Bose-Einstein condensation (BEC) of a noninteracting Bose gas of $N$ particles in a two-dimensional box with Dirichlet boundary conditions is studied. Confirming previous work, we find that BEC occurs at finite $N$ at low temperatures $T$ without the occurrence of a phase transition. The conventionally-defined transition temperature $T_{\mathrm{E}}$ for an infinite three-dimensional (3D) system is shown to correspond in a 2D system with finite $N$ to a crossover temperature between a slow and rapid increase in the fractional boson occupation $N_0/N$ of the ground state with decreasing $T$. We further show that $T_{\mathrm{E}}\sim 1/logN$ at fixed area per boson, so in the thermodynamic limit there is no significant BEC in 2D at finite $T$. Thus, paradoxically, BEC only occurs in 2D at finite $N$ with no phase transition associated with it. Calculations of thermodynamic properties versus $T$ and area $A$ are presented, including Helmholtz free energy, entropy $S$, pressure $p$, ratio of $p$ to the energy density $U/A$, heat capacity at constant volume (area) $C_{\mathrm{V}}$ and at constant pressure $C_{\mathrm{p}}$, isothermal compressibility ${\kappa }_{\mathrm{T}}$ and thermal expansion coefficient ${\alpha }_{\mathrm{p}}$, obtained using both the grand-canonical ensemble (GCE) and canonical ensemble (CE) formalisms. The GCE formalism gives acceptable predictions for $S, p, p/(U/A), {\kappa }_{\mathrm{T}}$ and ${\alpha }_{\mathrm{p}}$ at large $N, T$ and $A$ but fails for smaller values of these three parameters for which BEC becomes significant, whereas the CE formalism gives accurate results for all thermodynamic properties of finite systems even at low $T$ and/or $A$ where BEC occurs.

The motion of Brownian particles when temperature is spatially dependent is studied by stochastic simulations and theoretical analysis. Nonequilibrium steady probability distributions $P_{st}(z,v)$ for both underdamped and overdamped regimes are analyzed. The existence of local kinetic energy equipartition theorem is also discussed. The transition between both regimes is characterized by a dimensionless friction parameter. This study is applied to three physical systems of colloidal particles.

We study wave propagation in strongly nonlinear one-dimensional diatomic granular crystals under an impact load. Depending on the mass ratio of the “light” to “heavy” beads, this system exhibits rich wave dynamics from highly localized traveling waves to highly dispersive waves featuring strong attenuation. We demonstrate experimentally the nonlinear resonant and antiresonant interactions of particles, and we verify that the nonlinear resonance results in strong wave attenuation, leading to highly efficient nonlinear energy cascading without relying on material damping. In this process, mechanical energy is transferred from low to high frequencies, while propagating waves emerge in both ordered and chaotic waveforms via a distinctive spatial cascading. This energy transfer mechanism from lower to higher frequencies and wave numbers is of particular significance toward the design of novel nonlinear acoustic metamaterials with inherently passive energy redistribution properties.

Walls in discrete element method simulations of granular flows are sometimes modeled as a closely packed monolayer of fixed particles, resulting in a rough wall rather than a geometrically smooth wall. An implicit assumption is that the resulting rough wall differs from a smooth wall only locally at the particle scale. Here we test this assumption by considering the impact of the wall roughness at the periphery of the flowing layer on the flow of monodisperse particles in a rotating spherical tumbler. We find that varying the wall roughness significantly alters average particle trajectories even far from the wall. Rough walls induce greater poleward axial drift of particles near the flowing layer surface but decrease the curvature of the trajectories. Increasing the volume fill level in the tumbler has little effect on the axial drift for rough walls but increases the drift while reducing curvature of the particle trajectories for smooth walls. The mechanism for these effects is related to the degree of local slip at the bounding wall, which alters the flowing layer thickness near the walls, affecting the particle trajectories even far from the walls near the equator of the tumbler. Thus, the proper choice of wall conditions is important in the accurate simulation of granular flows, even far from the bounding wall.

We focus on the probability distribution function (PDF) $P(\mathrm{\Delta }\gamma ;\gamma )$ where $\mathrm{\Delta }\gamma$ are the measured strain intervals between plastic events in a athermal strained amorphous solids, and $\gamma$ measures the accumulated strain. The tail of this distribution as $\mathrm{\Delta }\gamma \to 0$ (in the thermodynamic limit) scales like $\mathrm{\Delta }{\gamma }^{\eta }$. The exponent $\eta$ is related via scaling relations to the tail of the PDF of the eigenvalues of the plastic modes of the Hessian matrix $P\left(\lambda \right)$ which scales like ${\lambda }^{\theta }, \eta =(\theta -1)/2$. The numerical values of $\eta$ or $\theta$ can be determined easily in the unstrained material and in the yielded state of plastic flow. Special care is called for in the determination of these exponents between these states as $\gamma$ increases. Determining the $\gamma$ dependence of the PDF $P(\mathrm{\Delta }\gamma ;\gamma )$ can shed important light on plasticity and yield. We conclude that the PDF's of both $\mathrm{\Delta }\gamma$ and $\lambda$ are not continuous functions of $\gamma$. In slowly quenched amorphous solids they undergo two discontinuous transitions, first at $\gamma =0^{+}$ and then at the yield point $\gamma ={\gamma }_{{}_{\mathrm{Y}}}$ to plastic flow. In quickly quenched amorphous solids the second transition is smeared out due to the nonexisting stress peak before yield. The nature of these transitions and scaling relations with the system size dependence of $\langle \mathrm{\Delta }\gamma \rangle$ are discussed.

We investigate through numerical simulations the dynamics of a neo-Hookean elastic prolate spheroid suspended in a Newtonian fluid under shear flow. Both initial orientations of the particle within and outside the shear plane and both unbounded and confined flow geometries are considered. In unbounded flow, when the particle starts on the shear plane, two stable regimes of motion are found, i.e., trembling, where the particle shape periodically elongates and compresses in the shear plane and the angle between its major semiaxis and the flow direction oscillates around a positive mean value, and tumbling, where the particle shape periodically changes and its major axis performs complete revolutions around the vorticity axis. When the particle is initially oriented out of the shear plane, more complex dynamics arise. Geometric confinement of the particle between the moving walls also influences its deformation and regime of motion. In addition, when the particle is initially located in an asymmetric position with respect to the moving walls, particle lateral migration is detected. The effects on the particle dynamics of the geometric and physical parameters that rule the system are investigated.

We introduce a simple model for a biaxial nematic liquid crystal. This consists of hard spheroids that can switch shape between prolate (rodlike) and oblate (platelike) subject to an energy penalty $\mathrm{\Delta }\epsilon$. The spheroids are approximated as hard Gaussian overlap particles and are treated at the level of Onsager's second-virial description. We use both bifurcation analysis and a numerical minimization of the free energy to show that, for additive particle shapes, (i) there is no stable biaxial phase even for $\mathrm{\Delta }\epsilon =0$ (although there is a metastable biaxial phase in the same density range as the stable uniaxial phase) and (ii) the isotropic-to-nematic transition is into either one of two degenerate uniaxial phases, rod rich or plate rich. We confirm that even a small amount of shape nonadditivity may stabilize the biaxial nematic phase.

The emergence of new techniques for the fabrication of nematic droplets with nontrivial topology provides new routes for the assembly of responsive devices. Here we explore some of the properties of nematic droplets on fibers, which constitute the basic units of a type of device that is able to respond to external stimuli, including the detection of gases. We perform a numerical study of spherical nematic droplets on fibers. We analyze the equilibrium textures for homogeneous and hybrid boundary conditions and find that in some cases the nematic avoids the nucleation of topological defects, which would provide a different optical response. We consider in detail a homeotropic nematic droplet wrapped around a fiber with planar anchoring. We investigate the effect of an electric field on the texture of this droplet. In the presence of a dc field, the system undergoes an orientational transition above a given threshold $E_c$, for which a ring defect is transformed into a figure-eight defect. We also consider ac fields, at high and low frequencies, and find that the textures are similar to those observed for static fields, in contrast with recently reported experiments.

Systems of many interacting components, as found in physics, biology, infrastructure, and the social sciences, are often modeled by simple networks of nodes and edges. The real-world systems frequently confront outside intervention or internal damage whose impact must be predicted or minimized, and such perturbations are then mimicked in the models by altering nodes or edges. This leads to the broad issue of how to best quantify changes in a model network after some type of perturbation. In the case of node removal there are many centrality metrics which associate a scalar quantity with the removed node, but it can be difficult to associate the quantities with some intuitive aspect of physical behavior in the network. This presents a serious hurdle to the application of network theory: real-world utility networks are rarely altered according to theoretic principles unless the kinetic impact on the network's users are fully appreciated beforehand. In pursuit of a kinetically interpretable centrality score, we discuss the f-score, or frustration score. Each f-score quantifies whether a selected node accelerates or inhibits global mean first passage times to a second, independently selected target node. We show that this is a natural way of revealing the dynamical importance of a node in some networks. After discussing merits of the f-score metric, we combine spectral and Laplacian matrix theory in order to quickly approximate the exact f-score values, which can otherwise be expensive to compute. Following tests on both synthetic and real medium-sized networks, we report f-score runtime improvements over exact brute force approaches in the range of 0 to $400\%$ with low error ($<3\%$).

For wall turbulence, moments of velocity fluctuations are known to be logarithmic functions of the height from the wall. This logarithmic scaling is due to the existence of a characteristic velocity and to the nonexistence of any characteristic height in the range of the scaling. By using the mathematics of random variables, we obtain its necessary and sufficient conditions. They are compared with characteristics of a phenomenological model of eddies attached to the wall and also with those of the logarithmic scaling of the mean velocity.

Decaying Hall magnetohydrodynamic (HMHD) turbulence is studied using three-dimensional (3D) direct numerical simulations with grids up to ${768}^3$ points and two different types of initial conditions. Results are compared to analogous magnetohydrodynamic (MHD) runs and both Laplacian and Laplacian-squared dissipative operators are examined. At scales below the ion inertial length, the ratio of magnetic to kinetic energy as a function of wave number transitions to a magnetically dominated state. The transition in behavior is associated with the advection term in the momentum equation becoming subdominant to dissipation. Examination of autocorrelation functions reveals that, while current and vorticity structures are similarly sized in MHD, HMHD current structures are narrower and vorticity structures are wider. The electric field autocorrelation function is significantly narrower in HMHD than in MHD and is similar to the HMHD current autocorrelation function at small separations. HMHD current structures are found to be significantly more intense than in MHD and appear to have an enhanced association with strong alignment between the current and magnetic field, which may be important in collisionless plasmas where field-aligned currents can be unstable. When hyperdiffusivity is used, a longer region consistent with a $k^{-7/3}$ scaling is present for right-polarized fluctuations when compared to Laplacian dissipation runs.

Maclaurin series approximant and Padé rational approximant are used to solve the Tonks-Langmuir theory for an annular plasma and investigate the radial transport behavior of charged particles. Coefficients of the well-known Maclaurin approximant are given in a novel form of recurrence relations which are convenient for computation and present a lower limit for the annular ratio of inner radius to outer radius (i.e., this approximant is not applicable to annular geometries with small inner radii). The newly introduced Padé approximant extrapolates the annular ratio limit determined by the Maclaurin approximant to a lower value and hence is applicable to most annular geometries. General radial profiles of the normalized plasma density and mean drift velocity of ions are given across the annulus and they are independent of the gas type and the Paschen number of the discharge. The annular modeling is applied to an argon plasma and obtains the electron temperature as a function of the Paschen number for different annular geometries.

We review the momentum exchange method to compute the flow force and torque on a submerged body in lattice-Boltzmann methods by presenting an alternative derivation. Our derivation does not depend on a particular implementation of the boundary conditions at the body surface, and it relies on general principles. After the introduction of the momentum exchange method in lattice-Boltzmann methods, some formulations were introduced to compute the fluid force on static and moving bodies. These formulations were introduced in a rather intuitive, ad hoc way. In our derivation, we recover the proposals most frequently used, in some cases with minor corrections, gaining some insight into the two most used formulations. At the end, we present some numerical tests to compare different approaches on a well-known benchmark test that support the correctness of the formulas derived.

A reconstruction methodology based on different-phase-neighbor (DPN) pixel swapping and multigrid hierarchical annealing is presented. The method performs reconstructions by starting at a coarse image and successively refining it. The DPN information is used at each refinement stage to freeze interior pixels of preformed structures. This preserves the large-scale structures in refined images and also reduces the number of pixels to be swapped, thereby resulting in a decrease in the necessary computational time to reach a solution. Compared to conventional single-grid simulated annealing, this method was found to reduce the required computation time to achieve a reconstruction by around a factor of 70–90, with the potential of even higher speedups for larger reconstructions. The method is able to perform medium sized (up to ${300}^3$ voxels) three-dimensional reconstructions with multiple correlation functions in 36–47 h.

The spontaneous formation of droplets via dewetting of a thin fluid film from a solid substrate allows materials nanostructuring. Often, it is crucial to be able to control the evolution, and to produce patterns characterized by regularly spaced droplets. While thermal fluctuations are expected to play a role in the dewetting process, their relevance has remained poorly understood, particularly during the nonlinear stages of evolution that involve droplet formation. Within a stochastic lubrication framework, we show that thermal noise substantially influences the process of droplets formation. Stochastic systems feature a smaller number of droplets with a larger variability in size and space distribution, when compared to their deterministic counterparts. Finally, we discuss the influence of stochasticity on droplet coarsening for asymptotically long times.

Flows of suspensions are often affected by wall slip, that is, the fluid velocity $v_f$ in the vicinity of a boundary differs from the wall velocity $v_w$ due to the presence of a lubrication layer. While the slip velocity $v_s=|v_f-v_w|$ robustly scales linearly with the stress $\sigma$ at the wall in dilute suspensions, there is no consensus regarding denser suspensions that are sheared in the bulk, for which slip velocities have been reported to scale as a $v_s\propto {\sigma }^p$ with exponents $p$ inconsistently ranging between 0 and 2. Here we focus on a suspension of soft thermoresponsive particles and show that $v_s$ actually scales as a power law of the viscous stress $\sigma -{\sigma }_c$, where ${\sigma }_c$ denotes the yield stress of the bulk material. By tuning the temperature across the jamming transition, we further demonstrate that this scaling holds true over a large range of packing fractions $\varphi$ on both sides of the jamming point and that the exponent $p$ increases continuously with $\varphi$, from $p=1$ in the case of dilute suspensions to $p=2$ for jammed assemblies. These results allow us to successfully revisit inconsistent data from the literature and pave the way for a continuous description of wall slip above and below jamming.

Here we show that under quantum reconnection, simulated by using the three-dimensional Gross-Pitaevskii equation, self-helicity of a system of two interacting vortex rings remains conserved. By resolving the fine structure of the vortex cores, we demonstrate that the total length of the vortex system reaches a maximum at the reconnection time, while both writhe helicity and twist helicity remain separately unchanged throughout the process. Self-helicity is computed by two independent methods, and topological information is based on the extraction and analysis of geometric quantities such as writhe, total torsion, and intrinsic twist of the reconnecting vortex rings.

We consider the dispersion properties of tracer particles moving in nonequilibrium heterogeneous periodic media. The tracer motion is described by a Fokker-Planck equation with arbitrary spatially periodic (but constant in time) local diffusion tensors and drifts, eventually with the presence of obstacles. We derive a Kubo-like formula for the time-dependent effective diffusion tensor valid in any dimension. From this general formula, we derive expressions for the late time effective diffusion tensor and drift in these systems. In addition, we find an explicit formula for the late finite-time corrections to these transport coefficients. In one dimension, we give a closed analytical formula for the transport coefficients. The formulas derived here are very general and provide a straightforward method to compute the dispersion properties in arbitrary nonequilibrium periodic advection-diffusion systems.