Journal articles on the topic 'Brownian configuration field'

A path integral method is applied to a statistical analysis of electron transport described as a Langevin equation in a disturbed magnetic field line structure; in particular, the transition probability of electrons strongly tied to field lines is considered. When the effect of the Coulomb collisions is interpreted as the Gaussian white noise in configuration space, the radial transport of electrons in the chaotic field line structure is different from Brownian diffusion with the diffusion coefficient of field lines, even if a sufficiently small diffusion coefficient of the collisions is considered.

Abstract We study the mean field Schrödinger problem (MFSP), that is the problem of finding the most likely evolution of a cloud of interacting Brownian particles conditionally on the observation of their initial and final configuration. Its rigorous formulation is in terms of an optimization problem with marginal constraints whose objective function is the large deviation rate function associated with a system of weakly dependent Brownian particles. We undertake a fine study of the dynamics of its solutions, including quantitative energy dissipation estimates yielding the exponential convergence to equilibrium as the time between observations grows larger and larger, as well as a novel class of functional inequalities involving the mean field entropic cost (i.e. the optimal value in (MFSP)). Our strategy unveils an interesting connection between forward backward stochastic differential equations and the Riemannian calculus on the space of probability measures introduced by Otto, which is of independent interest.

AbstractThe multiscale stochastic simulation method based on the marriage of the Brownian Configuration Field (BCF) and the Radial Basis Function mesh-free approximation for dilute fibre suspensions by our group, is further developed to simulate non-dilute fibre suspensions. For the present approach, the macro and micro processes proceeded at each time step are linked to each other by a fibre contributed stress formula associated with the used kinetic model. Due to the feature of non-dilute fibre suspensions, the interaction between fibres is introduced into the evolution equation to determine fibre configurations using the BCF method. The fibre stresses are then determined based on the fibre configuration fields using the Phan–Thien–Graham model. The efficiency of the simulation method is demonstrated by the analysis of the two challenging problems, the axisymmetric contraction and expansion flows, for a range of the fibre concentration from semi-dilute to concentrated regimes. Results evidenced by numerical experiments show that the present method would be potential in analysing and simulating various suspensions in food and medical industries.

The present exploration addresses the boundary layer electro-magnetohydrodynamic (EMHD) flow of time-dependant non-Newtonian tangent hyperbolic nanofluid that is electrically conducting past a Riga surface with variable thickness and slip boundary condition. Configuration flow modeling is deduced considering chemical reaction and heat generation/absorption with the impacts of Brownian motion and thermophoresis. Also a newly proposed boundary condition with zero mass flux has been presented in the current contribution. Numerical solution of the governing non-linear differential equations is presented by considering the shooting technique. Graphical illustrations pointing out the aspects of distinct physical parameters on the non-Newtonian nanofluid velocity, temperature and concentration fields are introduced. From the computational results, the concentration distribution gives a decreasing function of the chemical reaction and Brownian motion parameters. Higher values of shape parameter yield a negative influence on the mechanical properties of the surface. The Hartmann number leads to maximize both of velocity field and skin friction coefficient. Additionally, numerical computed values of the skin friction, local Nusselt and Sherwood numbers are depicted with the needful discussion.

The current research study is focusing on the investigation of the physical effects of thermal radiation on heat and mass transfer of a nanofluid located around a sphere. The configuration is investigated by solving the partial differential equations governing the phenomenon. By using suitable non-dimensional variables, the governing set of partial differential equations is transformed into a dimensionless form. For numerical simulation, the attained set of dimensionless partial differential equations is discretized by using the finite difference method. The effects of the governing parameters, such as the Brownian motion parameter, the thermophoresis parameter, the radiation parameter, the Prandtl number, and the Schmidt number on the velocity field, temperature distribution, and mass concentration, are presented graphically. Moreover, the impacts of these physical parameters on the skin friction coefficient, the Nusselt number, and the Sherwood number are displayed in the form of tables. Numerical outcomes reflect that the effects of the radiation parameter, thermophoresis parameter, and the Brownian motion parameter intensify the profiles of velocity, temperature, and concentration at different circumferential positions on the sphere.

Microscopic objects change the apparent permittivity and conductivity of aqueous systems and thus their overall polarizability. In inhomogeneous fields, dielectrophoresis (DEP) increases the overall polarizability of the system by moving more highly polarizable objects or media to locations with a higher field. The DEP force is usually calculated from the object’s point of view using the interaction of the object’s induced dipole or multipole moments with the inducing field. Recently, we were able to derive the DEP force from the work required to charge suspension volumes with a single object moving in an inhomogeneous field. The capacitance of the volumes was described using Maxwell–Wagner’s mixing equation. Here, we generalize this system’s-point-of-view approach describing the overall polarizability of the whole DEP system as a function of the position of the object with a numerical “conductance field”. As an example, we consider high- and low conductive 200 µm 2D spheres in a square 1 × 1 mm chamber with plain-versus-pointed electrode configuration. For given starting points, the trajectories of the sphere and the corresponding DEP forces were calculated from the conductance gradients. The model describes watersheds; saddle points; attractive and repulsive forces in front of the pointed electrode, increased by factors >600 compared to forces in the chamber volume where the classical dipole approach remains applicable; and DEP motions with and against the field gradient under “positive DEP” conditions. We believe that our approach can explain experimental findings such as the accumulation of viruses and proteins, where the dipole approach cannot account for sufficiently high holding forces to defeat Brownian motion.

The rheological properties of a cell suspension may play an important role in the flow field generated by populations of swimming micro-organisms (e.g. in bioconvection). In this paper, a swimming micro-organism is modelled as a squirming sphere with prescribed tangential surface velocity, in which the centre of mass of the sphere may be displaced from the geometric centre (bottom-heaviness). Effects of inertia and Brownian motion are neglected, because real micro-organisms swim at very low Reynolds numbers but are too large for Brownian effects to be important. The three-dimensional movement of 64 identical squirmers in a simple shear flow field, contained in a cube with periodic boundary conditions, is dynamically computed, for random initial positions and orientations. The computation utilizes a database of pairwise interactions that has been constructed by the boundary element method. The restriction to pairwise additivity of forces is expected to be justified if the suspension is semi-dilute. The results for non-bottom-heavy squirmers show that the squirming does not have a direct influence on the apparent viscosity. However, it does change the probability density in configuration space, and thereby causes a slight decrease in the apparent viscosity atO(c2), wherecis the volume fraction of spheres. In the case of bottom-heavy squirmers, on the other hand, the stresslet generated by the squirming motion directly contributes to the bulk stress atO(c), and the suspension shows strong non-Newtonian properties. When the background simple shear flow is directed vertically, the apparent viscosity of the semi-dilute suspension of bottom-heavy squirmers becomes smaller than that of inert spheres. When the shear flow is horizontal and varies with the vertical coordinate, on the other hand, the apparent viscosity becomes larger than that of inert spheres. In addition, significant normal stress differences appear for all relative orientations of gravity and the shear flow, in the case of bottom-heavy squirmers.

Purpose The purpose of this study is to numerically investigate the effect of jet impingement, magnetic field and nanoparticle shape (sphericity) on the hydrodynamic/heat transfer characteristics of nanofluids over stationary and vibrating plates. Design/methodology/approach A two-dimensional finite volume method-based homogeneous heat transfer model has been developed, validated and used in the present investigation. Three different shapes of non-spherical carbon nanoparticles namely nanotubes, nanorods and nanosheets are used in the analysis. Sphericity-based effective thermal conductivity of nanofluids with Brownian motion of nanoparticles is considered in the investigation. Moreover, the ranges of various comprehensive parameters used in the study are Re = 500 to 900, St = 0.0694 to 0.2083 and Ha = 0 to 80. Findings The hydrodynamic/heat transfer performance of jet impingement in the case of vibrating plate is 298 per cent higher than that of stationary plate at Re = 500. However, for the case of vibrating plate, a reduction in the heat transfer performance of 23.35 per cent is observed by increasing the jet Reynolds number from 500 to 900. In the case of vibrating plate, the saturation point for Strouhal number is found to be 0.0833 at Re = 900 and Ha = 0. Further decrement in St beyond this limit leads to a drastic reduction in the performance. Moreover, no recirculation in the flow is observed near the stagnation point for jet impingement over vibrating plate. It is also observed that the effect of magnetic field enhances the performance of jet impingement over a stationary plate by 36.18 per cent at Ha = 80 and Re = 900. Whereas, opposite trend is observed for the case of vibrating plate. Furthermore, at Re = 500, the percentage enhancement in the Nuavg values of 3 Vol.% carbon nanofluid with nanosheets, nanorods and nanotubes are found to be 47.53, 26.86 and 26.85 per cent when compared with the value obtained for pure water. Practical implications The present results will be useful in choosing nanosheets-based nanofluid as the efficient heat transfer medium in cooling of high power electronic devices. Moreover, the obtained saturation point in the Strouhal number of the vibrating plate will help in cooling of turbine blades, as well as paper and textile drying. Moreover, the developed homogeneous heat transfer model can also be used to study different micro-convection phenomena in nanofluids by considering them as source terms in the momentum equation. Originality/value Impingement of jet over two different plate types such as stationary and vibrating is completely analyzed with the use of a validated in-house FVM code. A complete investigation on the influence of external magnetic field on the performance of plate type configuration is evaluated. The three fundamental shapes of carbon nanoparticles are also evaluated to obtain sphericity based hydrodynamic/heat transfer performance of jet impingement.

The objects of the present study are one-parameter semigroups generated by Schrödinger operators with fairly general electromagnetic potentials. More precisely, we allow scalar potentials from the Kato class and impose on the vector potentials only local Kato-like conditions. The configuration space is supposed to be an arbitrary open subset of multi-dimensional Euclidean space; in case that it is a proper subset, the Schrödinger operator is rendered symmetric by imposing Dirichlet boundary conditions. We discuss the continuity of the image functions of the semigroup and show local-norm-continuity of the semigroup in the potentials. Finally, we prove that the semigroup has a continuous integral kernel given by a Brownian-bridge expectation. Altogether, the article is meant to extend some of the results in B. Simon's landmark paper [Bull. Amer. Math. Soc.7 (1982) 447] to non-zero vector potentials and more general configuration spaces.

We studied the impact of the cell thickness on configurations of line disclinations within a plane-parallel nematic cell. The Lebwohl-Lasher semimicroscopic approach was used and (meta)stable nematic configurations were calculated using Brownian molecular dynamics. Defect patterns were enforced topologically via boundary conditions. We imposed periodic circular nematic surface fields at each confining surface. The resulting structures exhibit line defects which either connect the facing plates or remain confined within the layers near confining plates. The first structure is stable in relatively thin cells and the latter one in thick cells. We focused on structures at the threshold regime where both structures compete. We demonstrated that “history” of samples could have strong impact on resulting nematic configurations.

We model continuous-time information flows generated by a number of information sources that switch on and off at random times. By modulating a multi-dimensional Lévy random bridge over a random point field, our framework relates the discovery of relevant new information sources to jumps in conditional expectation martingales. In the canonical Brownian random bridge case, we show that the underlying measure-valued process follows jump-diffusion dynamics, where the jumps are governed by information switches. The dynamic representation gives rise to a set of stochastically-linked Brownian motions on random time intervals that capture evolving information states, as well as to a state-dependent stochastic volatility evolution with jumps. The nature of information flows usually exhibits complex behavior, however, we maintain analytic tractability by introducing what we term the effective and complementary information processes, which dynamically incorporate active and inactive information, respectively. As an application, we price a financial vanilla option, which we prove is expressed by a weighted sum of option values based on the possible state configurations at expiry. This result may be viewed as an information-based analogue of Merton’s option price, but where jump-diffusion arises endogenously. The proposed information flows also lend themselves to the quantification of asymmetric informational advantage among competitive agents, a feature we analyze by notions of information geometry.

A nonlocal theory for stress in bound suspensions of rigid, slender fibres is developed and used to predict the rheology of dilute, rigid polymer suspensions when confined to capillaries or fine porous media. Because the theory is nonlocal, we describe transport in a fibre suspension where the velocity and concentration fields change rapidly on the fibre's characteristic length. Such rapid changes occur in a rigidly bound domain because suspended particles are sterically excluded from configurations near the boundaries. A rigorous no-flux condition resulting from the presence of solid boundaries around the suspension is included in our nonlocal stress theory and naturally gives rise to concentration gradients that scale on the length of the particle. Brownian motion of the rigid fibres is included within the nonlocal stress through a Fokker–Planck description of the fibres’ probability density function where gradients of this function are proportional to Brownian forces and torques exerted on the suspended fibres. This governing Fokker–Planck probability density equation couples the fluid flow and the nonlocal stress resulting in a nonlinear set of integral-differential equations for fluid stress, fluid velocity and fibre probability density. Using the method of averaged equations (Hinch 1977) and slender-body theory (Batchelor 1970), the system of equations is solved for a dilute suspension of rigid fibres experiencing flow and strong Brownian motion while confined to a gap of the same order in size as the fibre's intrinsic length. The full solution of this problem, as the fluid in the gap undergoes either simple shear or pressure-driven flow, is solved self-consistently yielding average fluid velocity, shear and normal stress profiles within the gap as well as the probability density function for the fibres’ position and orientation. From these results we calculate concentration profiles, effective viscosities and slip velocities and compare them to experimental data.

Blood circulating efficiently inside the veins and arteries, provides essential nutrients and oxygen to tissues and organs in the entire body. To highlight the fundamental properties of blood and gain insight into the regularizing effect of various formulations, we need to develop mathematical models. In order to do this, first we present the polymer dynamics in terms of an ensemble of Hookean dumbbells with Brownian configuration fields to derive the orientation stress tensor. Then, we describe the continuity and the momentum equations for time-dependent incompressible flow and the Oldroyd-B model. Finally, we present our numerical analysis of the model and give the effect of the orientation stress tensor in a blood vessel. The development of mathematical models and numerical procedures for the approximation of the blood specific flow equations have enabled us to understand the complex behaviors of blood flows inside the vessel.

Stokesian Dynamics has been used to investigate the origins of shear thickening in concentrated colloidal suspensions. For this study, we considered a monolayer suspension composed of charge-stabilized non-Brownian monosized rigid spheres dispersed at an areal fraction of ϕa=0.74 in a Newtonian liquid. The suspension was subjected to a linear shear field. In agreement with established experimental data, our results indicate that shear thickening in this system is associated with an order–disorder transition of the suspension microstructure. Below the critical shear rate at which this transition occurs, the suspension microstructure consists of two-dimensional analogues of experimentally observed sliding layer configurations. Above this critical shear rate, suspensions are disordered, contain particle clusters, and exhibit viscosities and microstructures characteristic of suspensions of non-Brownian hard spheres. In addition, suspensions possessing the sliding layer microstructure at the beginning of supercritical shearing tend to retain this microstructure for a period of time before disordering. The onset of this disorder is due to the formation of particle doublets within the suspension. Once formed, these doublets rotate, due to the bulk motion, and disrupt the long-range order of the suspension. The cross-stream component of the centre-to-centre separation vector associated with the two particles forming a doublet, which is zero when the doublet is perfectly aligned with the bulk velocity vector, grows exponentially with time. This strongly suggests that the evolution of these doublets is due to a change in the stability of the sliding layer configurations, with this type of ordered microstructure being linearly unstable above a critical shear rate. This contention is supported by results of a stability analysis. The analysis shows that a single string of particles is subject to a linear instability leading to the formation of particle doublets. Simulations were repeated with different numbers of particles in the computational domain, with the results found to be qualitatively independent of system size.

Abstract. Evaluating passive tracer advection is a common tool to study flow structures, particularly Lagrangian trajectories ranging from molecular scales up to the atmosphere and oceans. Here we report on numerical experiments in the region of the tropical Pacific (20∘ S–20∘ N), where 6600 tracer parcels are advected from a regular initial configuration (along a meridional line at 110∘ W between 15∘ S and 15∘ N) during periods of 1 year for 25 years altogether. We exploit AVISO surface flow fields and solve the kinematic equation for passive tracer movement in the 2D advection tests. We demonstrate that the strength of the advection defined by mean monthly westward displacements of the tracer clouds exhibit surprisingly large inter- and intra-annular variabilities. Furthermore, an analysis of cross-correlations between advection strength and the El-Niño and Southern Oscillation (SOI) indices reveal a significant anticorrelation between advection intensity and ONI (the Oceanic Niño Index) and a weaker positive correlation with SOI, both with a time lag of about 3 months (the two indices are strongly anticorrelated near real time). The statistical properties of advection (time-dependent mean squared displacement and first passage time distribution) suggest that the westward-moving tracers can be mapped into a simple 1D stochastic process, namely fractional Brownian motion. We fit the model parameters and show by numerical simulations of the fractional Brownian motion model that it is able to reproduce the observed statistical properties of the tracers' trajectories well. We argue that a traditional explanation based on the superposition of ballistic drift and a diffusion term yields different statistics and is incompatible with our observations.

PurposeA comprehensive study on the fluid flow and heat transfer in a nanofluid channel is carried out. The configuration of the channel is as like as quarter channel. The channel is filled with CuO–water nanofluid.Design/methodology/approachThe Koo–Kleinstreuer–Li model is used to estimate the dynamic viscosity and consider the Brownian motion. On the other hand, the influence of nanoparticles’ shapes on the heat transfer rate is considered in the simulations. The channel is included with the injection pipes which are modeled as active bodies with constant temperature in the 2D simulations.FindingsThe Rayleigh number, nanoparticle concentration and the thermal arrangements of internal pipes are the governing parameters. The hydrothermal aspects of natural convection are investigation using different approaches such as average Nusselt number, total entropy generation, Bejan number, streamlines, temperature fields, local heat transfer irreversibility, local fluid friction irreversibility and heatlines.Originality/valueThe originality of this work is investigation of fluid flow, heat transfer, entropy generation and heatline visualization within a nanofluid-filled channel using a finite volume method.

Magnetic skyrmions are currently gaining attention owing to their potential to act as information carriers in spintronic devices. However, conventional techniques which rely on modulating the electric current to write or manipulate information using skyrmions are not energy efficient. Therefore, in this study, a Ta/Co–Fe–B/Ta/MgO junction that hosts a skyrmion was utilized to fabricate a device to investigate the effect of applying a voltage in the direction perpendicular to the film plane. Magneto-optical Kerr effect microscopy was performed in a polar configuration to observe the difference in the perpendicular magnetic anisotropy by observing the behavior of the magnetic domain structure and the skyrmions. Our findings suggest that voltage-induced magnetic domain structure modulation and the creation/annihilation of skyrmions are both possible. Furthermore, manipulation of skyrmions was realized by utilizing repulsive magnetic dipole interaction between the voltage-created skyrmion and skyrmion, exhibiting Brownian motion, outside the top electrode. Thus, our proposed method can enable controlling the creation and annihilation of skyrmions and their positions by manipulating the externally applied voltage. These findings can advance unconventional computing fields, such as stochastic and ultra-low-power computing.

Purpose Entropy generation in nanofluids with peristaltic scheme occupies a primary consideration in the sense of its application in clinical, as well as the industrial field in terms of improved thermal conductivity of the original fluid. Three-dimensional cylindrical configurations are the most realistic and commonly used geometries which incorporate most of the experimental equipment. In the current study, three-dimensional cylindrical enclosures have been assumed to receive the results of entropy generation occurring due to viscous dissipation, heat transfer of nanofluid and mass concentration of nanoparticles through peristaltic pumping. Applications of the study can be found in peristaltic micro-pumps and novel drug delivery mechanism in pharmacological engineering. Design/methodology/approach The equations of interest have been structured under physical constraints of lubrication theory and dimensionless strategy. Finalized relations involve highly complicated partial differential equations whose solutions are tabulated through some perturbation procedure and expression of pressure rise is manipulated by a numerical technique through built-in command NIntegrate on Mathematical tool “Mathematica.” Findings It is evaluated that entropy production goes linear with the greater magnitudes of Brownian motion but inverse characteristics have been sorted against thermophoresis factor. Originality/value To the best of authors’ knowledge, this study does not exist in literature yet and it contains a new innovative idea.

Hydrodynamic diffusion refers to the fluctuating motion of non-Brownian particles (or droplets or bubbles) in a dispersion, which occurs due to multiparticle interactions. For example, in a concentrated sheared suspension, particles do not move along streamlines but instead exhibit fluctuating motions as they tumble around each other (figure 1a). This leads to a net migration of particles down gradients in particle concentration and in shear rate, due to the higher frequency of encounters of a test particle with other particles on the side of the test particle which has higher concentration or shear rate. As another example, suspended particles subject to sedimentation or fluidization do not generally move relative to the fluid with a constant velocity, but instead experience diffusion-like fluctuations in velocity due to interactions with neighbouring particles and the resulting variation in the microstructure or configuration of the suspended particles (figure 1b). In flowing granular materials, the particles interact through direct collisions or contacts; these collisions also cause the particles to undergo fluctuating motions characteristic of diffusion processes. Although the existence and importance of hydrodynamic diffusion of particles have been embraced only in the past several years, the subject has already captured the attention of a growing number of researchers in several diverse fields (e.g. suspension mechanics, fluidization, materials processing, and granular flows).

AbstractTo impart directionality to the motions of a molecular mechanism, one must overcome the random thermal forces that are ubiquitous on such small scales and in liquid solution at ambient temperature. In equilibrium without energy supply, directional motion cannot be sustained without violating the laws of thermodynamics. Under conditions away from thermodynamic equilibrium, directional motion may be achieved within the framework of Brownian ratchets, which are diffusive mechanisms that have broken inversion symmetry1–5. Ratcheting is thought to underpin the function of many natural biological motors, such as the F1F0-ATPase6–8, and it has been demonstrated experimentally in synthetic microscale systems (for example, to our knowledge, first in ref. 3) and also in artificial molecular motors created by organic chemical synthesis9–12. DNA nanotechnology13 has yielded a variety of nanoscale mechanisms, including pivots, hinges, crank sliders and rotary systems14–17, which can adopt different configurations, for example, triggered by strand-displacement reactions18,19 or by changing environmental parameters such as pH, ionic strength, temperature, external fields and by coupling their motions to those of natural motor proteins20–26. This previous work and considering low-Reynolds-number dynamics and inherent stochasticity27,28 led us to develop a nanoscale rotary motor built from DNA origami that is driven by ratcheting and whose mechanical capabilities approach those of biological motors such as F1F0-ATPase.

In the roadrunner cartoons, the unlucky coyote, in hot pursuit of the roadrunner, frequently finds himself running off the edge of a precipice. In sympathy with the coyote's plight, the laws of physics suspend their action. Gravity waits to exert its force until the coyote realizes his situation and resigns himself to the inevitable. Only then does the coyote fall, miraculously surviving the near-disaster without serious damage. What does this have to do with cell biology at the turn of the millennium? Blame it on JCS's Caveman or at least the infectiousness of the troglodyte's point of view. But it strikes this Editor that for much of cell biology, no less than for the roadrunner, the laws of physics are seemingly suspended. Pick up any contemporary text book or review article and look at the cartoons (diagrams) that grace the pages. You will find diagrams replete with circles, squares, ellipsoids and iconic representations of molecular components, supramolecular assemblies or membrane compartments. Arrows define signal cascades, pathways of transport and patterns of interaction. Even better, check out any of the supplementary instructional CDs that accompany text books and view the animations. You will see cell toons - molecules moving on smooth trajectories to interact with their partners, assembling into cellular machinery or arriving at cellular destinations. They all seem to know where to go and what to do in their cell toon life. It doesn't matter whether we are talking about DNA replication, protein synthesis, mitochondrial respiration, membrane trafficking, nuclear import, chromatin condensation or assembly of the mitotic spindle to mention just a few examples. In each case, the process unfolds before us as a molecular ballet choreographed by a hidden director. Or should I say anonymous animator. Please don't get me wrong. Cartoon diagrams are a necessary part of science. They help us to form and communicate concepts. Adages such as ‘a picture is worth a thousand words’ do not come into existence for nothing. Further, simplification is necessary to sharpen Occam's razor. Science progresses faster if a hypothesis is honed to the point where it can be readily refuted. Of course, it is best to be right. Next best is to be wrong. But the worst thing that can be said about a concept is that it is so hedged or ambiguous that it cannot even be wrong. Cartoons are invaluable in presenting clear alternatives. And cartoons, by definition, do not attempt to portray reality. We understand and accept that they deliberately omit details which may be important in some other context but which are extraneous to the story line. We do not have to know how the coyote recovers from his disastrous fall. It is sufficient that he resumes the chase. Likewise, much of Cell Biology can satisfactorily be ‘explained’ in terms of the behavior of toons. My thesis for this essay is that cell biology at the turn of the millennium has, for the first time, the real opportunity to burst the frames of the cartoons. The field has progressed to the point where the maxim that cells obey the laws of physics and chemistry can be made more than a creed. The time is approaching for the mystery of the hidden directornymous animator to be dispelled. What is driving this new orientation and what is required to bring it to fruition? Advances in structural biology provide part of the explanation. Atomic structures have been determined for a large variety of proteins, with the number increasing on a daily basis. Structural genomics will succeed genomics. It is possible to foresee that in the not too distant future atomic structures will be known for most if not all the major proteins in a cell. Not only individual proteins but supramolecular assemblies as complex as the ribosome have yielded to structural analysis. Of course, structures per se are static entities, but biology has taught that function is inherent in structure. Knowledge of molecular structures has provided atomic explanations for ligand binding, allosteric interaction, enzymatic catalysis, ion pumps, immune recognition, sensory detection and mechano-chemical transduction. When combined with kinetics, structural biology provides the chemical bedrock of cell biology. But the bedrock of structural biology, while necessary for the new cell biology, is almost certainly not sufficient. A major gap is in understanding the complex properties of self-organizing systems. Cells are ensembles of molecules interacting within boundaries. Some of the molecules are organized into supramolecular assemblies that have been likened to molecular machines. Examples include multi-enzyme complexes, DNA replication complexes, the ribosome and the proteasome. Understanding the operation of these molecular machines in chemical and physical terms is a major challenge in that they display exotic behavior such as solid-state channeling of substrates, error-checking, proof-reading, regulation and adaptiveness. Nevertheless, the conceptual basis for their formation is thought to rest on well-established principles: namely, the equilibrium self-assembly of molecular components whose specific affinities are inherent in their 3-D structure. However, other aspects of cellular organization manifest properties beyond self-assembly. The cytoskeleton, for example, is a steady-state system which requires the continuous input of energy to maintain its organization. It displays emergent properties of self-organization, self-centering, self-polarization and self-propagating motility. Membrane compartments such as the endoplasmic reticulum, the Golgi apparatus and transport vesicles provide additional examples of cellular organization dependent upon dynamic processes far from equilibrium. A further level of complexity is introduced by the fact that the self-organization of one system, such as membrane compartments, may be dependent upon another, such as the cytoskeleton. A challenge for the new cell biology is to go beyond ‘toon’ explanations, to understand the emergent, self-organizing properties of interdependent systems. It is likely that an adequate response to this challenge will be multidisciplinary, involving approaches not normally associated with mainstream cell biology. We are likely to be in for a heavy dose of biophysics, computer modeling and systems analysis. A serious problem will be to identify functional levels of decomposition and reconstitution. Because of the microscopic scale, thermal energy, randomness and stochastic processes will be an intrinsic part of the landscape. Brownian motions may present a Damoclean double edge. They are commonly thought to be responsible for the degradation of order into disorder. But, counterintuitively, random thermal processes may also provide the raw energy which, if biased by energy-dependent molecular switches and motors, generates order from disorder. Non-deterministic processes and selection from among alternative pathways may be a common strategy. Fluctuation theory, probabilistic formulations and rare events may underpin the capacity of molecular ensembles to ‘evolve’ into ordered configurations. Further, biological properties such as error-checking and adaptiveness imply an ‘intelligence’, which suggests that the systems analysis may have ‘software’ as well as ‘hardware’ dimensions. Molecular logic may be non-deterministic, ‘fuzzy’ and able to ‘learn’. The evolvability of the system may itself be an important consideration in understanding the design principles. The belief that cells obey the laws of physics and chemistry means that, in terms of the molecular ballet, the director is not only hidden - he doesn't exist. One is tempted to say that the challenge is to understand how the ballet came to be self- choreographed. But even this formulation misses the point that the individual dancers have no definite positions on the stage. Organization in the cell is a continuity of form, not individual molecules. The challenge is to understand how the ensemble is able to perform the dance with chaotic free substitution.

The random first order transition theory (RFOT) describing the transition from a supercooled liquid to an ideal glass has been actively developed over the last twenty years. This theory is formulated in a way that allows a description of the transition from the initial equilibrium state to the final metastable state without considering any kinetic processes. The RFOT and its applications for real molecular systems (multicomponent liquids with various intermolecular potentials, gel systems, etc.) are widely represented in English-language sources. However, these studies are practically not described in any Russian sources. This paper presents an overview of the studies carried out in this field. REFERENCES 1. Sanditov D. S., Ojovan M. I. Relaxation aspectsof the liquid—glass transition. Uspekhi FizicheskihNauk. 2019;189(2): 113–133. DOI: https://doi.org/10.3367/ufnr.2018.04.0383192. Tsydypov Sh. B., Parfenov A. N., Sanditov D. S.,Agrafonov Yu. V., Nesterov A. S. Application of themolecular dynamics method and the excited statemodel to the investigation of the glass transition inargon. Available at: http://www.isc.nw.ru/Rus/GPCJ/Content/2006/tsydypov_32_1.pdf (In Russ.). GlassPhysics and Chemistry. 2006;32(1): 83–88. DOI: https://doi.org/10.1134/S10876596060101113. Berthier L., Witten T. A. Glass transition of densefluids of hard and compressible spheres. PhysicalReview E. 2009;80(2): 021502. DOI: https://doi.org/10.1103/PhysRevE.80.0215024. Sarkisov G. N. Molecular distribution functionsof stable, metastable and amorphous classical models.Uspekhi Fizicheskih Nauk. 2002;172(6): 647–669. DOI:https://doi.org/10.3367/ufnr.0172.200206b.06475. Hoover W. G., Ross M., Johnson K. W., HendersonD., Barker J. A., Brown, B. C. Soft-sphere equationof state. The Journal of Chemical Physics, 1970;52(10):4931–4941. DOI: https://doi.org/10.1063/1.16727286. Cape J. N., Woodcock L. V. Glass transition in asoft-sphere model. The Journal of Chemical Physics,1980;72(2): 976–985. DOI: https://doi.org/10.1063/1.4392177. Franz S., Mezard M., Parisi G., Peliti L. Theresponse of glassy systems to random perturbations:A bridge between equilibrium and off-equilibrium.Journal of Statistical Physics. 1999;97(3–4): 459–488.DOI: https://doi.org/10.1023/A:10046029063328. Marc Mezard and Giorgio Parisi. Thermodynamicsof glasses: a first principles computation. J. of Phys.:Condens. Matter. 1999;11: A157–A165.9. Berthier L., Jacquin H., Zamponi F. Microscopictheory of the jamming transition of harmonic spheres.Physical Review E, 2011;84(5): 051103. DOI: https://doi.org/10.1103/PhysRevE.84.05110310. Berthier L., Biroli, G., Charbonneau P.,Corwin E. I., Franz S., Zamponi F. Gardner physics inamorphous solids and beyond. The Journal of ChemicalPhysics. 2019;151(1): 010901. DOI: https://doi.org/10.1063/1.5097175 11. Berthier L., Ozawa M., Scalliet C. Configurationalentropy of glass-forming liquids. The Journal ofChemical Physics. 2019;150(16): 160902. DOI: https://doi.org/10.1063/1.509196112. Bomont J. M., Pastore G. An alternative schemeto find glass state solutions using integral equationtheory for the pair structure. Molecular Physics.2015;113(17–18): 2770–2775. DOI: https://doi.org/10.1080/00268976.2015.103832513. Bomont J. M., Hansen J. P., Pastore G.Hypernetted-chain investigation of the random firstordertransition of a Lennard-Jones liquid to an idealglass. Physical Review E. 2015;92(4): 042316. DOI:https://doi.org/10.1103/PhysRevE.92.04231614. Bomont J. M., Pastore G., Hansen J. P.Coexistence of low and high overlap phases in asupercooled liquid: An integral equation investigation.The Journal of Chemical Physics. 2017;146(11): 114504.DOI: https://doi.org/10.1063/1.497849915. Bomont J. M., Hansen J. P., Pastore G. Revisitingthe replica theory of the liquid to ideal glass transition.The Journal of Chemical Physics. 2019;150(15): 154504.DOI: https://doi.org/10.1063/1.508881116. Cammarota C., Seoane B. First-principlescomputation of random-pinning glass transition, glasscooperative length scales, and numerical comparisons.Physical Review B. 2016;94(18): 180201. DOI: https://doi.org/10.1103/PhysRevB.94.18020117. Charbonneau P., Ikeda A., Parisi G., Zamponi F.Glass transition and random close packing above threedimensions. Physical Review Letters. 2011;107(18):185702. DOI: https://doi.org/10.1103/PhysRevLett.107.18570218. Ikeda A., Miyazaki K. Mode-coupling theory asa mean-field description of the glass transition.Physical Review Letters. 2010;104(25): 255704. DOI:https://doi.org/10.1103/PhysRevLett.104.25570419. McCowan D. Numerical study of long-timedynamics and ergodic-nonergodic transitions in densesimple fluids. Physical Review E. 2015;92(2): 022107.DOI: https://doi.org/10.1103/PhysRevE.92.02210720. Ohtsu H., Bennett T. D., Kojima T., Keen D. A.,Niwa Y., Kawano M. Amorphous–amorphous transitionin a porous coordination polymer. ChemicalCommunications. 2017;53(52): 7060–7063. DOI:https://doi.org/10.1039/C7CC03333H21. Schmid B., Schilling R. Glass transition of hardspheres in high dimensions. Physical Review E.2010;81(4): 041502. DOI: https://doi.org/10.1103/PhysRevE.81.04150222. Parisi G., Slanina, F. Toy model for the meanfieldtheory of hard-sphere liquids. Physical Review E.2000;62(5): 6554. DOI: https://doi.org/10.1103/Phys-RevE.62.655423. Parisi G., Zamponi F. The ideal glass transitionof hard spheres. The Journal of Chemical Physics.2005;123(14): 144501. DOI: https://doi.org/10.1063/1.204150724. Parisi G., Zamponi F. Amorphous packings ofhard spheres for large space dimension. Journal ofStatistical Mechanics: Theory and Experiment. 2006;03:P03017. DOI: https://doi.org/10.1088/1742-5468/2006/03/P0301725. Parisi G., Procaccia I., Shor C., Zylberg J. Effectiveforces in thermal amorphous solids with genericinteractions. Physical Review E. 2019;99(1): 011001. DOI:https://doi.org/10.1103/PhysRevE.99.01100126. Stevenson J. D., Wolynes P. G. Thermodynamic −kinetic correlations in supercooled liquids: a criticalsurvey of experimental data and predictions of therandom first-order transition theory of glasses. TheJournal of Physical Chemistry B. 2005;109(31): 15093–15097. DOI: https://doi.org/10.1021/jp052279h27. Xia X., Wolynes P. G. Fragilities of liquidspredicted from the random first order transition theoryof glasses. Proceedings of the National Academy ofSciences. 2000;97(7): 2990–2994. DOI: https://doi.org/10.1073/pnas.97.7.299028. Kobryn A. E., Gusarov S., Kovalenko A. A closurerelation to molecular theory of solvation formacromolecules. Journal of Physics: Condensed Matter.2016; 28 (40): 404003. DOI: https://doi.org/10.1088/0953-8984/28/40/40400329. Coluzzi B. , Parisi G. , Verrocchio P.Thermodynamical liquid-glass transition in a Lennard-Jones binary mixture. Physical Review Letters.2000;84(2): 306. DOI: https://doi.org/10.1103/PhysRevLett.84.30630. Sciortino F., Tartaglia P. Extension of thefluctuation-dissipation theorem to the physical agingof a model glass-forming liquid. Physical Review Letters.2001;86(1): 107. DOI: https://doi.org/10.1103/Phys-RevLett.86.10731. Sciortino, F. One liquid, two glasses. NatureMaterials. 2002;1(3): 145–146. DOI: https://doi.org/10.1038/nmat75232. Farr R. S., Groot R. D. Close packing density ofpolydisperse hard spheres. The Journal of ChemicalPhysics. 2009;131(24): 244104. DOI: https://doi.org/10.1063/1.327679933. Barrat J. L., Biben T., Bocquet, L. From Paris toLyon, and from simple to complex liquids: a view onJean-Pierre Hansen’s contribution. Molecular Physics.2015;113(17-18): 2378–2382. DOI: https://doi.org/10.1080/00268976.2015.103184334. Gaspard J. P. Structure of Melt and Liquid Alloys.In Handbook of Crystal Growth. Elsevier; 2015. 580 p.DOI: https://doi.org/10.1016/B978-0-444-56369-9.00009-535. Heyes D. M., Sigurgeirsson H. The Newtonianviscosity of concentrated stabilized dispersions:comparisons with the hard sphere fluid. Journal ofRheology. 2004;48(1): 223–248. DOI: https://doi.org/10.1122/1.163498636. Ninarello A., Berthier L., Coslovich D. Structureand dynamics of coupled viscous liquids. MolecularPhysics. 2015;113(17-18): 2707–2715. DOI: https://doi.org/10.1080/00268976.2015.103908937. Russel W. B., Wagner N. J., Mewis J. Divergencein the low shear viscosity for Brownian hard-spheredispersions: at random close packing or the glasstransition? Journal of Rheology. 2013;57(6): 1555–1567.DOI: https://doi.org/10.1122/1.482051538. Schaefer T. Fluid dynamics and viscosity instrongly correlated fluids. Annual Review of Nuclearand Particle Science. 2014;64: 125–148. DOI: https://doi.org/10.1146/annurev-nucl-102313-02543939. Matsuoka H. A macroscopic model thatconnects the molar excess entropy of a supercooledliquid near its glass transition temperature to itsviscosity. The Journal of Chemical Physics. 2012;137(20):204506. DOI: https://doi.org/10.1063/1.476734840. de Melo Marques F. A., Angelini R., Zaccarelli E.,Farago B., Ruta B., Ruocco, G., Ruzicka B. Structuraland microscopic relaxations in a colloidal glass. SoftMatter. 2015;11(3): 466–471. DOI: https://doi.org/10.1039/C4SM02010C41. Deutschländer S., Dillmann P., Maret G., KeimP. Kibble–Zurek mechanism in colloidal monolayers.Proceedings of the National Academy of Sciences.2015;112(22): 6925–6930. DOI: https://doi.org/10.1073/pnas.150076311242. Chang J., Lenhoff A. M., Sandler S. I.Determination of fluid–solid transitions in modelprotein solutions using the histogram reweightingmethod and expanded ensemble simulations. TheJournal of Chemical Physics. 2004;120(6): 3003–3014.DOI: https://doi.org/10.1063/1.163837743. Gurikov P., Smirnova I. Amorphization of drugsby adsorptive precipitation from supercriticalsolutions: a review. The Journal of Supercritical Fluids.2018;132: 105–125. DOI: https://doi.org/10.1016/j.supflu.2017.03.00544. Baghel S., Cathcart H., O’Reilly N. J. Polymericamorphoussolid dispersions: areviewofamorphization, crystallization, stabilization, solidstatecharacterization, and aqueous solubilization ofbiopharmaceutical classification system class II drugs.Journal of Pharmaceutical Sciences. 2016;105(9):2527–2544. DOI: https://doi.org/10.1016/j.xphs.2015.10.00845. Kalyuzhnyi Y. V., Hlushak S. P. Phase coexistencein polydisperse multi-Yukawa hard-sphere fluid: hightemperature approximation. The Journal of ChemicalPhysics. 2006;125(3): 034501. DOI: https://doi.org/10.1063/1.221241946. Mondal C., Sengupta S. Polymorphism,thermodynamic anomalies, and network formation inan atomistic model with two internal states. PhysicalReview E. 2011;84(5): 051503. DOI: https://doi.org/10.1103/PhysRevE.84.05150347. Bonn D., Denn M. M., Berthier L., Divoux T.,Manneville S. Yield stress materials in soft condensedmatter. Reviews of Modern Physics. 2017;89(3): 035005.DOI: https://doi.org/10.1103/RevModPhys.89.03500548. Tanaka H. Two-order-parameter model of theliquid–glass transition. I. Relation between glasstransition and crystallization. Journal of Non-Crystalline Solids. 2005;351(43-45): 3371–3384. DOI:https://doi.org/10.1016/j.jnoncrysol.2005.09.00849. Balesku R. Ravnovesnaya i neravnovesnayastatisticheskaya mekhanika [Equilibrium and nonequilibriumstatistical mechanics]. Moscow: Mir Publ.;1978. vol. 1. 404 c. (In Russ.)50. Chari S., Inguva R., Murthy K. P. N. A newtruncation scheme for BBGKY hierarchy: conservationof energy and time reversibility. arXiv preprintarXiv: 1608. 02338. DOI: https://arxiv.org/abs/1608.0233851. Gallagher I., Saint-Raymond L., Texier B. FromNewton to Boltzmann: hard spheres and short-rangepotentials. European Mathematical Society.arXiv:1208.5753. DOI: https://arxiv.org/abs/1208.575352. Rudzinski J. F., Noid W. G. A generalized-Yvon-Born-Green method for coarse-grained modeling. TheEuropean Physical Journal Special Topics. 224(12),2193–2216. DOI: https://doi.org/10.1140/epjst/e2015-02408-953. Franz B., Taylor-King J. P., Yates C., Erban R.Hard-sphere interactions in velocity-jump models.Physical Review E. 2016;94(1): 012129. DOI: https://doi.org/10.1103/PhysRevE.94.01212954. Gerasimenko V., Gapyak I. Low-Densityasymptotic behavior of observables of hard spherefluids. Advances in Mathematical Physics. 2018:6252919. DOI: https://doi.org/10.1155/2018/625291955. Lue L. Collision statistics, thermodynamics,and transport coefficients of hard hyperspheres inthree, four, and five dimensions. The Journal ofChemical Physics. 2005;122(4): 044513. DOI: https://doi.org/10.1063/1.183449856. Cigala G., Costa D., Bomont J. M., Caccamo C.Aggregate formation in a model fluid with microscopicpiecewise-continuous competing interactions.Molecular Physics. 2015;113(17–18): 2583–2592.DOI: https://doi.org/10.1080/00268976.2015.107800657. Jadrich R., Schweizer K. S. Equilibrium theoryof the hard sphere fluid and glasses in the metastableregime up to jamming. I. Thermodynamics. The Journalof Chemical Physics. 2013;139(5): 054501. DOI: https://doi.org/10.1063/1.481627558. Mondal A., Premkumar L., Das S. P. Dependenceof the configurational entropy on amorphousstructures of a hard-sphere fluid. Physical Review E.2017;96(1): 012124. DOI: https://doi.org/10.1103/PhysRevE.96.01212459. Sasai M. Energy landscape picture ofsupercooled liquids: application of a generalizedrandom energy model. The Journal of Chemical Physics.2003;118(23): 10651–10662. DOI: https://doi.org/10.1063/1.157478160. Sastry S. Liquid limits: Glass transition andliquid-gas spinodal boundaries of metastable liquids.Physical Review Letters. 2000;85(3): 590. DOI: https://doi.org/10.1103/PhysRevLett.85.59061. Uche O. U., Stillinger F. H., Torquato S. On therealizability of pair correlation functions. Physica A:Statistical Mechanics and its Applications. 2006;360(1):21–36. DOI: https://doi.org/10.1016/j.physa.2005.03.05862. Bi D., Henkes S., Daniels K. E., Chakraborty B.The statistical physics of athermal materials. Annu.Rev. Condens. Matter Phys. 2015;6(1): 63–83. DOI:https://doi.org/10.1146/annurev-conmatphys-031214-01433663. Bishop M., Masters A., Vlasov A. Y. Higher virialcoefficients of four and five dimensional hardhyperspheres. The Journal of Chemical Physics.2004;121(14): 6884–6886. DOI: https://doi.org/10.1063/1.177757464. Sliusarenko O. Y., Chechkin A. V., SlyusarenkoY. V. The Bogolyubov-Born-Green-Kirkwood-Yvon hierarchy and Fokker-Planck equation for manybodydissipative randomly driven systems. Journal ofMathematical Physics. 2015;56(4): 043302. DOI:https://doi.org/10.1063/1.491861265. Tang Y. A new grand canonical ensemblemethod to calculate first-order phase transitions. TheJournal of chemical physics. 2011;134(22): 224508. DOI:https://doi.org/10.1063/1.359904866. Tsednee T., Luchko T. Closure for the Ornstein-Zernike equation with pressure and free energyconsistency. Physical Review E. 2019;99(3): 032130.DOI: https://doi.org/10.1103/PhysRevE.99.03213067. Maimbourg T., Kurchan J., Zamponi, F. Solutionof the dynamics of liquids in the large-dimensionallimit. Physical review letters. 2016;116(1): 015902. DOI:https://doi.org/10.1103/PhysRevLett.116.01590268. Mari, R., & Kurchan, J. Dynamical transition ofglasses: from exact to approximate. The Journal ofChemical Physics. 2011;135(12): 124504. DOI: https://doi.org/10.1063/1.362680269. Frisch H. L., Percus J. K. High dimensionalityas an organizing device for classical fluids. PhysicalReview E. 1999;60(3): 2942. DOI: https://doi.org/10.1103/PhysRevE.60.294270. Finken R., Schmidt M., Löwen H. Freezingtransition of hard hyperspheres. Physical Review E.2001;65(1): 016108. DOI: https://doi.org/10.1103/PhysRevE.65.01610871. Torquato S., Uche O. U., Stillinger F. H. Randomsequential addition of hard spheres in high Euclideandimensions. Physical Review E. 2006;74(6): 061308.DOI: https://doi.org/10.1103/PhysRevE.74.06130872. Martynov G. A. Fundamental theory of liquids;method of distribution functions. Bristol: Adam Hilger;1992, 470 p.73. Vompe A. G., Martynov G. A. The self-consistentstatistical theory of condensation. The Journal ofChemical Physics. 1997;106(14): 6095–6101. DOI:https://doi.org/10.1063/1.47327274. Krokston K. Fizika zhidkogo sostoyaniya.Statisticheskoe vvedenie [Physics of the liquid state.Statistical introduction]. Moscow: Mir Publ.; 1978.400 p. (In Russ.)75. Rogers F. J., Young D. A. New, thermodynamicallyconsistent, integral equation for simple fluids. PhysicalReview A. 1984;30(2): 999. DOI: https://doi.org/10.1103/PhysRevA.30.99976. Wertheim M. S. Exact solution of the Percus–Yevick integral equation for hard spheres Phys. Rev.Letters. 1963;10(8): 321–323. DOI: https://doi.org/10.1103/PhysRevLett.10.32177. Tikhonov D. A., Kiselyov O. E., Martynov G. A.,Sarkisov G. N. Singlet integral equation in thestatistical theory of surface phenomena in liquids. J.of Mol. Liquids. 1999;82(1–2): 3– 17. DOI: https://doi.org/10.1016/S0167-7322(99)00037-978. Agrafonov Yu., Petrushin I. Two-particledistribution function of a non-ideal molecular systemnear a hard surface. Physics Procedia. 2015;71. 364–368. DOI: https://doi.org/10.1016/j.phpro.2015.08.35379. Agrafonov Yu., Petrushin I. Close order in themolecular system near hard surface. Journal of Physics:Conference Series. 2016;747: 012024. DOI: https://doi.org/10.1088/1742-6596/747/1/01202480. He Y., Rice S. A., Xu X. Analytic solution of theOrnstein-Zernike relation for inhomogeneous liquids.The Journal of Chemical Physics. 2016;145(23): 234508.DOI: https://doi.org/10.1063/1.497202081. Agrafonov Y. V., Petrushin I. S. Usingmolecular distribution functions to calculate thestructural properties of amorphous solids. Bulletinof the Russian Academy of Sciences: Physics. 2020;84:783–787. DOI: https://doi.org/10.3103/S106287382007003582. Bertheir L., Ediger M. D. How to “measure” astructural relaxation time that is too long to bemeasured? arXiv:2005.06520v1. DOI: https://arxiv.org/abs/2005.0652083. Karmakar S., Dasgupta C., Sastry S. Lengthscales in glass-forming liquids and related systems: areview. Reports on Progress in Physics. 2015;79(1):016601. DOI: https://doi.org/10.1088/0034-4885/79/1/01660184. De Michele C., Sciortino F., Coniglio A. Scalingin soft spheres: fragility invariance on the repulsivepotential softness. Journal of Physics: CondensedMatter. 2004;16(45): L489. DOI: https://doi.org/10.1088/0953-8984/16/45/L0185. Niblett S. P., de Souza V. K., Jack R. L., Wales D. J.Effects of random pinning on the potential energylandscape of a supercooled liquid. The Journal ofChemical Physics. 2018;149(11): 114503. DOI: https://doi.org/10.1063/1.504214086. Wolynes P. G., Lubchenko V. Structural glassesand supercooled liquids: Theory, experiment, andapplications. New York: John Wiley & Sons; 2012. 404p. DOI: https://doi.org/10.1002/978111820247087. Jack R. L., Garrahan J. P. Phase transition forquenched coupled replicas in a plaquette spin modelof glasses. Physical Review Letters. 2016;116(5): 055702.DOI: https://doi.org/10.1103/PhysRevLett.116.05570288. Habasaki J., Ueda A. Molecular dynamics studyof one-component soft-core system: thermodynamicproperties in the supercooled liquid and glassy states.The Journal of Chemical Physics. 2013;138(14): 144503.DOI: https://doi.org/10.1063/1.479988089. Bomont J. M., Hansen J. P., Pastore G. Aninvestigation of the liquid to glass transition usingintegral equations for the pair structure of coupledreplicae. J. Chem. Phys. 2014;141(17): 174505. DOI:https://doi.org/10.1063/1.490077490. Parisi G., Urbani P., Zamponi F. Theory of SimpleGlasses: Exact Solutions in Infinite Dimensions.Cambridge: Cambridge University Press; 2020. 324 p.DOI: https://doi.org/10.1017/978110812049491. Robles M., López de Haro M., Santos A., BravoYuste S. Is there a glass transition for dense hardspheresystems? The Journal of Chemical Physics.1998;108(3): 1290–1291. DOI: https://doi.org/10.1063/1.47549992. Grigera T. S., Martín-Mayor V., Parisi G.,Verrocchio P. Asymptotic aging in structural glasses.Physical Review B, 2004;70(1): 014202. DOI: https://doi.org/10.1103/PhysRevB.70.01420293. Vega C., Abascal J. L., McBride C., Bresme F.The fluid–solid equilibrium for a charged hard spheremodel revisited. The Journal of Chemical Physics.2003; 119 (2): 964–971. DOI: https://doi.org/10.1063/1.157637494. Kaneyoshi T. Surface amorphization in atransverse Ising nanowire; effects of a transverse field.Physica B: Condensed Matter. 2017;513: 87–94. DOI:https://doi.org/10.1016/j.physb.2017.03.01595. Paganini I. E., Davidchack R. L., Laird B. B.,Urrutia I. Properties of the hard-sphere fluid at a planarwall using virial series and molecular-dynamicssimulation. The Journal of Chemical Physics. 2018;149(1):014704. DOI: https://doi.org/10.1063/1.502533296. Properzi L., Santoro M., Minicucci M., Iesari F.,Ciambezi M., Nataf L., Di Cicco A. Structural evolutionmechanisms of amorphous and liquid As2 Se3 at highpressures. Physical Review B. 2016;93(21): 214205. DOI:https://doi.org/10.1103/PhysRevB.93.21420597. Sesé L. M. Computational study of the meltingfreezingtransition in the quantum hard-sphere systemfor intermediate densities. I. Thermodynamic results.The Journal of Chemical Physics. 2007;126(16): 164508.DOI: https://doi.org/10.1063/1.271852398. Shetty R., Escobedo F. A. On the application ofvirtual Gibbs ensembles to the direct simulation offluid–fluid and solid–fluid phase coexistence. TheJournal of Chemical Physics. 2002;116(18): 7957–7966.DOI: https://doi.org/10.1063/1.1467899

Design of effective microcooling systems to address the challenges of ever increasing heat flux from microdevices requires deep examination of real-time problems and has been tackled in depth. The most common (and apparently misleading) assumption while designing microcooling systems is that the heat flux generated by the device is uniform, but the reality is far from this. Detailed simulations have been performed by considering nonuniform heat load employing the configurations U, I, and Z for parallel microchannel systems with water and nanofluids as the coolants. An Intel® Core™ i7-4770 3.40 GHz quad core processor has been mimicked using heat load data retrieved from a real microprocessor with nonuniform core activity. This study clearly demonstrates that there is a nonuniform thermal load induced temperature maldistribution along with the already existent flow maldistribution induced temperature maldistribution. The suitable configuration(s) for maximum possible overall heat removal for a hot zone while maximizing the uniformity of cooling have been tabulated. An Eulerian–Lagrangian model of the nanofluids shows that such “smart” coolants not only reduce the hot spot core temperature but also the hot spot core region and thermal slip mechanisms of Brownian diffusion and thermophoresis are at the crux of this. The present work conclusively shows that high flow maldistribution leads to high thermal maldistribution, as the common prevalent notion is no longer valid and existing maldistribution can be effectively utilized to tackle specific hot spot location, making the present study important to the field.

Binary fluid mixtures are examples of complex fluids whose microstructure and flow are strongly coupled. For pairs of simple fluids, the microstructure consists of droplets or bicontinuous demixed domains and the physics is controlled by the interfaces between these domains. At continuum level, the structure is defined by a composition field whose gradients – which are steep near interfaces – drive its diffusive current. These gradients also cause thermodynamic stresses which can drive fluid flow. Fluid flow in turn advects the composition field, while thermal noise creates additional random fluxes that allow the system to explore its configuration space and move towards the Boltzmann distribution. This article introduces continuum models of binary fluids, first covering some well-studied areas such as the thermodynamics and kinetics of phase separation, and emulsion stability. We then address cases where one of the fluid components has anisotropic structure at mesoscopic scales creating nematic (or polar) liquid-crystalline order; this can be described through an additional tensor (or vector) order parameter field. We conclude by outlining a thriving area of current research, namely active emulsions, in which one of the binary components consists of living or synthetic material that is continuously converting chemical energy into mechanical work. Such activity can be modelled with judicious additional terms in the equations of motion for simple or liquid-crystalline binary fluids. Throughout, the emphasis of the article is on presenting the theoretical tools needed to address a wide range of physical phenomena. Examples include the kinetics of fluid–fluid demixing from an initially uniform state; the result of imposing a steady macroscopic shear flow on this demixing process; and the diffusive coarsening, Brownian motion and coalescence of emulsion droplets. We discuss strategies to create long-lived emulsions by adding trapped species, solid particles, or surfactants; to address the latter, we outline the theory of bending energy for interfacial films. In emulsions where one of the components is liquid-crystalline, ‘anchoring’ terms can create preferential orientation tangential or normal to the fluid–fluid interface. These allow droplets of an isotropic fluid in a liquid crystal (or vice versa) to support a variety of topological defects, which we describe, altering their interactions and stability. Addition of active terms to the equations of motion for binary simple fluids creates a model of ‘motility-induced’ phase separation, where demixing stems from self-propulsion of particles rather than their interaction forces, altering the relation between interfacial structure and fluid stress. Coupling activity to binary liquid crystal dynamics creates models of active liquid-crystalline emulsion droplets. Such droplets show various modes of locomotion, some of which strikingly resemble the swimming or crawling motions of biological cells.

ABSTRACTIndividually propulsive catalytic Janus particle swimmers are observed to self-assemble into aggregate swimmers with a wide variety of translational and rotational velocities. The trajectory for a given doublet is shown to be determined by the frozen in relative orientation of the particles. The new swimmers suggest applications as transport and mixing devices, and will allow study of the interplay between propulsion and Brownian phenomena. Furthermore this random assembly process can be controlled using external magnetic fields to orientate individual ferromagnetic swimming particles so as to favor the production of swimmers with particular desirable configurations resulting in linear trajectories. This approach also produces swimmers that can be orientated, and so “steered” by external fields.

Purpose This study aims to employ a modern numerical approach for conducting the simulations, which uses the smoothed-profile lattice Boltzmann method. Two separate distribution functions for flow and temperature fields are used to solve the Navier–Stokes equations in the most efficient manner. In addition, the Koo–Kleinstreuer–Li model is used to calculate the dynamic viscosity and thermal conductivity in the desired volume fractions, and the effect of Brownian motion is taken into consideration. Design/methodology/approach Nowadays, because of enhanced global price of oil and critical issue of global warming, a significant demand for using renewable energy exists. The solar energy is one of the most popular forms of renewable energy. The solar collector can be used to collect and trap the energy received from the sun. The present work focuses on introducing and investigating a parabolic-trough solar collector. Findings To analyze all hydrodynamic and thermal views of the solar collector, the structure of nanofluid stream, distribution of temperature, local dissipations because of flow and heat transfer, volumetric entropy production, Bejan number vs Rayleigh number and volume fraction are presented. Also, three different configurations for profile of solar receiver are designed and studied. Originality/value The originality of the present work is in using a modern numerical approach for a well-known application. Also, the effect of Brownian motion is taken into account which significantly enhances the accuracy.

Abstract This paper presents a numerical study of the magnetohydrodynamics, natural convection, and thermodynamic irreversibilities in an I-shape enclosure, filled with CuO-water nanofluid and subject to a uniform magnetic field. The lateral walls of the enclosure are maintained at different but constant temperatures, while the top and bottom surfaces are adiabatic. The Brownian motion of the nanoparticles is taken into account and an extensive parametric study is conducted. This involves the variation of Rayleigh and Hartmann numbers, and the concentration of nanoparticles and also the geometrical specifications of the enclosure. Further, the behaviors of streamlines and isotherms under varying parameters are visualized. Unlike that in other configurations, the rate of heat transfer in the I-shaped enclosure appears to be highly location dependent and convection from particular surfaces dominates the heat transfer process. It is shown that interactions between the magnetic field and natural convection currents in the investigated enclosure can lead to some peculiarities in the thermal behavior of the system. The results also demonstrate that different parts of the enclosure may feature significantly different levels of heat transfer sensitivity to the applied magnetic field. Further, the analysis of entropy generation indicates that the irreversibility of the system is a strong function of the geometrical parameters and that the variations in these parameters can minimize the total generation of entropy. This study clearly shows that ignoring the exact shape of the enclosure may result in major errors in the prediction of heat transfer and second law performances of the system.

ABSTRACTWeak non-covalent interactions between single molecules govern many aspects of microscopic biological structure and function, e.g. cell adhesion, protein folding, molecular motors and mechanical enzymes. The dynamics of a weak biomolecular bond are suitably characterized by the kinetic transport of molecular states over an effective energy landscape defined along one or more optimal reaction pathways. Motivated by earlier developments [1,2], we present a novel method to quantify subtle features of weak chemical transitions by analyzing the 3D Brownian fluctuations of a functionalized microsphere held near a reactive substrate. A weak optical-trapping potential is used to confine motion of the bead to a nanoscale domain, and to apply a controlled bias field to the interaction. Stochastic interruptions in the monitored bead dynamics report formation and release of single molecular bonds. In addition, variations in the motion of a bead linked to the substrate via a biomolecule (a protein or nucleic acid) signal conformational changes in the molecule, such as the folding/unfolding of protein domains or the unzipping of DNA. Thus, energy landscapes of complex biomolecular interactions are mapped by identifying distinct fluctuation regimes in the 3D motion of a test microsphere, and by quantifying the rates of transition between these regimes as mediated by the applied confining potential.The 3D motion of the bead is tracked using a reflection interference technique combined with high-speed video microscopy. The position of the bead is measured over 100 times per second with a lateral resolution of ∼3–5 nm and a vertical resolution of ∼1–2 nm. Crucial to the interpretation of results, a Brownian Dynamics simulation has been developed to relate the statistics of bead displacements to molecular-scale kinetics of chemical interactions and structural transitions. The experimental approach is designed to enlarge the scope of current techniques (e.g. dynamic force spectroscopy [3]) to encompass near-equilibrium forward/reverse transitions of weak-complex interactions with multiple binding configurations and more than one transition pathway.