The propagation of Alfvén envelope solitons through a Fermionic quantum plasma is considered. Starting from the governing equations for Hall magnetohydrodynamics including quantum corrections, coupled Zakharov-type equations are derived for circularly polarized Alfvén waves. The equations are numerically solved for time-independent and time-dependent cases. The time-independent case shows that variations in density take the form of dressed density solitons in which an approximately Gaussian peak is surrounded by smaller sinusoidal variations in the density envelope. The mathematical basis for this behavior is explained. A limited time-dependent case is obtained which uses the numerical time-independent soliton solutions as the initial conditions. This confirms that the soliton solutions retain the same profile as they propagate. The relevance of this work to dense astrophysical plasmas like the interiors of white dwarf stars is discussed.

We calculate the nondiffusive contribution to the intensity of coherent backscattering from a disordered medium composed of large-scale scatterers. The wings of the coherent backscattering cone are shown to be governed by short-path waves that experience small-angle multiple scattering before and after single scattering in the backward direction. For relatively large angles $\theta$ of deviation from the backward direction, $\theta >\lambda /l_{\mathrm{tr}}$ ($\lambda$ is the wavelength of light, $l_{\mathrm{tr}}$ is the transport mean free path), the intensity falls off slower than ${\theta }^{-1}$ and is directly related to a law of single scattering through small angles. Our calculations are in good agreement with experimental data for large Mie spheres.

We modify the formulation of Hertz contact theory between two elastic half-solids with axial symmetry and show that these modifications to Hertz’s original framework allow the development of force laws of the form $\mathcal{F}\propto z^n$, $1<n<\infty$, where $\mathcal{F}$ is the force and $z$ is the distance between the centers of the two solids. The study suggests that it may be possible to design physical systems that can realize such force laws. We let the half-solids be characterized by radii of curvatures $R_1$ and $R_2$ and invoke a factor $m>0$ to describe any aspect ratio in the two bodies, all being valid near the contact surface. We let the $x$-$y$ plane be the contact surface with an averaged pressure across the same as opposed to a pressure profile that depends on the contact area of a nonconformal contact as originally used by Hertz. We let the $z$ axis connect the centers of the masses and define $z_{1,2}=x^{\alpha }/R_{1,2}^{\alpha -1}+y^{\alpha }/({\mathit{mR}}_{1,2}){}^{\alpha -1}$, where $z_{1,2}⩾0$ refers to the compression of bodies $1$, $2$, $\alpha >1$, $m>0$, $x,y⩾0$. The full cross section can be generated by appropriate reflections using the first quadrant part of the area. We show that the nonlinear repulsive force is $F=a{z}^n$, where $n\equiv 1+1/\alpha$, and $z\equiv z_1+z_2$ is the overlap and we present an expression for $a=f(E,\sigma ,m,\alpha ,R_1,R_2)$ with $E$ and $\sigma$ as Young’s modulus and the Poisson ratio, respectively. For $\alpha =2,\infty$, to similar geometry-dependent constants, we recover Hertz’s law and the linear law, describing the repulsion between compressed spheres and disks, respectively. The work provides a connection between the contact geometry and the nonlinear repulsive law via $\alpha$ and $m$.

The prediction of events is of substantial interest in many research areas. To evaluate the performance of prediction methods, the statistical validation of these methods is of utmost importance. Here, we compare an analytical validation method to numerical approaches that are based on Monte Carlo simulations. The comparison is performed in the field of the prediction of epileptic seizures. In contrast to the analytical validation method, we found that for numerical validation methods insufficient but realistic sample sizes can lead to invalid high rates of false positive conclusions. Hence we outline necessary preconditions for sound statistical tests on above chance predictions.

Two-dimensional asymmetrical Ising models consisting of two weakly coupled dissimilar segments, coupled to heat baths with different temperatures at the two ends, are studied by Monte Carlo simulations. The heat rectifying effect, namely asymmetric heat conduction, is clearly observed. The underlying mechanisms are the different temperature dependencies of thermal conductivity $\kappa$ at two dissimilar segments and the match (mismatch) of flipping frequencies of the interface spins.

We investigate the characteristics of reliability and synchronization of a neuronal network of delay-coupled integrate and fire neurons. Reliability and synchronization appear in separated regions of the phase space of the parameters considered. The effect of including synaptic plasticity and different delay values between the connections are also considered. We found that plasticity strongly changes the characteristics of reliability and synchronization in the parameter space of the coupling strength and the drive amplitude for the neuronal network. We also found that delay does not affect the reliability of the network but has a determinant influence on the synchronization of the neurons.

We explore the scattering of particles evolving in a two-degree-of-freedom Hamiltonian system, in which both degrees of freedom are open. Particles, initially having all kinetic energy, are sent into a so-called “interaction region,” where there will be an exchange of energy with particles that are initially at rest. The open nature of both components of this system eliminates any restrictions on which particles can escape from the interaction region. Notably, it is shown that two particles can cooperate in a mutual exchange of energy allowing both particles to escape and travel large distances. It is also shown that this level of cooperation is highly sensitive to the coupling strength between both components of the system. Indeed, large fluctuations of the magnitude and direction of the current are observed for small changes of this coupling parameter. Further, it is seen that current reversals are a prominent feature of this model. Another interesting observation is that even with the presence of chaotic scattering, it is possible that the system, for certain parameter regimes, will express a vanishing current, suggesting that there is a restoration of symmetry which, due to the initial setup, is broken. For an explanation of the different features of particle motion, we relate the phase-space dynamics to the various regimes of particle current.

Recently, there has been a growing interest in the impact of inertial effects on the development of the Saffman-Taylor instability. Experiments and theory indicate that inertia may have a significant influence on the system’s behavior. We employ a perturbative-mode-coupling method to examine how the stability and morphology of the viscosity-driven fingering patterns are affected by inertia. Both rectangular and radial Hele-Shaw flow geometries are considered. In the rectangular configuration useful results can be deduced analytically, and in closed form. In particular, we have found that inertia has a stabilizing role at the linear stage, and tends to widen the fingers at the weakly nonlinear regime. These analytical results are consistent with existing experimental findings. The analysis of the system is not as simple in radial flow geometry, but it still allows the capture of inertially induced, enhanced finger tip splitting events at the onset of nonlinearities.

With the appropriate approximation, we have formulated the equation of multibubble motion for two cases: a filament of bubbles and a small spherical cluster of bubbles. Our results have yielded a collective mode of bubble motion in which individual bubbles of similar size expand and compress almost simultaneously. Each vibrating bubble radiates sound waves and originates the radiation sound pressure, which affects the motion of the other bubbles. The numerical simulation has revealed that this interaction suppresses single-bubble motion and tends to homogeneously spread the energy of the acoustic standing wave to each individual bubble.

We study the axisymmetric breakup and satellite formation of slender jets surrounded by a concentrically placed cylindrical electrode and subjected to time-dependent AC electric fields. The jet is assumed to be a perfectly conducting viscous fluid and surrounded by a dielectric inviscid gas. We use the long-wave approximation to derive coupled evolution equations for the interface position and the axial velocity component, which accounts for electrostatic forcing. The electrostatic force in this case is large and competes with capillary forces near the rupture point, causing the interface to oscillate and the satellite to have shapes that are distinct from the DC case. In particular, our results indicate that it may be possible to use the AC field to control the number of satellites accompanying breakup as well as their size.

Based on direct numerical simulations and symmetry arguments, we show that the large-scale Fourier modes are useful tools to describe the flow structures and dynamics of flow reversals in Rayleigh-Bénard convection (RBC). We observe that during the reversals, the amplitude of one of the large-scale modes vanishes, while another mode rises sharply, very similar to the “cessation-led” reversals observed earlier in experiments and numerical simulations. We find anomalous fluctuations in the Nusselt number during the reversals. Using the structures of the RBC equations in the Fourier space, we deduce two symmetry transformations that leave the equations invariant. These symmetry transformations help us in identifying the reversing and nonreversing Fourier modes.

Inspired by biological chemotaxis along circular paths, we propose a hydrodynamic molecular scale hunter that can swim and can find its target. The system is essentially a stochastic low-Reynolds-number swimmer with the ability to move in two-dimensional space and to sense the local value of the chemical concentration emitted by a target. We show that, by adjusting the geometrical and dynamical variables of the swimmer, we can always achieve a swimmer that can navigate and can search for the region with a higher concentration of a chemical emitted by a source.

The phenomenon of stochastic resonance (SR) is known to occur mostly in bistable systems. However, the question of the occurrence of SR in periodic potential systems has not been resolved conclusively. Our present numerical work shows that the periodic potential system indeed exhibits SR in the high-frequency regime, where the linear-response theory yields maximum frequency-dependent mobility as a function of noise strength. The existence of two (and only two) distinct dynamical states of trajectories in this moderately feebly damped periodically driven noisy periodic potential system plays an important role in the occurrence of SR.

The dynamics in an overdamped bistable system subject to the action of two periodic forces (assuming their frequencies are $\omega$ and $\Omega$, and amplitudes are $A$ and $B$, respectively) is studied. For the usual vibrational resonance, the nonmonotonic dependence of signal output of the low frequency $\omega$ on the change of $B$ for a fixed $\Omega$, the condition $\Omega \gg \omega$ is always assumed in all previous studies. Here, removing this restriction, we find that a resonant behavior can extensively occur with respect to the changes of both the frequency $\Omega$ and amplitude $B$. Especially, the resonance becomes stronger when $\Omega$ is chosen such that it is exactly in frequency resonance with $\omega$. This combinative behavior, called frequency-resonance-enhanced vibrational resonance, is of great interest and may shed an improved light on our understanding of the dynamics of nonlinear systems subject to a biharmonic force.

We study the coherent dynamics of excitations on vibrating chains. By applying an external field and matching the field strength with the oscillation frequency of the chain it is possible to obtain an (average) transport of an initial Gaussian wave packet. We distinguish between a uniform oscillation of all nodes of the chain and the chain being in its lowest eigenmode. Both cases can lead to directed transport.

We report on the numerical measures on different spin interfaces and Fortuin-Kasteleyn (FK) cluster boundaries in the Askhin-Teller (AT) model. For a general point on the AT critical line, we find that the fractal dimension of a generic spin cluster interface can take one of four different possible values. In particular we found spin interfaces whose fractal dimension is $d_f=3/2$ all along the critical line. Furthermore, the fractal dimension of the boundaries of FK clusters was found to satisfy all along the AT critical line a duality relation with the fractal dimension of their outer boundaries. This result provides clear numerical evidence that such duality, which is well known in the case of the $\text{O}(n)$ model, exists in an extended conformal field theory.

We investigate functions $g(\alpha ,\beta ;x)$ which are heavy-tailed Lévy stable probability distributions of index $0<\alpha ⩽2$ and appropriate asymmetry parameter $\beta$. They are of central importance in physics of amorphous and disordered systems, econophysics, geology, hydrology, internet traffic, dynamics of human relations, etc. We present an ensemble of exact and explicit solutions of $g(\alpha ,\beta ;x)$ for all admissible rational values of $\alpha$ and $\beta$. We reproduce all the previously known cases and furnish distributions for values $\alpha$ and $\beta$ which were previously inaccessible. We point out many instances of experimental and statistical data that could be described by our results.

The statistical mechanics of a two-state Ising spin-glass model with finite random connectivity, in which each site is connected to a finite number of other sites, is extended in this work within the replica technique to study the phase transitions in the three-state Ghatak-Sherrington (or random Blume-Capel) model of a spin glass with a crystal-field term. The replica symmetry ansatz for the order function is expressed in terms of a two-dimensional effective-field distribution, which is determined numerically by means of a population dynamics procedure. Phase diagrams are obtained exhibiting phase boundaries that have a reentrance with both a continuous and a genuine first-order transition with a discontinuity in the entropy. This may be seen as “inverse freezing,” which has been studied extensively lately, as a process either with or without exchange of latent heat.

We study the Potts model on a rectangular lattice with aperiodic modulations in its interactions along one direction. Numerical results are obtained using the Wolff algorithm and for many lattice sizes, allowing for a finite-size scaling analyses to be carried out. Three different self-dual aperiodic sequences are employed, which leads to more precise results, since the exact critical temperature is known. We analyze two models, with 6 and 15 number of states: both present first-order transitions on their uniform versions. We show that the Harris-Luck criterion, originally introduced in the study of continuous transitions, is obeyed also for first-order ones. Also, we show that the new universality class that emerges for relevant aperiodic modulations depends on the number of states of the Potts model, as obtained elsewhere for random disorder, and on the aperiodic sequence. We determine the occurrence of log-periodic behavior, as expected for models with aperiodic modulated interactions.