Quantized vortices in a complex wave field described by a defocusing nonlinear Schrödinger equation with a space-varying dispersion coefficient are studied theoretically and compared to vortices in the Gross-Pitaevskii model with external potential. A discrete variant of the equation is used to demonstrate numerically that vortex knots in three-dimensional arrays of oscillators coupled by specially tuned weak links can exist for as long times as many as tens of typical vortex turnover periods.

Newman et al. [Phys. Rev. E 86, 026103 (2012)] showed that points uniformly distributed as independent and identically distributed random variables with nearest-neighbor interactions form clusters with a mean number of three points in each. Here, we extend our analysis to higher dimensions, ultimately going to infinite dimensions, and we show that the mean number of points per cluster rises monotonically with a limiting value of four.

A numerical simulation shows that the osmotic pressure of compressed lattice knots is a function of knot type, and so of entanglements. The osmotic pressure for the unknot goes through a negative minimum at low concentrations, but in the case of nontrivial knot types $3_1$ and $4_1$ it is negative for low concentrations. At high concentrations the osmotic pressure is divergent, as predicted by Flory-Huggins theory. The numerical results show that each knot type has an equilibrium length where the osmotic pressure for monomers to migrate into and out of the lattice knot is zero. Moreover, the lattice unknot is found to have two equilibria, one unstable, and one stable, whereas the lattice knots of type $3_1$ and $4_1$ have one stable equilibrium each.

Rheological properties of supramolecular polymers (SMPs) depend on their equilibrium structure including the size, the number, and the topology of aggregates. A polymer with a hydrogen bonding (H-bonding) motif at both ends is one widely used precursor to build SMPs. Due to the complex interplay between chain stiffness, H-bonding interaction, polarity along a chain, and polymer conformational entropy, it is difficult to theoretically predict the structure of SMPs. In this work we investigate thermodynamics of SMPs with H-bonding ends in a wide range of densities. A replica exchange stochastic approximation Monte Carlo method with coarse-grained models for polyethylene and polybuthylene glycols is used. Our simulation shows that SMPs have two morphological transition lines with increasing temperature, a ring-linear transition, and a linear-free chain transition. The latter is a thermodynamic transition and turns out to be continuous. Comparing the two different spacers, we find that ring-linear transition temperatures differ from each other at the constant volume fraction due to different looping probabilities, which can be calculated from the average polymer size by mean field. However, the linear-free chain transition temperatures are similar because the entropic penalty to form a hydrogen bond mainly depends on the probability of finding H-bonding groups in a system, which is the same for both systems at a given volume fraction.

Semigrand hybrid Monte Carlo simulations are used to measure equilibrium properties of micelles formed in a simple bead-spring model of asymmetric A-B diblock copolymer surfactant molecules in an A homopolymer solvent, over a range of values of surfactant solubility. Simulations are used to accurately measure the free energy of formation of micellar clusters as a function of aggregation number over a wide range of values, and to characterize the crossover from spherical to rodlike micelle shape with increasing aggregation number. Dynamical properties of the same model are considered in an accompanying paper [Phys. Rev. E 100, 012603 (2019)].

Molecular dynamics (MD) simulations are used to measure dynamical properties of a simple bead-spring model of A-B diblock copolymer molecules, and to characterize rates and mechanisms of several dynamical processes. Dynamical properties are analyzed within the context of a kinetic population model that allows for both stepwise insertion and expulsion of individual free molecules and occasional fission and fusion of micelles. Kinetic coefficients for stepwise processes and micelle fission have been extracted from MD simulations of individual micelles. Insertion of a free surfactant molecule into a preexisting micelle is shown to be a completely diffusion-controlled process for the model studied here. Estimates are given for rates of rare events that create and destroy entire micelles by competing mechanisms involving stepwise association and dissociation or fission and fusion. Both mechanisms are shown to be relevant over the range of parameters studied here, with association and dissociation dominating in systems with more soluble surfactants and fission and fusion dominating in systems with less soluble surfactants.

It has been known that at high density, banana-shaped molecules are packed into a bent configuration locally, giving rise to interesting liquid-crystalline phases such as splay bend and twist bend. These spontaneous bend states can be modeled theoretically by allowing the bend elastic constant in the Frank elastic energy to become negative. Here, we extend this idea to banana-shaped and pizza-slice-shaped molecules with ferrointeractions, which can display both splayed and bent states. We model this by allowing both splay and bend elastic constants in the effective Frank elastic energy to be negative. In particular, we predict two new liquid-crystalline splay-bend phases. Furthermore, using renormalization group analysis, we showed that the phase transition belongs to a new constrained ferromagnet universality class.

In this study, we perform experiments that reveal the distribution of dynamic forces in the bulk of granular free-surface flows. We release photoelastic disks from an incline to create steady two-dimensional avalanches. These gravity-driven dry granular flows are in the slow to intermediate regime ($I\le 1$), dense ($\phi \approx 0.8$), and thin ($h\approx 10d$). The transition between solidlike (quasisteady) and fluidlike (inertial) regimes is observable for certain experimental settings. We measure constant density and quasilinear velocity profiles through particle tracking at several points down the chute, for two different basal topographies. The photoelastic technique allows the visualization and quantification of instantaneous forces transmitted between particles during individual collisions. From the measured forces we obtain coarse-grained profiles of all stress tensor components at various positions along the chute. The discreteness of the system leads to highly fluctuating individual force chains which form preferentially in the directions of the bulk external forces: in this case, gravity and shear. The behavior of the coarse-grained stress tensor within a dynamic granular flow is analogous to that of a continuous fluid flow, in that we observe a hydrostatic increase of the mean pressure with depth. Furthermore, we identify a preferential direction for the principal stress orientation, which depends on the local magnitudes of the frictional and gravitational forces. These results allow us to draw an analogy between discrete and continuous flow models.

Granular material in a swirled container exhibits a curious transition as the number of particles is increased: At low densities, the particle cluster rotates in the same direction as the swirling motion of the container, while at high densities it rotates in the opposite direction. We investigate this phenomenon experimentally and numerically using a corotating reference frame in which the system reaches a statistical steady state. In this steady state, the particles form a cluster whose translational degrees of freedom are stationary, while the individual particles constantly circulate around the cluster's center of mass, similar to a ball rolling along the wall within a rotating drum. We show that the transition to counterrotation is friction dependent. At high particle densities, frictional effects result in geometric frustration, which prevents particles from cooperatively rolling and spinning. Consequently, the particle cluster rolls like a rigid body with no-slip conditions on the container wall, which necessarily counterrotates around its own axis. Numerical simulations verify that both wall-disk friction and disk-disk friction are critical for inducing counterrotation.

We present a mathematical formalism for the topology and stochasticity of vector fields based on renormalization group methodology. The concept of a scale-split energy density, ${\psi }_{l,L}={\mathbf{B}}_l·{\mathbf{B}}_L/2$ for vector field $\mathbf{B}(\mathbf{x},t)$ renormalized at scales $l$ and $L$, is introduced in order to quantify the notion of the field topological deformation, topology change, and stochasticity level. In particular, for magnetic fields, it is shown that the evolution of the field topology is directly related to the field-fluid slippage, which has already been linked to magnetic reconnection in previous work. The magnitude and direction of stochastic magnetic fields, shown to be governed, respectively, by the parallel and vertical components of the renormalized induction equation with respect to the magnetic field, can be studied separately by dividing ${\psi }_{l,L}$ into two ($3+1$)-dimensional scalar fields. The velocity field can be approached in a similar way. Magnetic reconnection can then be defined in terms of the extrema of the $L_p$ norms of these scalar fields. This formulation in fact clarifies different definitions of magnetic reconnection, which vaguely rely on the magnetic field topology, stochasticity, and energy conversion. Our results support the well-founded yet partly overlooked picture in which magnetic reconnection in turbulent fluids occurs on a wide range of scales as a result of nonlinearities at large scales (turbulence inertial range) and nonidealities at small scales (dissipative range). Lagrangian particle trajectories, as well as magnetic field lines, are stochastic in turbulent magnetized media in the limit of small resistivity and viscosity. The magnetic field tends to reduce its stochasticity induced by the turbulent flow by slipping through the fluid, which may accelerate fluid particles. This suggests that reconnection is a relaxation process by which the magnetic field lowers both its topological entanglements induced by turbulence and its energy level.

This paper describes a computational model that self-consistently combines physics of kinetic electrons and atomic processes in a single framework. The formulation consists of a kinetic Vlasov-Boltzmann-Fokker-Planck equation for free electrons and a non-Maxwellian collisional-radiative model for atomic state populations. We utilize this model to examine the influence of atomic kinetics on inverse bremsstrahlung (IB) heating and nonlocal thermal transport. We show that atomic kinetics affects nonlinear IB absorption rates by further modifying the electron distribution in addition to laser heating. We also show that accurate modeling of nonlocal heat flow requires a self-consistent treatment of atomic kinetics, because the effective thermal conductivity strongly depends on the ionization balance of the plasma.

The dynamics of the boundary layer in between two distinct collisionless plasmas created by the interaction between a dense object modeling a cluster and a short laser pulse in the presence of an ambient gas is studied with two dimensional relativistic particle-in-cell simulations, which are found to be described by three successive processes. In the first phase, a collisionless electrostatic shock wave, launched near the cluster expansion front, reflects the ambient gas ions at a contact surface as a moving wall, which allows a particle acceleration with a narrower energy spread. In the second phase, the contact surface disappears and the compressed surface of the ambient gas ions passes over the shock potential, forming an overlapping region between the cluster expansion front and the compressed surface of the ambient gas. Here, another type of nonlinear wave is found to be evolved, leading to a relaxation of the shock structure, while continuing to reflect the ambient gas ions. The nonlinear wave exhibits a bipolar electric field structure that is sustained for a long timescale coupled with slowly evolving ion dynamics, suggesting that a quasistationary kinetic equilibrium dominated by electron vortices in the phase space is established. In the third phase, a rarefaction wave is triggered and evolves at the compressed surface of ambient gas. This is because some of the ambient gas ions tend to pass over the potential of the bipolar electric field. Simultaneously, a staircase structure, i.e., a kind of internal shock, is formed in the cluster due to the deceleration of cluster ions. Such structure formations and successive dynamics accompanied by the transitions from the shock wave phase through the overlapping phase to the rarefaction wave phase are considered to be a unique nature at the boundary layer created by an explosion of a dense plasma object in an ambient dilute plasma.

Open subwavelength cylindrical resonators of finite height are widely used in various photonics applications. Circular cylindrical resonators are particularly important in nanophotonics, since they are relatively easy to fabricate and can be designed to exhibit different resonance effects. In this paper, an efficient and robust numerical method is developed for computing resonant modes of circular cylinders which may have a few layers and may be embedded in a layered background. The resonant modes are complex-frequency outgoing solutions of the Maxwell's equations with no sources or incident waves. The method uses field expansions in one-dimensional (1D) “vertical” modes to reduce the original three-dimensional eigenvalue problem to 1D problems and uses Chebyshev pseudospectral method to compute the 1D modes and set up the discretized eigenvalue problem. In addition, a new iterative scheme is developed so that the 1D nonlinear eigenvalue problems can be reliably solved. For metallic cylinders, the resonant modes are calculated based on analytic models for the dielectric functions of metals. The method is validated by comparisons with existing numerical results, and it is also used to explore subwavelength dielectric cylinders with high-$Q$ resonances and analyze gold nanocylinders.

We present a direct-forcing fictitious domain method for simulating non-Brownian squirmer particles with both the hydrodynamic interactions and collisions being fully resolved. In this method, we solve the particle motion by distributing collocation points inside the particle interior domain that overlay upon a fixed Eulerian mesh. The fluid motions, including those of the “fictitious fluids” being extended into the particle, are solved on the entire computation domain. Pseudo-body forces are used to enforce the fictitious fluids to follow the particle movement. A direct-forcing approach is employed to map physical variables between the overlaid meshes, which does not require additional iterations to achieve convergence. We perform a series of numerical studies at both small and finite Reynolds numbers. First, accuracy of the algorithm is examined in studying benchmark problems of a free-swimming squirmer and two side-by-side squirmers. Then we investigate statistic properties of the quasi-two-dimensional collective dynamics for a monolayer of squirmer particles that are confined on a surface immersed in a bulk flow. Finally, we explore the physical mechanisms of how a freely moving short cylinder interacts with a monolayer of active particles, and find out that the cylinder movement is dominated by collision. We demonstrate that a more directional migration of cylinder can be resultant from an inhomogeneous distribution of active particles around the cylinder that has an anisotropic shape.

We propose a computational method to quantitatively evaluate the systematic uncertainties that arise from undetectable sources in biological measurements using live-cell imaging techniques. We then demonstrate this method in measuring the biological cooperativity of molecular binding networks, in particular, ligand molecules binding to cell-surface receptor proteins. Our results show how the nonstatistical uncertainties lead to invalid identifications of the measured cooperativity. Through this computational scheme, the biological interpretation can be more objectively evaluated and understood under a specific experimental configuration of interest.

We investigate the heat capacity of simple liquids through a theoretical approach based on a quasiparticle description. By interpreting the microscopic dynamics of particles in liquids in terms of quasiparticles, we suggest a simplified understanding of the number of degrees of freedom in liquids. A equivalence between hydrodynamics and U(1) gauge theory, which is proposed in the present paper, develops the quasiparticle description to construct a new Lagrangian which correctly reproduces the number of modes at the melting points and at the critical points. The heat capacity evaluated from this Lagrangian naturally interpolates between these two points, and agrees with the phonon theory of liquids [Sci. Rep. 2, 421 (2012)].

Nonequilibrium phase transitions can be typified in a similar way to equilibrium systems, for instance, by the use of the order parameter. However, this characterization hides the irreversible character of the dynamics as well as its influence on the phase transition properties. Entropy production has been revealed to be an important concept for filling this gap since it vanishes identically for equilibrium systems and is positive for the nonequilibrium case. Based on distinct and general arguments, the characterization of phase transitions in terms of the entropy production is presented. Analysis for discontinuous and continuous phase transitions has been undertaken by taking regular and complex topologies within the framework of mean-field theory (MFT) and beyond the MFT. A general description of entropy production portraits for $Z_2$ (“up-down”) symmetry systems under the MFT is presented. Our main result is that a given phase transition, whether continuous or discontinuous has a specific entropy production hallmark. Our predictions are exemplified by an icon system, perhaps the simplest nonequilibrium model presenting an order-disorder phase transition and spontaneous symmetry breaking: the majority vote model. Our work paves the way to a systematic description and classification of nonequilibrium phase transitions through a key indicator of system irreversibility.

The nervous system can be represented as a multiscale network comprised by single cells or ensembles that are linked by physical or functional connections. Groups of morphologically and physiologically diverse neurons are wired as connectivity patterns with a certain degree of universality across species and individual variability. Thereby, community detection approaches are often used to characterize how neural units cluster into such densely interconnected groups. However, the communities may possess deeper structural features that remain undetected by current algorithms. We present a scheme for refined parcellation of neuronal networks, by identifying local integrator units (LU) that are contained in network communities. An LU is defined as a connected subnetwork in which all neuronal connections are constrained within this unit, and can be formed for instance by a set of interneurons. Our method uses the Louvain algorithm to detect communities and participation coefficients to discriminate local neurons from global hubs. The sensitivity of the algorithm for discovering LUs with respect to the choice of community detection algorithm and network parameters was tested by simulations of different synthetic networks. The appropriateness of the algorithm for real-world scenarios was demonstrated on weighted and binary Caenorhabditis elegans connectomes. The detected LUs are distinctly localized within the worm body and clearly define functional groups. This approach provides a robust, observer-independent parcellation strategy that is useful for functional structure confirmation and potentially contributes to the current efforts in quantitative whole-brain architectonics of different species as well as the analysis of functional connectivity networks.

Given the crucial role of electrostatic forces in biological systems, accurate and rapid calculations of electrostatic forces are imperative in faithfully simulating biological systems. More than a decade ago, we proposed a surface charge method, applied it to a system of an arbitrary number of charged dielectric spheres, and obtained an exact solution for arbitrary configuration of the spheres. The precision depends only on the number of terms kept in a series expansion, and can therefore be controlled at will. However, the numerical implementation can be significantly slowed down by the need to compute a large number of Wigner rotation matrix elements each time the electrostatic energy is calculated. In this paper, we provide the proof of a formula introduced in 1992 and apply it to arrive at a useful closed form for the electrostatic interaction energy without computing any Wigner rotation matrix elements, hence significantly improving the efficiency for numeric implementation of the rigorous surface charge method. This new Wigner-matrix-free formalism may also be used to speed up the computation of the electrostatic energy in the presence of permanent and induced multipoles, which can be very important for atomic modeling with polarization effect included.

Continuous attractor neural networks are used extensively to model a variety of experimentally observed coherent brain states, ranging from cortical waves of activity to stationary activity bumps. The latter are thought to play an important role in various forms of neural information processing, including population coding in primary visual cortex (V1) and working memory in prefrontal cortex. However, one limitation of continuous attractor networks is that the location of the peak of an activity bump (or wave) can diffuse due to intrinsic network noise. This reflects marginal stability of bump solutions with respect to the action of an underlying continuous symmetry group. Previous studies have used perturbation theory to derive an approximate stochastic differential equation for the location of the peak (phase) of the bump. Although this method captures the diffusive wandering of a bump solution, it ignores fluctuations in the amplitude of the bump. In this paper, we show how amplitude fluctuations can be analyzed by reducing the underlying stochastic neural field equation to a finite-dimensional stochastic gradient dynamical system that tracks the stochastic motion of both the amplitude and phase of bump solutions. This allows us to derive exact expressions for the steady-state probability density and its moments, which are then used to investigate two major issues: (i) the input-dependent suppression of neural variability and (ii) noise-induced transitions to bump extinction. We develop the theory by considering the particular example of a ring attractor network with $\text{SO}\left(2\right)$ symmetry, which is the most common architecture used in attractor models of working memory and population tuning in V1. However, we also extend the analysis to a higher-dimensional spherical attractor network with $\text{SO}\left(3\right)$ symmetry which has previously been proposed as a model of orientation and spatial frequency tuning in V1. We thus establish how a combination of stochastic analysis and group theoretic methods provides a powerful tool for investigating the effects of noise in continuous attractor networks.