity of a critical demixing point belonging to the two-dimensional Ising universality class. Therefore one can expect the emergence of critical Casimir forces between membrane inclusions. These forces are governed by universal scaling functions, which we derive for simple defects. We prove that the scaling law appearing at criticality is the same for all types of defects considered here.

We study critical Casimir forces (CCF) $f_{\mathrm C}$ for films of thickness $L$ which in the three-dimensional bulk belong to the Ising universality class and which are exposed to random surface fields (RSF) on both surfaces. We consider the case that, in the absence of RSF, the surfaces of the film belong to the surface universality class of the so-called ordinary transition. We carry out a finite-size scaling analysis and show that for weak disorder CCF still exhibit scaling, acquiring a random field scaling variable $w$ which is zero for pure systems. We confirm these analytic predictions by MC simulations. Moreover, our MC data show that $f_{\mathrm C}$ varies as $f_{\mathrm C}(w\to 0)-f_{\mathrm C}(w=0)\sim w^2$. Asymptotically, for large $L$, $w$ scales as $w \sim L^{-0.26} \to 0$ indicating that this type of disorder is an irrelevant perturbation of the ordinary surface universality class. However, for thin films such that $w \simeq 1$, we find that the presence of RSF with vanishing mean value increases significantly the strength of CCF, as compared to systems without them, and shifts the extremum of the scaling function of $f_{\mathrm C}$ towards lower temperatures. But $f_{\mathrm C}$ remains attractive., Comment: 20 pages, 3 figures

Fluid parts of the phase diagram of (3)He-(4)He mixtures are obtained from a mean-field analysis of a suitable lattice gas model for binary liquid mixtures. The proposed model takes into account the continuous rotational symmetry O(2) of the superfluid degrees of freedom associated with (4)He and includes the occurrence of vacancies. This latter degree of freedom allows the model to exhibit a vapor phase and hence can provide the theoretical framework to describe the experimental conditions for measurements of tricritical Casimir forces in (3)He-(4)He wetting films.

The solvation force of a simple fluid confined between identical planar walls is studied in two model systems with short ranged fluid-fluid interactions and long ranged wall-fluid potentials decaying as $-Az^{-p}, z\to \infty$, for various values of $p$. Results for the Ising spins system are obtained in two dimensions at vanishing bulk magnetic field $h=0$ by means of the density-matrix renormalization-group method; results for the truncated Lennard-Jones (LJ) fluid are obtained within the nonlocal density functional theory. At low temperatures the solvation force $f_{solv}$ for the Ising film is repulsive and decays for large wall separations $L$ in the same fashion as the boundary field $f_{solv}\sim L^{-p}$, whereas for temperatures larger than the bulk critical temperature $f_{solv}$ is attractive and the asymptotic decay is $f_{solv}\sim L^{-(p+1)}$. For the LJ fluid system $f_{solv}$ is always repulsive away from the critical region and decays for large $L$ with the the same power law as the wall-fluid potential. We discuss the influence of the critical Casimir effect and of capillary condensation on the behaviour of the solvation force., Comment: 48 pages, 12 figures

The density profile and Gibbs adsorption of a near-critical fluid confined between two identical planar walls is studied by means of Monte Carlo simulation and by density functional theory for a Lennard-Jones fluid. By reducing the strength of wall-fluid interactions relative to fluid-fluid interactions we observe a crossover from behaviour characteristic of the normal surface universality class, strong critical adsorption, to behaviour characteristic of a 'neutral' wall. The crossover is reminiscent of that which occurs near the ordinary surface transition in Ising films subject to vanishing surface fields. For the 'neutral' wall the density profile, away from the walls, is almost constant throughout the slit capillary and gives rise to an adsorption that is constant along the critical isochore. The same 'neutral' wall yields a line of capillary coexistence that is almost identical to the bulk coexistence line. In the crossover regime we observe features in the density profile similar to those found in the magnetisation profile of the critical Ising film subject to weak surface fields, namely two smooth maxima, located away from the walls, which merge into a single maximum at midpoint as the strength of the wall-fluid interaction is reduced or as the distance between walls is decreased. We discuss similarities and differences between the surface critical behaviour of fluids and of Ising magnets., Comment: 34 pages, 10 figures, submitted to the Journ. Chem. Phys

Two-dimensional Ising films L x infinity in a nonvanishing bulk magnetic field H are studied at the bulk critical temperature Tc for two choices of surface fields (a) H1 = HL = 0 (ordinary transition), and (b) H1 = HL = infinity (normal transition) by the density-matrix renormalization-group method. Universal scaling functions for magnetization profiles, the excess magnetization gamma, the longitudinal correlation length xi parallel, and for the analog of the solvation force fsolv are found and discussed. When H1 = 0 the scaling function for fsolv has two symmetric minima at y = sgn(H)L magnitude of H nu/delta approximately +/- 1 with an amplitude at the minimum about 3.8 times the value at H = 0, the Casimir amplitude. For the normal transition the scaling function for fsolv has a single minimum near the continuation of the pseudocoexistence (capillary condensation) line, with an amplitude about 100 times the Casimir amplitude.

Surface phenomena in fluids exhibiting structure on the nanoscale (microemulsions, copolymers etc.) are studied. We argue that for such systems the Landau-Ginzburg functional of suitably chosen order parameter should on the nanoscale have the same form, as the Landau-Ginzburg density-functional for simple fluids on the microscale. We define such order parameter for lamellar ordering by averaging the lamellar structure given by density profiles over a period of the density oscillations. The resulting Landau-Ginzburg functional leads to surface-induced order or disorder and to the associated wetting phenomena. We verify our hypothesis by explicit mean-field calculations in a lattice model of microemulsions in the presence of a surface. Perfect agreement is found. Our results also agree with recent experiments.

The two-dimensional Ising films with bulk H and surface H1 fields of opposite sign are studied above and close to bulk criticality by the density matrix renormalization group method. This technique, applied recently to d=2 Ising films, allows for very accurate results for the adsorption as a function of the reduced deviation from the critical temperature .For strong H1 three distinct classes of shapes of ,determined by the value of the parameter ,where L is the width of the film, are found in agreement with earlier predictions [A. Macio ek, A. Ciach, R. Evans, J. Chem. Phys. 108, 9765 (1998)]. For strong and for weak bulk fields is a monotonic function, increasing for strong H and decreasing for weak H, in agreement with scaling analysis and earlier mean-field results. For H between these extreme cases assumes a maximum for and for a depletion occurs, as in recent experiments for critical adsorption in porous materials. For a limited range of H a qualitatively new behavior of is found. In addition to a maximum, a minimum of for appears, which in the mean-field analysis was absent.

We investigate the effects of competing bulk and surface fields on the adsorption of near-critical fluids confined in model pores. Our study is motivated by recent measurements for SF6 adsorbed in a mesoporous glass which showed the phenomenon of critical depletion in that the adsorption excess first increases but then decreases rapidly to negative values as the temperature approaches the bulk critical temperature from above, following a near-critical isochore. We argue on the basis of (i) critical scaling ideas, (ii) exact transfer matrix calculations in two dimensions, and (iii) mean-field calculations, for the lattice gas confined between two planar walls, that critical depletion is a general phenomenon resulting from competition between positive adsorption (the walls or surface fields favor the dense liquid phase) and negative adsorption associated with the presence of a bulk field which favors the dilute gas phase. The temperature at which crossover from critical adsorption, of the type associated wi...

Critical adsorption for weak surface field h1 is reconsidered. On the basis of physical heuristic arguments, approximate behavior of the scaling function is derived. New form of a scaling for weak h1 in finite systems is proposed and verified by testing against exact results obtained for this purpose in the 2D Ising strips. For weak h1 we find the approximate behavior of adsorption Γ∼τβ−Δ1 for the reduced temperatures h11/Δ1∼τ≪1. This behavior is consistent with experimental data [N. S. Desai, S. Peach, and C. Franck, Phys. Rev. E 52, 4129 (1995)] obtained for τ=10−5, and is in a very good agreement with exact results in the 2D Ising strip.

We present a system exhibiting extraordinarily long-range cooperative effects, on a length scale far exceeding the bulk correlation length. We give a theoretical explanation of these phenomena based on the mesoscopic picture of phase coexistence in finite systems, which is confirmedly Monte Carlo (MC) simulation studies. Our work demonstrates that such action-at-a-distance can occur in classical systems involving simple or complex fluids, such as colloid-polymer mixtures, or ferromagnets.

Using quasi-exact numerical density-matrix renormalization-group techniques we calculate the critical Casimir force for a two-dimensional (2D) Ising strip with equal strong surface fields, along the thermodynamic paths corresponding to the fixed nonzero bulk field h<>0. Using the Derjaguin approximation we also determine the critical Casimir force and its potential for two discs. We find that varying the temperature along the iso-fields lying between the bulk coexistence and the capillary condensation critical point leads to a dramatic increase of the critical Casimir interactions with a qualitatively different functional dependence on the temperature than along h=0. These findings might be of relevance for biomembranes, whose heterogeneity is recently interpreted as being connected with a critical behavior belonging to the 2D Ising universality class., 9 pages, 12 figures, submitted to Physical Review E

We study a planar two-temperature diffusion of a Brownian particle in a parabolic potential. The diffusion process is defined in terms of two Langevin equations with two different effective temperatures in the X and the Y directions. In the stationary regime the system is described by a non-trivial particle position distribution P(x,y), which we determine explicitly. We show that this distribution corresponds to a non-equilibrium stationary state, characterised by the presence of space-dependent particle currents which exhibit a non-zero rotor. Theoretical results are confirmed by the numerical simulations., 9 pages, 2 figures

We obtain an exact solution of the d = 2 infinite Ising strip with surface fields of opposite signs , . Earlier predictions by Parry et al are confirmed of the crucial importance of wetting for a system confined between two parallel walls that exert competitive surface fields. The transition of the magnetization profile m(z) from the partial wetting regime below the critical wetting temperature at a single wall with a surface field , to the soft-mode single phase in the temperature range , where is the critical temperature of the bulk system, is described in detail. A scaling ansatz is verified for the singular part of the surface excess free energy, and for the profile, . The modification of the magnetization profile near one wall, due to wetting, is studied. Near the (-) wall at the profile is found to be a linear function of the scaled distance but its slope is different than for the case of perfect asymmetry system hence these two cases belong to the different universality regime.