The determination of the densest packings of regular tetrahedra (one of the five Platonic solids) is attracting great attention as evidenced by the rapid pace at which packing records are being broken and the fascinating packing structures that have emerged. Here we provide the most general analytical formulation to date to construct dense periodic packings of tetrahedra with four particles per fundamental cell. This analysis results in six-parameter family of dense tetrahedron packings that includes as special cases recently discovered “dimer” packings of tetrahedra, including the densest known packings with density $\varphi =\frac{4000}{4671}=0.856347\dots$. This study strongly suggests that the latter set of packings are the densest among all packings with a four-particle basis. Whether they are the densest packings of tetrahedra among all packings is an open question, but we offer remarks about this issue. Moreover, we describe a procedure that provides estimates of upper bounds on the maximal density of tetrahedron packings, which could aid in assessing the packing efficiency of candidate dense packings.

In this paper, molecular dynamics simulations are employed to study the liquid-crystal phases of 2-(4-butyloxyphenyl)-5-octyloxypyrimidine and 5-(4-butyloxyphenyl)-2-octyloxypyrimidine. Both mesogens consist of aromatic phenyl-pyrimidine cores in between two identical alkoxy tails, but they differ in the preferred core conformation. The ab initio–based derivation of suitable molecular models is discussed in detail, with particular emphasis on capturing proper ring-ring interactions. The presence of ring quadrupoles in the molecular model is shown to be essential to the correct reproduction of the experimentally observed phases. Simulations of these fluids at various temperatures are performed and order, for the aromatic core and the flexible tails, is analyzed. To differentiate smectic-$A$ from smectic-$C$ phases, intermolecular structure is divided into contributions parallel and perpendicular to the director and layer normal.

The multidensity Ornstein-Zernike integral equation theory is applied to study a simple model of hard sphere/sticky hard sphere diblock chains. The multidensity integral equation formalism has been successfully used to model the equilibrium structure and thermodynamic properties of homonuclear chains and shorter dimer fluids; to our knowledge it has not been applied to model diblock chains. In this work, a diblock chain fluids is represented by an $m$-component equal molar mixture of hard spheres with species $1,2,\dots ,m_h$ and sticky hard spheres with species $m_h+1,m_h+2,\dots ,m$. Each spherical particle has two attractive sites $A$ and $B$ except species 1 and $m$, which have only one site per particle. In the limit of complete association, this mixture yields a system of monodisperse diblock chains. A general solution of this model is obtained in the Percus-Yevick, Polymer Percus-Yevick and ideal chain approximations. Both structural and thermodynamic properties of this model are investigated. From this study, a microphase separation is predicted for relatively short diblock symmetric and asymmetric chains. This microphase separation is enhanced at lower temperature and higher density. When chain length increases, the phase transition changes from a microphase level to a macrophase level. The size of microdomain structure is found to be dependent on total chain length, relative ratio of block lengths, temperature, and density.

In this paper, the Fitzhugh-Nagumo (FHN) equations and a modified FHN (MFHN) are considered. For the modified version, the recovery variable $v$ has three different time scales. By considering different parameters in the local dynamics of the MFHN equations, it is observed that the phenomenon of reflection and annihilation at an impermeable boundary is observed just as in the Beeler-Reuter model. The interaction of spirals obtained with the FHN, MFHN, and Beeler-Reuter model, and an obstacle is also considered. The phenomenon of reflection of the spiral wave at a boundary changes when the boundary becomes an obstacle. Four properties for attachment of a spiral wave to an obstacle are presented in this work.

Icosahedral viral shells are characterized by intrinsic elastic stress focused on the 12 structurally required pentamers. We show that, according to thin-shell theory, assembling icosahedral viral shells should be subject to the Asaro-Grinfeld-Tiller instability (AGTI). AGTIs are encountered in growing epitaxial films exposed to extrinsic elastic stress. For viral shells, the AGTI relieves intrinsic elastic stresses by generating corrugation along the perimeter of the assembling shell. The buckling transition of Lidmar, Mirny, and Nelson provides an alternative mechanism for stress release, which in principle would allow for avoidance of AGTIs. For system parameters appropriate for viral shells however, the AGTI appears to be unavoidable. The azimuthal stress condensation produced by the AGTI might actually assist assembly by providing a guiding mechanism for the insertion of pentamers during viral assembly.

The loop structure plays an important role in many aspects of complex networks and attracts much attention. Among the previous works, Bianconi et al. [Phys. Rev. Lett. 100, 118701 (2008)] found that real networks often have very few short loops as compared to random models. In this paper, we focus on the uneven location of loops which makes some parts of the network rich while some other parts sparse in loops. We propose a node removing process to analyze the unevenness and find rich loop cores can exist in many real networks such as neural networks and food web networks. Finally, an index is presented to quantify the unevenness of loop location in complex networks.

We develop an effective description of noise-induced oscillations based on deterministic phase dynamics. The phase equation is constructed to exhibit correct frequency and distribution density of noise-induced oscillations. In the simplest one-dimensional case the effective phase equation is obtained analytically, whereas for more complex situations a simple method of data processing is suggested. As an application an effective coupling function is constructed that quantitatively describes periodically forced noise-induced oscillations.

We explore the dynamics of noninteracting particles loaded into a phase-modulated one-dimensional lattice formed by laterally oscillating square barriers. Tuning the parameters of the driven unit cell of the lattice selected parts of the classical phase space can be manipulated in a controllable manner. We find superdiffusion in position space for all parameters regimes. A directed current of an ensemble of particles can be created through locally breaking the spatiotemporal symmetries of the time-driven potential. Magnitude and direction of the current are tunable. Several mechanisms for transient localization and trapping of particles in different wells of the driven unit cell are presented and analyzed.

Swarm oscillator model derived by one of the authors (Tanaka), where interacting motile elements form various kinds of patterns, is investigated. We particularly focus on the cluster patterns in one-dimensional space. We mathematically derive all static and stable configurations in final states for a particular but a large set of parameters. In the derivation, we introduce renormalized expression of this model. We find that the static final states are hierarchical cluster structures in which a cluster consists of smaller clusters in a nesting manner.

We investigate the draining of a vertical magnetic soap film in the presence of a strong, nonuniform magnetic field. A colloidal suspension of magnetic nanoparticles in a regular soap solution yields a magnetic soap solution, from which a soap film is formed across an isolated frame. Experiments demonstrate that with a strong magnet placed above the frame, the film may be made to flow upward against gravity. The amount of film draining upward is altered by varying the distance between the frame and magnet. A first mathematical model is developed for the evolution of the film. Simulations demonstrate qualitative agreement with the experiment.

Disorder-induced heating (DIH) is one of the main reasons reducing the coupling strength in ultracold plasma. We propose applying an optical lattice as periodic confinement before the ultracold atomic cloud is ionized to eliminate its effect. We demonstrate a numerical simulation for the dynamics of the ultracold plasmas using classical molecular dynamics method with open boundary. DIH is reproduced in the simulation with the random Gaussian initial distribution and is absent in the results with the ordered lattice initial distribution. We further find that the collisional heating from electrons is important for ultracold plasmas with chosen spatial correlations in the optical lattice. Carefully preparing the initial condition (e.g., the ion density, initial electron temperature, and so on), collisional heating for the ions would be significantly reduced and eventually negligible. This allows a much stronger coupling in ultracold plasma to be realized.

The dynamic least-squares kernel density (LSQKD) model [C. Pantano and B. Shotorban, Phys. Rev. E 76, 066705 (2007)] is used to solve the Fokker-Planck equations. In this model the probability density function (PDF) is approximated by a linear combination of basis functions with unknown parameters whose governing equations are determined by a global least-squares approximation of the PDF in the phase space. In this work basis functions are set to be Gaussian for which the mean, variance, and covariances are governed by a set of partial differential equations (PDEs) or ordinary differential equations (ODEs) depending on what phase-space variables are approximated by Gaussian functions. Three sample problems of univariate double-well potential, bivariate bistable neurodynamical system [G. Deco and D. Martí, Phys. Rev. E 75, 031913 (2007)], and bivariate Brownian particles in a nonuniform gas are studied. The LSQKD is verified for these problems as its results are compared against the results of the method of characteristics in nondiffusive cases and the stochastic particle method in diffusive cases. For the double-well potential problem it is observed that for low to moderate diffusivity the dynamic LSQKD well predicts the stationary PDF for which there is an exact solution. A similar observation is made for the bistable neurodynamical system. In both these problems least-squares approximation is made on all phase-space variables resulting in a set of ODEs with time as the independent variable for the Gaussian function parameters. In the problem of Brownian particles in a nonuniform gas, this approximation is made only for the particle velocity variable leading to a set of PDEs with time and particle position as independent variables. Solving these PDEs, a very good performance by LSQKD is observed for a wide range of diffusivities.

We use computer simulations to study the dynamics of a physical gel at high densities where gelation and the glass transition interfere. We report and provide detailed physical understanding of complex relaxation patterns for time-correlation functions which generically decay in a three-step process. For certain combinations of parameters we find logarithmic decays of the correlators and subdiffusive particle motion.

Ten necessary criteria for stability of various dissipative fluids and plasmas are derived from the first and the second principle of thermodynamics applied to a generic small mass element of the system, under the assumption that local thermodynamic equilibrium holds everywhere at all times. We investigate the stability of steady states of a mixture of different chemical species at the same temperature against volume-preserving perturbations. We neglect both electric and magnetic polarization, and assume negligible net mass sources and particle diffusion. We assume that both conduction- and radiation-induced heat losses increase with increasing temperature. We invoke no Onsager symmetry, no detailed model of heat transport and production, no “Extended Thermodynamics,” no “Maxent” method, and no “new” universal criterion of stability for steady states of systems with dissipation. Each criterion takes the form of—or is a consequence of—a variational principle. We retrieve maximization of entropy for isolated systems at thermodynamic equilibrium, as expected. If the boundary conditions keep the relaxed state far from thermodynamic equilibrium, the stability criterion we retrieve depends also on the detailed balance of momentum of a small mass element. This balance may include the $\nabla p$-related force, the Lorenz force of electromagnetism and the forces which are gradients of potentials. In order to be stable, the solution of the steady-state equations of motion for a given problem should satisfy the relevant stability criterion. Retrieved criteria include (among others) Taylor’s minimization of magnetic energy with the constraint of given magnetic helicity in relaxed, turbulent plasmas, Rayleigh’s criterion of stability in thermoacoustics, Paltridge et al.’s maximum entropy production principle for Earth’s atmosphere, Chandrasekhar’ minimization of the adverse temperature gradient in Bénard’s convective cells, and Malkus’ maximization of viscous power with the constraint of given mean velocity for turbulent shear flow in channels. It turns out that characterization of systems far from equilibrium, e.g., by maximum entropy production is not a general property but—just like minimum entropy production—is reserved to special systems. A taxonomy of stability criteria is derived, which clarifies what is to be minimized, what is to be maximized and with which constraint for each problem.

The size scaling behavior of the granular Rayleigh-Taylor instability [J. L. Vinningland et al., Phys. Rev. Lett. 99, 048001 (2007)] is investigated experimentally, numerically, and theoretically. An upper layer of grains displaces a lower gap of air by organizing into dense fingers of falling grains separated by rising bubbles of air. The dependence of these structures on the system and grain sizes is investigated. A spatial measurement of the finger structures is obtained by the Fourier power spectrum of the wave number $k$. As the size of the grains increases the wave number decreases accordingly which leaves the dimensionless product of wave number and grain diameter, $dk$, invariant. A theoretical interpretation of the invariance, based on the scaling properties of the model equations, suggests a gradual breakdown of the invariance for grains smaller than $\sim 70\mu \text{m}$ or greater than $\sim 570\mu \text{m}$ in diameter.

In this paper, we analytically examine the influence of synaptic short-term plasticity (STP) on the transfer of rate-coded information through synapses. STP endows each presynaptic input spike with an amplitude that depends on previous input spikes. We develop a method to calculate the spectral statistics of this amplitude modulated spike train (postsynaptic input) for the case of an inhomogeneous Poisson process. We derive in particular analytical approximations for cross-spectra, power spectra, and for the coherence function between the postsynaptic input and the time-dependent rate modulation for a specific model. We give simple expressions for the coherence in the limiting cases of pure facilitation and pure depression. Using our analytical results and extensive numerical simulations, we study the spectral coherence function for postsynaptic input resulting from a single synapse or from a group of synapses. For a single synapse, we find that the synaptic coherence function is largely independent of frequency indicating broadband information transmission. This effect is even more pronounced for a large number of synapses. However, additional noise gives rise to frequency-dependent information filtering.

We present a method for simulating fluid vesicles with in-plane orientational ordering. The method involves computation of local curvature tensor and parallel transport of the orientational field on a randomly triangulated surface. It is shown that the model reproduces the known equilibrium conformation of fluid membranes and work well for a large range of bending rigidities. Introduction of nematic ordering leads to stiffening of the membrane. Nematic ordering can also result in anisotropic rigidity on the surface leading to formation of membrane tubes.

Membrane waves have been observed near the leading edge of a motile cell. Such phenomenon is the result of the interplay between hydrodynamics and adhesive dynamics. Here we consider membrane dynamics on a thin fluid gap supported by adhesive bonds. Using coupled lubrication theory and adhesive dynamics, we derive an evolution equation to account for membrane tension, bending, adhesion, and viscous lubrication. Four adhesion scenarios are examined: no adhesion, uniform adhesion, clustered adhesion, and focal adhesion. Two contrasting traveling wave types are found, namely, tension and adhesion waves. Tension waves disperse with time and space, whereas adhesion waves show increased amplitudes and are highly persistent. We show that the transition from tension to adhesion waves depends on a necessary, but insufficient, criterion that the wave amplitude must exceed a critical gap height, which is dependent on adhesion binding probability. We also show that strong adhesion results in sharp tension-to-adhesion wave transitions. The present work could explain the strong persistence of the waves observed in adhered cells using differential inference contrast (DIC) microscopy and the observation that the wavelengths decrease shortly after leading edge retraction.

Synchrotron radiation imaging technique was used to in situ observe the dendrite growth of a solidifying Sn-Bi binary alloy under a direct current (dc) electric field. By applying a dc $\left(7–32\text{A}/{\text{cm}}^2\right)$, the dendrite branching was suppressed, the dendrite tip was modified to be round or flat, and no tertiary dendrite was found. With increasing dc density, the dendrite morphology was changed from columnar dendritic to equiaxed cellular to equiaxed dendritic. In particular, the primary dendrite branched following a tip-split manner in a higher intensity dc. The influence of dc on the evolution of dendrite morphology was discussed.

We study vaccine control for disease spread on an adaptive network modeling disease avoidance behavior. Control is implemented by adding Poisson-distributed vaccination of susceptibles. We show that vaccine control is much more effective in adaptive networks than in static networks due to feedback interaction between the adaptive network rewiring and the vaccine application. When compared to extinction rates in static social networks, we find that the amount of vaccine resources required to sustain similar rates of extinction are as much as two orders of magnitude lower in adaptive networks.