Relaxation of suspended magnetic nanoparticles occurs via Brownian rotational diffusion of the particle as well as internal magnetization dynamics. The latter is often modeled by the stochastic Landau-Lifshitz equation, but its numerical treatment becomes prohibitively expensive in many practical applications due to a timescale separation between fast, Larmor-type precession and slow, barrier-crossing dynamics. Here, a diffusion-jump model is proposed to take advantage of the timescale separation and to approximate barrier-crossings as thermally activated jump processes that occur alongside rotational diffusion. The predictions of our diffusion-jump model are compared to reference results obtained by solving the stochastic Landau-Lifshitz equation coupled to rotational Brownian motion. Good agreement is found in the regime of high-energy barriers where Néel relaxation can be considered a thermally activated rare event. While many works in the field have neglected Néel relaxation altogether, our approach opens the possibility to efficiently include Néel relaxation also into interacting many-particle models.

We conduct an in-depth analysis of the electroclinic effect in chiral, ferroelectric liquid crystal systems that have a first-order smectic-$A^{*}$–smectic-$C^{*}$ (Sm-$A^{*}$–Sm-$C^{*}$) transition, and show that such systems can be either type I or type II. In temperature-field parameter space type-I systems exhibit a macroscopically achiral (in which the Sm-$C_M^{*}$ helical superstructure is expelled) low-tilt (LT) Sm-$C_U^{*}$–high-tilt (HT) Sm-$C_U^{*}$ critical point, which terminates a LT Sm-$C_U^{*}$–HT Sm-${}^{*}{C}_U$ first-order boundary. Notationally, Sm-$C_M^{*}$ or Sm-$C_U^{*}$ denotes the Sm-$C^{*}$ phase with or without a modulated superstructure. This boundary extends to an achiral-chiral triple point at which the macroscopically achiral LT Sm-$C_U^{*}$ and HT Sm-$C_U^{*}$ phases coexist along with the chiral Sm-$C_M^{*}$ phase. In type-II systems the critical point, triple point, and first-order boundary are replaced by a Sm-$C_M^{*}$ region, sandwiched between LT and HT Sm-$C_U^{*}$ phases, at low and high fields, respectively. Correspondingly, as the field is ramped up, the type-II system will display a reentrant Sm-$C_U^{*}$–Sm-$C_M^{*}$–Sm-$C_U^{*}$ phase sequence. Moreover, discontinuity in the tilt of the optical axis at each of the two phase transitions means the type-II system is tristable, in contrast to the bistable nature of the LT Sm-$C_U^{*}$–HT Sm-$C_U^{*}$ transition in type-I systems. Whether the system is type I or type II is determined by the ratio of two length scales, one of which is the zero-field Sm-$C^{*}$ helical pitch. The other length scale depends on the size of the discontinuity (and thus the latent heat) at the zero-field first-order Sm-$A^{*}$–Sm-$C^{*}$ transition. We note that this type-I vs type-II behavior in this ferroelectric smectic is the Ising universality class analog of type-I vs type-II behavior in XY universality class systems. Lastly, we make a complete mapping of the phase boundaries in all regions of temperature–field–enantiomeric-excess parameter space (not just near the critical point) and show that various interesting features are possible, including a multicritical point, tricritical points, and a doubly reentrant Sm-$C_U^{*}$–Sm-$C_M^{*}$–Sm-$C_U^{*}$–Sm-$C_M^{*}$ phase sequence.

We identify putatively maximally dense packings of tangent-sphere trimers with fixed bond angles ($\theta ={\theta }_0$), and contrast them to the disordered jammed states they form under quasistatic and dynamic athermal compression. Incommensurability of ${\theta }_0$ with three-dimensional (3D) close packing does not by itself inhibit formation of dense 3D crystals; all ${\theta }_0$ allow formation of crystals with ${\varphi }_{\max }\left({\theta }_0\right)>0.97{\varphi }_{\mathrm{cp}}$. Trimers are always able to arrange into periodic structures composed of close-packed bilayers or trilayers of triangular-lattice planes, separated by “gap layers” that accommodate the incommensurability. All systems have ${\varphi }_J$ significantly below the monomeric value, indicating that trimers' quenched bond-length and bond-angle constraints always act to promote jamming. ${\varphi }_J$ varies strongly with ${\theta }_0$; straight (${\theta }_0=0$) trimers minimize ${\varphi }_J$ while closed (${\theta }_0={120}^{\circ }$) trimers maximize it. Marginally jammed states of trimers with lower ${\varphi }_J\left({\theta }_0\right)$ exhibit quantifiably greater disorder, and the lower ${\varphi }_J$ for small ${\theta }_0$ is apparently caused by trimers' decreasing effective configurational freedom as they approach linearity.

Spatiotemporal dynamics of short- and long-time structural relaxation are measured experimentally as a function of packing fraction, $\varphi$, in quasi-two-dimensional colloidal supercooled liquids and glasses. The relaxation times associated with long-time dynamic heterogeneity and short-time intracage motion are found to be strongly correlated and to grow by orders of magnitude with increasing $\varphi$ toward dynamic arrest. We find that clusters of fast particles on the two timescales often overlap, and, interestingly, the distribution of minimum-spatial-separation between closest nonoverlapping clusters across the two timescales is revealed to be exponential with a decay length that increases with $\varphi$. In total, the experimental observations suggest short-time relaxation events are very often precursors to heterogeneous relaxation at longer timescales in glassy materials.

We present an iterative method to compute traveling wave exact coherent states (ECS) in Couette and Poiseuille flows starting from an initial laminar profile. The approach utilizes the resolvent operator for a two-dimensional, three-component streamwise-averaged mean and exploits the underlying physics of the self-sustaining process. A singular value decomposition of the resolvent operator is used to obtain the mode shape for a single streamwise-varying Fourier mode. The self-interaction of the single mode is computed and used to generate an updated mean velocity input to the resolvent operator. The process is repeated until a nearly neutrally stable mean flow that self-sustains is obtained, as defined by suitable convergence criteria; the results are further verified with direct numerical simulation. The approach requires the specification of only two unknown parameters: the wave speed and amplitude of the mode. It is demonstrated that within as few as three iterations, the initial one-dimensional laminar field can be transformed into three-dimensional ECS.

Phase field crystal (PFC) theory is extensively used for modeling the phase behavior, structure, thermodynamics, and other related properties of solids. PFC theory can be derived from dynamical density functional theory (DDFT) via a sequence of approximations. Here, we carefully identify all of these approximations and explain the consequences of each. One approximation that is made in standard derivations is to neglect a term of form $\mathbf{\nabla }·\left[n\mathbf{\nabla }\mathcal{L}n\right]$, where $n$ is the scaled density profile and $\mathcal{L}$ is a linear operator. We show that this term makes a significant contribution to the stability of the crystal, and that dropping this term from the theory forces another approximation, that of replacing the logarithmic term from the ideal gas contribution to the free energy with its truncated Taylor expansion, to yield a polynomial in $n$. However, the consequences of doing this are (i) the presence of an additional spinodal in the phase diagram, so the liquid is predicted first to freeze and then to melt again as the density is increased; and (ii) other periodic structures, such as stripes, are erroneously predicted to be thermodynamic equilibrium structures. In general, $\mathcal{L}$ consists of a nonlocal convolution involving the pair direct correlation function. A second approximation sometimes made in deriving PFC theory is to replace $\mathcal{L}$ with a gradient expansion involving derivatives. We show that this leads to the possibility of the density going to zero, with its logarithm going to $-\infty$ while being balanced by the fourth derivative of the density going to $+\infty$. This subtle singularity leads to solutions failing to exist above a certain value of the average density. We illustrate all of these conclusions with results for a particularly simple model two-dimensional fluid, the generalized exponential model of index 4 (GEM-4), chosen because a DDFT is known to be accurate for this model. The consequences of the subsequent PFC approximations can then be examined. These include the phase diagram being both qualitatively incorrect, in that it has a stripe phase, and quantitatively incorrect (by orders of magnitude) regarding the properties of the crystal phase. Thus, although PFC models are very successful as phenomenological models of crystallization, we find it impossible to derive the PFC as a theory for the (scaled) density distribution when starting from an accurate DDFT, without introducing spurious artifacts. However, we find that making a simple one-mode approximation for the logarithm of the density distribution $ln\rho \left(\mathit{x}\right)$ rather than for $\rho \left(\mathit{x}\right)$ is surprisingly accurate. This approach gives a tantalizing hint that accurate PFC-type theories may instead be derived as theories for the field $ln\rho \left(\mathit{x}\right)$, rather than for the density profile itself.

We derive a linear thermodynamics theory for general Markov dynamics with both steady-state and time-periodic drivings. Expressions for thermodynamic quantities, such as chemical work, heat, and entropy production are obtained in terms of equilibrium probability distribution and the drivings. The entropy production is derived as a bilinear function of thermodynamic forces and the associated fluxes. We derive explicit formulae for the Onsager coefficients and use them to verify the Onsager-Casimir reciprocal relations. Our results are illustrated on a periodically driven quantum dot in contact with two electron reservoirs and optimization protocols are discussed.

Wave-number selection in pattern-forming systems remains a long-standing puzzle in physics. Previous studies have shown that external noise is a possible mechanism for wave-number selection. We conduct an extensive numerical study of the noisy stabilized Kuramoto-Sivashinsky equation. We use a fast spectral method of integration, which enables us to investigate long-time behavior for large system sizes that could not be investigated by earlier work. We find that a state with a unique wave number has the highest probability of occurring at very long times. We also find that this state is independent of the strength of the noise and initial conditions, thus making a convincing case for the role of noise as a mechanism of state selection.

One of the most widely used methods for determination of the bending elasticity modulus of model lipid membranes is the analysis of the shape fluctuations of nearly spherical lipid vesicles. The theoretical basis of this analysis is given by Milner and Safran [Phys. Rev. A 36, 4371 (1987)]. In their theory the stretching effects are not considered. In the present study we generalized their approach including the stretching effects deduced after application of the statistical mechanics to vesicles.

We discuss the nonequilibrium statistical mechanics of a thermally driven micromachine consisting of three spheres and two harmonic springs [Y. Hosaka et al., J. Phys. Soc. Jpn. 86, 113801 (2017)]. We obtain the nonequilibrium steady state probability distribution function of such a micromachine and calculate its probability flux in the corresponding configuration space. The resulting probability flux can be expressed in terms of a frequency matrix that is used to distinguish between a nonequilibrium steady state and a thermal equilibrium state satisfying detailed balance. The frequency matrix is shown to be proportional to the temperature difference between the spheres. We obtain a linear relation between the eigenvalue of the frequency matrix and the average velocity of a thermally driven micromachine that can undergo a directed motion in a viscous fluid. This relation is consistent with the scallop theorem for a deterministic three-sphere microswimmer.

Barkley's bipartite pipe model is a continuous two-state reaction-diffusion system that models the transition to turbulence in pipes, and reproduces many qualitative features of puffs and slugs, localized turbulent structures seen during the transition. Extensions to the continuous model, including the incorporation of time delays and constraining the system to finite open domains—a trigger for convective instability—reveal additional solutions to the system, including periodic solutions and chaos unseen in the original $1+1$-dimensional system. It is found that the nature of solutions depends strongly on the size of the domain under study as well as choice of boundary conditions: on a finite domain for a particular window of parameter space, period doubling and chaos are observed.

This paper deals with the Taylor-Couette flow of shear-thinning fluids. It focuses on the first principles understanding of the influence of the viscosity stratification and the nonlinear variation of the effective viscosity $\mu$ with the shear rate $\dot{\gamma }$ on the flow structure in the Taylor-vortex flow regime. A wide gap configuration ($\eta =0.4$) is mainly considered. A weakly nonlinear analysis, using the amplitude expansion method at high order, is adopted as a first approach to study nonlinear effects. For the numerical computation, the shear-thinning behavior is described by the Carreau model. The rheological parameters are varied in a wide range. The results indicate that the flow field undergoes a significant change as shear-thinning effects increase. First, vortices are squeezed against the inner wall and the center of the patterns is shifted axially toward the radial outflow boundaries ($z=0,z/{\lambda }_z=1$). This axial shift leads to increasing concentration of vorticity at these positions. The outflow becomes stronger than the inflow and the extent of the inflow zone where the vorticity is low increases acoordingly. Nevertheless, the strength of the vortices relative to the velocity of the inner cylinder is weaker. Second, the pseudo-Nusselt number, ratio of the torque to that obtained in the laminar flow, decreases. Third, higher harmonics become more relevant and grow faster with Reynolds number. Finally, the modification of the viscosity field is described.

In 1922 Becker found an exact solution for shock waves in gases using the Navier–Stokes–Fourier constitutive equations for a Prandtl number of value 3/4 with constant transport coefficients. His analysis has been extended to study some cases where an implicit solution can be found in an exact way. In this work we consider this problem for the so-called soft-spheres model in which the viscosity and thermal conductivity are proportional to a power of the temperature $\eta ,\kappa \propto T^{\sigma }$. In particular, we give implicit exact solutions for the Maxwell model ($\sigma =1$), hard spheres ($\sigma =1/2$), and when $\sigma$ (the viscosity index) is a natural number.

The correct modeling of velocity distribution functions for particles in steady-state plasmas is a central element in the study of nuclear fusion and also in the description of space plasmas. In this paper, a statistical mechanical formalism for the description of collisionless plasmas in a steady state is presented, based solely on the application of the rules of probability and not relying on the concept of entropy. Beck and Cohen's superstatistical framework [Beck and Cohen, Physica A 322, 267 (2003)] is recovered as a limiting case, and a “microscopic” definition of inverse temperature $\beta$ is given. Nonextensivity is not invoked a priori but enters the picture only through the analysis of correlations between parts of the system.

A lattice Boltzmann method for miscible gases is presented. In this model, the standard lattice Boltzmann method is employed for each species composing the mixture. Diffusion interaction among species is taken into account by means of a force derived from kinetic theory of gases. Transport coefficients expressions are recovered from the kinetic theory. Species with dissimilar molar masses are simulated by also introducing a force. Finally, mixing dynamics is recovered as shown in different applications: an equimolar counterdiffusion case, Loschmidt's tube experiment, and an opposed jets flow simulation. Since collision is not altered, the present method can easily be introduced in any other lattice Boltzmann algorithms.

The critical behaviors of driven lattice gas models have been studied for decades as a paradigm to explore nonequilibrium phase transitions and critical phenomena. However, there exists a long-standing controversy in their universality classes. This is of paramount importance as it implies the question of whether or not a microscopic model and its mesoscopic field theory may possess different symmetries in nonequilibrium critical phenomena in contrast to their equilibrium counterparts. Here, we heat with finite rates two generic models of driven lattice gases across their respective nonequilibrium critical points into further nonequilibrium situations. Employing the theory of finite-time scaling, we are able to unambiguously discriminate the universality classes between the two models. In particular, the infinitely driven lattice gas and the randomly driven lattice gas models belong to different universality classes. These results show that finite-time scaling is effective even in nonequilibrium phase transitions.

The characterization of the formation mechanisms of amorphous solids is a large avenue for research, since understanding its non-Arrhenius behavior is challenging to overcome. In this context, we present one path toward modeling the diffusive processes in supercooled liquids near glass transition through a class of nonhomogeneous continuity equations, providing a consistent theoretical basis for the physical interpretation of its non-Arrhenius behavior. More precisely, we obtain the generalized drag and diffusion coefficients that allow us to model a wide range of non-Arrhenius processes. This provides a reliable measurement of the degree of fragility of the system and an estimation of the fragile-to-strong transition in glass-forming liquids, as well as a generalized Stokes-Einstein equation, leading to a better understanding of the classical and quantum effects on the dynamics of nonadditive stochastic systems.

Two scroll rings, placed in close proximity, can interact. When they come within one core length of each other, these waves can reconnect to form a single, large filament. In this article we show that three or more scroll rings can also reconnect when they come within the critical distance. Multiple scroll rings form larger vortices of varied filament geometry, depending on their initial sizes and placements. Different filaments, resulting from a reconnection of the same number of scroll rings placed in diverse ways, can have different lifetimes. In experiments with the Belousov-Zhabotinsky reaction and numerical simulations based on a corresponding reaction-diffusion model, we demonstrate the interaction and reconnection of multiple scroll waves and try to elucidate their lifetimes and dynamics.