We consider shock probes in a one-dimensional driven diffusive medium with nearest-neighbor Ising interaction (KLS model). Earlier studies based on an approximate mapping of the present system to an effective zero-range process concluded that the exponents characterizing the decays of several static and dynamical correlation functions of the probes depend continuously on the strength of the Ising interaction. On the contrary, our numerical simulations indicate that over a substantial range of the interaction strength, these exponents remain constant and their values are the same as in the case of no interaction (when the medium executes an ASEP). We demonstrate this by numerical studies of several dynamical correlation functions for two probes and also for a macroscopic number of probes. Our results are consistent with the expectation that the short-ranged correlations induced by the Ising interaction should not affect the large time and large distance properties of the system, implying that scaling forms remain the same as in the medium with no interactions present.

The dielectric response of liquid crystals in their nematic phase shows an acceleration of the relaxation associated with the rotation around the short molecular axis when dispersed with aerosils. However, in the isotropic phase, this acceleration is only seen for certain liquid crystalline molecules. In this paper, an associating liquid crystal (5CB) and a shorter monotropic liquid crystalline member of the same homologous series (4CB), a liquid crystal that does not show association (5NCS) and a nonassociating liquid crystal $\left(\overline{5}\text{O}5\right)$ have been studied by dielectric spectroscopy in the isotropic phase. Both 4CB and 5CB show a constant acceleration in the isotropic phase, observed over a broad temperature range. 5NCS and $\overline{5}\text{O}5$ do not show an acceleration in their isotropic phase. It seems that the disturbance of the dipole-dipole association process for the associating molecules is an important factor in the explanation of the acceleration of the relaxation in the isotropic phase.

Motor proteins are active enzyme molecules that play a crucial role in many biological processes. They transform chemical energy into mechanical work and move unidirectionally along rigid cytoskeleton filaments. Single-molecule experiments indicate that motor proteins, consisting of two motor domains, move in a hand-over-hand mechanism where each subunit changes between trailing and leading positions in alternating steps, and it is assumed that these subunits do not interact with each other. However, recent experiments on heterodimeric kinesins suggest that the motion of motor domains is not independent, but rather strongly coupled and coordinated, although the mechanism of these interactions is not known. We propose a simple discrete stochastic model to describe the dynamics of homodimeric and heterodimeric two-headed motor proteins. It is argued that interactions between motor domains modify original free energy landscapes for each motor subunit, while motor proteins still move via the hand-over-hand mechanism but with different transition rates specified by the new free energy profiles. Our calculations of biophysical properties agree with experimental observations. Several ways to test the theoretical model are proposed.

Meiosis is the specialized cell division required in sexual reproduction. During its early stages, in the mother cell nucleus, homologous chromosomes recognize each other and colocalize in a crucial step that remains one of the most mysterious of meiosis. Starting from recent discoveries on the system molecular components and interactions, we discuss a statistical mechanics model of chromosome early pairing. Binding molecules mediate long-distance interaction of special DNA recognition sequences and, if their concentration exceeds a critical threshold, they induce a spontaneous colocalization transition of chromosomes, otherwise independently diffusing.

We present a model for predicting the transport of biofunctional magnetic nanoparticles in a passive magnetophoretic system that consists of a fluidic chamber positioned above a rare-earth magnet. The model is based on a drift-diffusion equation that governs the particle concentration in the chamber. We solve this equation numerically using the finite volume method. We apply the model to the magnetofection process wherein the magnetic force produced by the magnet attracts magnetic carrier particles with surface-bound gene vectors toward the bottom of the chamber for transfection with target cells. We study particle transport and accumulation as a function of key variables. Our analysis indicates that the particles are magnetically focused toward the center of the chamber during transport, and that the rate of accumulation at the base can be enhanced using larger particles and/or by reducing the spacing between the magnet and the chamber. The model provides insight into the physics of particle transport at the nanoscale and enables rapid parametric analysis of particle accumulation, which is useful for optimizing novel magnetofection systems.

Ensemble averaging of advection-dispersion equations describing transport of a passive scalar in incompressible random velocity fields requires a closure approximation. Commonly used approaches, such as the direct interaction approximation and large-eddy simulations as well as equivalent renormalization schemes, employ so-called two-point (or one-loop) closures. These approaches have proven to be adequate for transport in zero-mean (unbiased) time-dependent random velocity fields with increasing accuracy for decreasing temporal coherence. In the opposite limit of steady velocity fields with finite bias, however, these schemes fail to predict effective transport properties both quantitatively and qualitatively, leading to an obvious inconsistency for transverse dispersion in two spatial dimensions. For this case, two-point closures predict that macroscopic transverse dispersion increases as the square root of the disorder variance while it has been proven rigorously that there is no disorder-induced contribution to macroscopic transverse dispersion for purely advective transport. Furthermore, two-point closures significantly underestimate the disorder-induced contribution to longitudinal dispersion. We derive a four-point closure for stochastically averaged transport equations that goes beyond classical one-loop schemes and demonstrate that it is exact for transverse dispersion and correctly predicts an increase of the longitudinal disorder-induced dispersion coefficient with the square of the variance of the strong disorder. The predicted values of asymptotic longitudinal dispersion coefficients are consistent with those obtained via Monte Carlo random walk simulations.

All transducers used in biological sensing suffer from fouling resulting from nonspecific binding of protein molecules to the device surface. The acoustic-streaming phenomenon, which results from the fluid motion induced by high-intensity sound waves, can be used to remove these nonspecifically bound proteins to allow more accurate determinations and reuse of these devices. We present a computational and experimental study of the acoustic-streaming phenomenon induced by surface acoustic waves.A coupled-field fluid-structure interaction (FSI) model of a surface-acoustic-wave (SAW) device based on a micrometer-sized piezoelectric substrate $\left(YZ{\text{-LiNbO}}_3\right)$ in contact with a liquid loading was developed to study the surface-acoustic-wave interaction with fluid loading. The fluid domain was modeled using the Navier-Stokes equation; the arbitrary Lagrangian-Eulerian approach was employed to handle the mesh distortions arising from the motion of the solid substrate. The fluid-solid coupling was established by maintaining stress and displacement continuity at the fluid-structure interface. A transient analysis was carried out by applying a time-varying voltage to the transmitter interdigital transducer (IDT) fingers. Simulation results predict strong coupling of ultrasonic surface waves on the piezoelectric substrate with the thin liquid layer causing wave mode conversion from Rayleigh to leaky SAWs, which leads to acoustic streaming. The transient solutions generated from the FSI model were utilized to predict trends in acoustic-streaming velocity for varying design parameters such as voltage intensity, device frequency, fluid viscosity, and density. The induced streaming velocities typically vary from $1\mu \text{m}/\text{s}$ to 1 cm/s, with the exact values dictated by the device operating conditions as well as fluid properties. Additionally, the model predictions were utilized to compute the various interaction forces involved and thereby identify the possible mechanisms for removal of nonspecifically bound proteins. Our study indicates that the SAW body force overcomes the adhesive forces of the fouling proteins to the device surface and the fluid-induced drag and lift forces prevent their reattachment. The streaming velocity fields computed using the finite-element model in conjunction with the proposed mechanism were used to identify the conditions leading to improved removal efficiency. Predictions of the model are in good agreement with those of simple analytical theories as well as the experimentally observed trends of nonspecific protein removal in typical SAW biosensing operations.

Numerical results are presented for hydrodynamic instabilities surrounding the parameter space of sonoluminescing bubbles. The Rayleigh-Taylor instability is shown to limit bubble oscillations only in a small region near a border at small radii in noisy environments. Also, two different noise-induced instabilities by secondary collapses are identified. The reason for period-doubled, anisotropic emission is found to be the coupling of radial and surface oscillations. Furthermore, an approximate universal border is shown to exist above which the bubble is destroyed by the parametric instability. The results are compared to experimental results from several publications using different experimental setups.

We study numerically the deformation of sessile dielectric drops immersed in a second fluid when submitted to the optical radiation pressure of a continuous Gaussian laser wave. Both drop stretching and drop squeezing are investigated at steady state where capillary effects balance the optical radiation pressure. A boundary integral method is implemented to solve the axisymmetric Stokes flow in the two fluids. In the stretching case, we find that the drop shape goes from prolate to near-conical for increasing optical radiation pressure whatever the drop to beam radius ratio and the refractive index contrast between the two fluids. The semiangle of the cone at equilibrium decreases with the drop to beam radius ratio and is weakly influenced by the index contrast. Above a threshold value of the radiation pressure, these “optical cones” become unstable and a disruption is observed. Conversely, when optically squeezed, the drop shifts from an oblate to a concave shape leading to the formation of a stable “optical torus.” These findings extend the electrohydrodynamics approach of drop deformation to the much less investigated “optical domain” and reveal the openings offered by laser waves to actively manipulate droplets at the micrometer scale.

We show how the capillary filling of microchannels is affected by posts or ridges on the sides of the channels. Ridges perpendicular to the flow direction introduce contact line pinning, which slows, or sometimes prevents, filling, whereas ridges parallel to the flow provide extra surface that may enhance filling. Patterning the microchannel surface with square posts has little effect on the ability of a channel to fill for equilibrium contact angle ${\theta }_e\lesssim 30°$. For ${\theta }_e\gtrsim 60°$, however, even a small number of posts can pin the advancing liquid front.

Topological phase space disconnection has been recently found to be a general phenomenon in many-body spin system with anisotropic interaction. We show that the power law divergence of magnetic reversal time at the energy signaling such disconnection is generic for long-range interacting systems with an exponent proportional to the number of particles. We also study the modifications induced putting the system in contact with a thermal bath. Using the canonical formalism we analyze the magnetic reversal times at any temperature. Moreover, due to the divergence of reversal time at the energy disconnection threshold we can recover, using saddle point approximation, a simple exponential dependence on the inverse temperature showing the explicit relevance of the energy disconnection threshold for finite many-body interacting systems at finite temperature. This sets a general framework to understand the emergence of ferromagnetism in finite magnetic systems starting from microscopic models without phenomenological on-site barriers.

We present the exact solution of the one-dimensional extended Hubbard model in the atomic limit within the Green’s function and equations of motion formalism. We provide a comprehensive and systematic analysis of the model by considering all the relevant response and correlation functions as well as thermodynamic quantities in the whole parameters space. At zero temperature we identify four phases in the plane $\left(U,n\right)$ ($U$ is the on-site potential and $n$ is the filling) and relative phase transitions as well as different types of charge ordering. These features are endorsed by investigating at $T=0$ the chemical potential and pertinent local correlators, the particle and double occupancy correlation functions, the entropy, and by studying the behavior in the limit $T\to 0$ of the charge and spin susceptibilities. A detailed study of the thermodynamic quantities is also presented at finite temperature. This study evidences that a finite-range order persists for a wide range of the temperature, as shown by the behavior of the correlation functions and by the two-peak structure exhibited by the charge susceptibility and by the entropy. Moreover, the equations of motion formalism, together with the use of composite operators, allows us to exactly determine the set of elementary excitations. As a result, the density of states can be determined and a detailed analysis of the specific heat allows for identifying the excitations and for ascribing its two-peak structure to a redistribution of the charge density.

A square-lattice model for the formation of secondary structures in proteins, the hydrogen-bonding model, extended to include the effects of solvent quality, is examined in the framework of the Bethe approximation.

Here we report dynamics of 1,3-butadiene molecules adsorbed in Na-Y zeolite as studied using molecular dynamics (MD) simulations. The results showed that the translational motion of the guest molecule exists in three different time scales one of which matches well with the quasielastic neutron scattering (QENS) measurement reported earlier. The translational motion in the component, which has been measured by QENS, is found to occur through discrete jumps, in agreement with the analysis of the experiments. The diffusion coefficients obtained from the correlation functions are compared to those obtained earlier for other hydrocarbons in Na-Y zeolite from MD simulation studies. The diffusion of 1,3-butadiene is found to be slower than that of acetylene but faster than that of propane. The rotational motion is found to be isotropic in nature. Rotational diffusion coefficient of 1,3-butadiene is found to be smaller than that of propane in Na-Y as expected due to the larger inertia of the former.

We introduce the ideal Gaussian glass-forming system as a model to describe the thermodynamics and dynamics of supercooled liquids on a local scale in terms of the properties of the potential energy landscape (PEL). The first ingredient is the Gaussian distribution of inherent structures, the second a specific relation between energy and mobility. This model is compatible with general considerations as well as with several computer simulations on atomic computer glass formers. Important observables such as diffusion constants, structural relaxation times, and kinetic as well as thermodynamic fragilities can be calculated analytically. In this way it becomes possible to identify a relevant PEL parameter determining the kinetic fragility. Several experimental observations can be reproduced. The remaining discrepancies in the experiment can be qualitatively traced back to the difference between small and large systems.

In large-scale neural networks in the brain the emergence of global behavioral patterns, manifested by electroencephalographic activity, is driven by the self-organization of local neuronal groups into synchronously functioning ensembles. However, the laws governing such macrobehavior and its disturbances, in particular epileptic seizures, are poorly understood. Here we use a mean-field population network model to describe a state of baseline physiological activity and the transition from the baseline state to rhythmic epileptiform activity. We describe principles which explain how this rhythmic activity arises in the form of spatially uniform self-sustained synchronous oscillations. In addition, we show how the rate of migration of the leading edge of the synchronous oscillations can be theoretically predicted, and compare the accuracy of this prediction with that measured experimentally using multichannel electrocorticographic recordings obtained from a human subject experiencing epileptic seizures. The comparison shows that the experimentally measured rate of migration of the leading edge of synchronous oscillations is within the theoretically predicted range of values. Computer simulations have been performed to investigate the interactions between different regions of the brain and to show how organization in one spatial region can promote or inhibit organization in another. Our theoretical predictions are also consistent with the results of functional magnetic resonance imaging (fMRI), in particular with observations that lower-frequency electroencephalographic (EEG) rhythms entrain larger areas of the brain than higher-frequency rhythms. These findings advance the understanding of functional behavior of interconnected populations and might have implications for the analysis of diverse classes of networks.

The fractional reaction-diffusion system is investigated. The linear stage of the stability is studied for a two-component system with a different order of fractional derivatives for activator and inhibitor. Three different cases are considered: the derivative order for an activator is greater than that for an inhibitor, the inhibitor order derivative is greater than the activator one, and the orders of time derivatives are comparable. Based on the stability analysis, computer simulation of a Bonhoeffer–van der Pol type reaction-diffusion system with fractional time derivatives is performed, and the diversity of the pattern formation phenomena is shown.

We investigate the structure and dynamics of biphasic colloidal mixtures composed of coexisting attractive and repulsive microspheres by confocal microscopy. Attractive gels formed in the presence of repulsive microspheres are more spatially homogeneous and, on average, are both more locally tenuous and have fewer large voids than their unary counterparts. The repulsive microspheres within these mixtures display heterogeneous dynamics, with some species exhibiting freely diffusive Brownian motion while others are trapped within the gel network during aggregation.

We investigate the role of the boundary in the symmetric simple exclusion process with competing nonlocal and local hopping events. With open boundaries, the system undergoes a first-order phase transition from a finite density phase to an empty road phase as the nonlocal hopping rate increases. Using a cluster stability analysis, we determine the location of such an abrupt nonequilibrium phase transition, which agrees well with numerical results. Our cluster analysis provides physical insight into the mechanism behind this transition. We also explain why the transition becomes discontinuous in contrast to the case with periodic boundary conditions, in which the continuous phase transition has been observed.

An intruder to a group of identical beads contained in a circular plate which is subjected to a circular vibration will trace approximately a cyclic spiral. The trajectory is a result of both migration and rotation. The intruder migrates in the radial direction while rotating with a constant speed with respect to the center of mass of the whole group of beads. The rotation velocity is due to friction between the beads and the container wall and determined by the vibration amplitude and the number of beads. The migration direction is dependent on the size ratio and mass ratio of the intruder to the background beads. The migration speed is constant for the outward migration, but decreases gradually when the intruder migrates toward the center of mass of the whole cluster for the inward case.