We consider a generalized Langevin equation that can be used to describe thermal motion of a tracer in a viscoelastic medium by accounting for inertial and hydrodynamic effects at short times, subdiffusive scaling at intermediate times, and eventual optical trapping at long times. We derive a Laplace-type integral representation for the linear response function that governs the diffusive dynamics. This representation is particularly well suited for rapid numerical computation and theoretical analysis. In particular, we deduce explicit formulas for the mean and variance of the time averaged (TA) mean square displacement (MSD) and velocity autocorrelation function (VACF). The asymptotic behavior of the TA MSD and TA VACF is investigated at different time scales. Some biophysical and microrheological applications are discussed, with an emphasis on the statistical analysis of optical tweezers' single-particle tracking experiments in polymer networks and living cells.

A key feature of nonequilibrium thermodynamics is the Markovian, deterministic relaxation of coarse observables such as, for example, the temperature difference between two macroscopic objects which evolves independently of almost all details of the initial state. We demonstrate that the unitary dynamics for moderately sized spin-1/2 systems may yield the same type of relaxation dynamics for a given magnetization difference. This observation might contribute to the understanding of the emergence of thermodynamics within closed quantum systems.

We study experimentally the distributions of force chains in granular materials, which are slightly different in sheared systems compared to isotropically compressed systems, especially at the tails, reflecting the shear-induced anisotropy of the contact force network. Ignoring this anisotropy allows us to establish a relationship between the mean force-chain length $L_m$ and the average contact number $Z$ of particles for both systems, independent of the system size. We also demonstrate that force-chain distributions are not related to the exponential-like distributions of stresses.

We show how the inclusions of the nanoparticles or the clusters of nanoparticles in the liquid-crystalline smectic-$A$ phase lead to layer deformations and may create a tilt in their vicinity, thus inducing locally a smectic-$A$–smectic-$C$ transition. We have studied a freestanding film of “de Vries” compound, which exhibits the smectic-$A$–smectic-$C$ transition without layer shrinkage, mixed with functionalized gold nanoparticles. The tilt induced by nanoparticle clusters, which decorate the edge dislocations, has been observed in the smectic-$A$ phase. The tilt of liquid-crystal molecules near nanoparticles is a consequence of interaction of liquid-crystalline molecules with the surface of nanoparticles. The observed tilt may prove the concept of existence of a disordered tilt in the smectic-$A$ phase of de Vries compounds. The tilt distribution near nanoparticles is discussed using both the smectic-$A$ elasticity and local smectic-$A$–smectic-$C$ transition.

We investigate the effect of anisotropic lattice deformation on the Kerr coefficient of polymer-stabilized blue-phase liquid crystals (PSBP-LCs). PSBPs with orthorhombic and tetragonal symmetry were prepared by polymer-stabilizing a blue-phase liquid crystal under electrostriction. Both orthorhombic and tetragonal PSBPs showed smaller Kerr coefficients than the cubic PSBP, despite an increase in the unit cell volume caused by the elongation of the lattice along the direction of light propagation. Our results indicate that the Kerr coefficient of PSBPs is not determined simply by the volume of the unit lattice but by the lattice size perpendicular to the direction of light propagation.

Protein translation is one of the most important processes in cell life, but despite being well-understood biochemically, the implications of its intrinsic stochastic nature have not been fully elucidated. In this paper we develop a microscopic and stochastic model which describes a crucial step in protein translation, namely the binding of the tRNA to the ribosome. Our model explicitly takes into consideration tRNA recharging dynamics, spatial inhomogeneity, and stochastic fluctuations in the number of charged tRNAs around the ribosome. By analyzing this nonequilibrium system we are able to derive the statistical distribution of the times needed by the tRNAs to bind to the ribosome, and to show that it deviates from an exponential due to the coupling between the fluctuations of charged and uncharged populations of tRNA.

Alternative splicing (AS) is a fundamental process during gene expression and has been found to be ubiquitous in eukaryotes. However, how AS impacts gene expression levels both quantitatively and qualitatively remains to be fully explored. Here, we analyze two common models of gene expression, each incorporating a simple splice mechanism that a pre-mRNA is spliced into two mature mRNA isoforms in a probabilistic manner. In the constitutive expression case, we show that the steady-state molecular numbers of two mature mRNA isoforms follow mutually independent Poisson distributions. In the bursting expression case, we demonstrate that the tail decay of the steady-state distribution for both mature mRNA isoforms that in general are not mutually independent can be characterized by the product of mean burst size and splicing probability. In both cases, we find that AS can efficiently modulate both the variability (measured by variance) and the noise level of the total mature mRNA, and in particular, the latter is always lower than the noise level of the pre-mRNA, implying that AS always reduces the noise. These results altogether reveal that AS is a mechanism of efficiently controlling the gene expression noise.

The ultrasonic sound velocities of cross-linked orthorhombic hen egg-white lysozyme (HEWL) crystals, including a large amount of water in the crystal, were measured using an ultrasonic pulse-echo method. As a result, seven elastic constants of orthorhombic crystals were observed to be $C_{11}$ = 5.24 GPa, $C_{22}$ = 4.87 GPa, $C_{12}$ = 4.02 GPa, $C_{33}$ = 5.23 GPa, $C_{44}$ = 0.30 GPa, $C_{55}$ = 0.40 GPa, and $C_{66}$ = 0.43 GPa, respectively. However, $C_{13}$ and $C_{23}$ could not be observed because the suitable crystal planes could not be cut from bulk crystals. We conclude that the observed elastic constants of the cross-linked crystals are coincident with those of the intrinsic crystals without cross-linking. Moreover, the characteristics of the elastic constants in orthorhombic HEWL crystals are due to the fact that the shear elastic constants, $C_{44}$, $C_{55}$, and $C_{66}$, are softer than in tetragonal crystals. That is, the shear components, $C_{44}$, $C_{55}$, and $C_{66}$, are one half of those of the tetragonal crystals.

Observation of phenotypic diversity in a population of genetically identical cells is often linked to the stochastic nature of chemical reactions involved in gene regulatory networks. We investigate the distribution of population-averaged gene expression levels as a function of population, or sample, size for several stochastic gene expression models to find out to what extent population-averaged quantities reflect the underlying mechanism of gene expression. We consider three basic gene regulation networks corresponding to transcription with and without gene state switching and translation. Using analytical expressions for the probability generating function of observables and large deviation theory, we calculate the distribution and first two moments of the population-averaged mRNA and protein levels as a function of model parameters, population size, and number of measurements contained in a data set. We validate our results using stochastic simulations also report exact results on the asymptotic properties of population averages which show qualitative differences among different models.

The time evolution equation of motion and shape are derived for a self-propelled droplet driven by a chemical reaction. The coupling between the chemical reaction and motion makes an inhomogeneous concentration distribution as well as a surrounding flow leading to the instability of a stationary state. The instability results in spontaneous motion by which the shape of the droplet deforms from a sphere. We found that the self-propelled droplet is elongated perpendicular to the direction of motion and is characterized as a pusher.

The present work studies the influence of nonlocal spatial coupling on the existence of localized structures in one-dimensional extended systems. We consider systems described by a real field with a nonlocal coupling that has a linear dependence on the field. Leveraging spatial dynamics we provide a general framework to understand the effect of the nonlocality on the shape of the fronts connecting two stable states. In particular we show that nonlocal terms can induce spatial oscillations in the front tails, allowing for the creation of localized structures, that emerge from pinning between two fronts. In parameter space the region where fronts are oscillatory is limited by three transitions: the modulational instability of the homogeneous state, the Belyakov-Devaney transition in which monotonic fronts acquire spatial oscillations with infinite wavelength, and a crossover in which monotonically decaying fronts develop spatial oscillations with a finite wavelength. We show how these transitions are organized by codimension 2 and 3 points and illustrate how by changing the parameters of the nonlocal coupling it is possible to bring the system into the region where localized structures can be formed.

We study the influence of a linear nonlocal spatial coupling on the interaction of fronts connecting two equivalent stable states in the prototypical 1-dimensional real Ginzburg-Landau equation. While for local coupling the fronts are always monotonic and therefore the dynamical behavior leads to coarsening and the annihilation of pairs of fronts, nonlocal terms can induce spatial oscillations in the front, allowing for the creation of localized structures, emerging from pinning between two fronts. We show this for three different nonlocal influence kernels. The first two, mod-exponential and Gaussian, are positive definite and decay exponentially or faster, while the third one, a Mexican-hat kernel, is not positive definite.

We study the effect of a constant magnetic field on the dynamics of a system that may present Fermi acceleration (FA). The model in consideration is the nondissipative annular billiard with breathing boundaries. There is a field threshold, from which the mechanism of FA can be deactivated. The presence of the magnetic field curves the particle trajectories and for some combinations of the parameters FA is totally, and nontrivially, suppressed without considering any kind of dissipation.

The classical nonlinear dynamics of a dilute gas of rubidium atoms in an optical lattice is studied for a range of polarizations of the laser beams forming the lattice. The dynamics ranges from integrable to chaotic, and mechanisms leading to the onset of chaos in the lattice are described.

We study the collective dynamics of interacting deformable self-propelled particles whose migration velocity increases with increasing local density. In two-dimensional numerical simulations of this system, the local density dependence on migration velocity leads to traveling bands similar to those previously reported for Vicsek-type models. We show that a pair of straight bands moving in opposite directions survives a head-on collision. Although traveling bands also appear in systems of constant migration velocity subjected to random noise, they are found to be unstable in a head-on collision.

This study investigates drop impingement on highly wetting porous films and papers. Experiments reveal previously unexplored impingement modes on porous surfaces designated as necking, spreading, and jetting. Dimensional analysis yields a nondimensional parameter, denoted the Washburn-Reynolds number, relating droplet kinetic energy and surface energy. The impingement modes correlate with Washburn-Reynolds number variations spanning four orders of magnitude and a corresponding energy conservation analysis for droplet spreading shows good agreement with the experimental results. The simple scaling laws presented will inform the investigation of dynamic interactions between porous surfaces and liquid drops.

The development of the viscous fingering instability in Hele-Shaw cells has great practical and scientific importance. Recently, researchers have proposed different strategies to control the number of interfacial fingering structures, or to minimize as much as possible the amplitude of interfacial disturbances. Most existing studies address the situation in which an inviscid fluid displaces a viscous Newtonian fluid. In this work, we report on controlling and minimizing protocols considering the situation in which the displaced fluid is a non-Newtonian, power-law fluid. The necessary changes on the controlling schemes due to the shear-thinning and shear thickening nature of the displaced fluid are calculated analytically and discussed.

We report the results of a study of the role of prescribed geometrical structures on the front of a target in determining the energy and spatial distribution of relativistic laser-plasma electrons. Our three-dimensional particle-in-cell simulation studies apply to short-pulse, high-intensity laser pulses, and indicate that a judicious choice of target front-surface geometry provides the realistic possibility of greatly enhancing the yield of high-energy electrons while simultaneously confining the emission to narrow ($<$$5^{\circ }$) angular cones.

Acoustic streaming underpins an exciting range of fluid manipulation phenomena of rapidly growing significance in microfluidics, where the streaming often assumes the form of a steady, laminar jet emanating from the device surface, driven by the attenuation of acoustic energy within the beam of sound propagating through the liquid. The frequencies used to drive such phenomena are often chosen ad hoc to accommodate fabrication and material issues. In this work, we seek a better understanding of the effects of sound frequency and power on acoustic streaming. We present and, using surface acoustic waves, experimentally verify a laminar jet model that is based on the turbulent jet model of Lighthill, which is appropriate for acoustic streaming seen at micro- to nanoscales, between 20 and 936 MHz and over a broad range of input power. Our model eliminates the critically problematic acoustic source singularity present in Lighthill's model, replacing it with a finite emission area and enabling determination of the streaming velocity close to the source. At high acoustic power $P$ (and hence high jet Reynolds numbers ${\mathrm{Re}}_{\mathrm{J}}$ associated with fast streaming), the laminar jet model predicts a one-half power dependence ($U\sim P^{1/2}\sim$ ${\mathrm{Re}}_{\mathrm{J}}$) similar to the turbulent jet model. However, the laminar model may also be applied to jets produced at low powers—and hence low jet Reynolds numbers ${\mathrm{Re}}_{\mathrm{J}}$—where a linear relationship between the beam power and streaming velocity exists: $U\sim P\sim {\mathrm{Re}}_{\mathrm{J}}^2$. The ability of the laminar jet model to predict the acoustic streaming behavior across a broad range of frequencies and power provides a useful tool in the analysis of microfluidics devices, explaining peculiar observations made by several researchers in the literature. In particular, by elucidating the effects of frequency on the scale of acoustically driven flows, we show that the choice of frequency is a vitally important consideration in the design of small-scale devices employing acoustic streaming for microfluidics.