Microstructural evolution during thermally induced phase separation in a polymer solution with a highly asymmetrical miscibility gap is analyzed using Flory-Huggins thermodynamics and nonlinear Cahn-Hilliard kinetics. Computer simulation results demonstrate that, in contrast to systems with symmetric miscibility gaps, interesting morphological-evolution pathways (MEPs) including cluster-to-percolation and percolation-to-cluster transitions are identified. These MEPs are rationalized according to asynchronous evolution of the two product phases. For a highly asymmetric polymer system, the initial solution composition is also found to play a critical role in determining the MEPs. According to the simulation results a map of MEPs in terms of initial solution composition and aging time of phase separation is established to guide future microstructural design in asymmetrical polymer solutions.

We study the effect of an impressing AC magnetic field at the bottom of a liquid metal layer of thickness $h$. In this situation the fluid is set in motion by the buoyancy forces caused by internal heat sources. The heat sources, caused by the Joule effect induced by the AC field, present an exponentially decaying profile, with characteristic length $\delta$. As the magnetic field is horizontal, the Lorentz force has no influence on the dynamics of the system since it contributes only to the magnetic pressure. We propose an analysis of both the transient and fully developed regimes using linear stability analysis (LSA) and direct numerical simulations (DNSs). The transient period is governed by the temporal evolution of the temperature field as well as the development of the convective instability, which can be concomitant and therefore requires adopting a transient LSA algorithm to track these two effects. The DNSs have been performed for various distributions of the heat sources and various total heat input. This corresponds to independently varying $\delta /h$ in the range $0.04\le \delta /h\le 0.45$ and a Rayleigh number $1.1\times {10}^4\le \text{Ra}\le 1.2\times {10}^5$. We observe the relaxation of the temperature up to the steady conductive profile before the transition to the nonlinear regime when $\text{Ra}$ is small, whereas for larger $\text{Ra}$, nonlinear effects appear during the relaxation of the temperature profile. The unsteadiness of the temperature field significantly alters the development of the instability because of a much smaller growth rate. Surprisingly, we observe that $\delta /h$ has only a limited influence on averaged quantities as well as on the patterns for both the linear and nonlinear regimes. This comes with the fact that the profiles present an apparent reflectional symmetry, despite the asymmetry of the governing equations.

We examine the dynamics associated with weakly compressible convection in a spherical shell by running 3D direct numerical simulations using the Boussinesq formalism [Spiegel and Veronis, Astrophys. J. 131, 442 (1960)]. Motivated by problems in astrophysics, we assume the existence of a finite adiabatic temperature gradient $\mathbf{\nabla }{T}_{\mathrm{ad}}$ and use mixed boundary conditions for the temperature with fixed flux at the inner boundary and fixed temperature at the outer boundary. This setup is intrinsically more asymmetric than the more standard case of Rayleigh-Bénard convection in liquids between parallel plates with fixed temperature boundary conditions. Conditions where there is substantial asymmetry can cause a dramatic change in the nature of convection and we demonstrate that this is the case here. The flows can become pressure- rather than buoyancy-dominated, leading to anomalous heat transport by upflows. Counterintuitively, the background temperature gradient $\mathbf{\nabla }\overline{T}$ can develop a subadiabatic layer (where $\mathit{g}·\mathbf{\nabla }\overline{T}<\mathit{g}·\mathbf{\nabla }{T}_{\mathrm{ad}}$, where $\mathit{g}$ is gravity) although convection remains vigorous at every point across the shell. This indicates a high degree of nonlocality.

The position of floating spheres trapped within an immersed turbulent water jet is investigated. Using the self-similarity properties of the jet velocity profile, the equilibrium problem is formulated in a rescaled space where the sphere is static and deformable. This approach is found to be related to a problem of elastic reconfiguration where elasticity arises here from the geometry of the flow instead of an actual deformation of a body.

With the advent of petawatt class lasers, the very large laser intensities attainable on target should enable the production of intense high-order Doppler harmonics from relativistic laser-plasma mirror interactions. At present, the modeling of these harmonics with particle-in-cell (PIC) codes is extremely challenging as it implies an accurate description of tens to hundreds of harmonic orders on a broad range of angles. In particular, we show here that due to the numerical dispersion of waves they induce in vacuum, standard finite difference time domain (FDTD) Maxwell solvers employed in most PIC codes can induce a spurious angular deviation of harmonic beams potentially degrading simulation results. This effect was extensively studied and a simple toy model based on the Snell-Descartes law was developed that allows us to finely predict the angular deviation of harmonics depending on the spatiotemporal resolution and the Maxwell solver used in the simulations. Our model demonstrates that the mitigation of this numerical artifact with FDTD solvers mandates very high spatiotemporal resolution preventing realistic three-dimensional (3D) simulations even on the largest computers available at the time of writing. We finally show that nondispersive pseudospectral analytical time domain solvers can considerably reduce the spatiotemporal resolution required to mitigate this spurious deviation and should enable in the near future 3D accurate modeling on supercomputers in a realistic time to solution.

A lattice Boltzmann method (LBM) with enhanced stability and accuracy is presented for various Hermite tensor-based lattice structures. The collision operator relies on a regularization step, which is here improved through a recursive computation of nonequilibrium Hermite polynomial coefficients. In addition to the reduced computational cost of this procedure with respect to the standard one, the recursive step allows to considerably enhance the stability and accuracy of the numerical scheme by properly filtering out second- (and higher-) order nonhydrodynamic contributions in under-resolved conditions. This is first shown in the isothermal case where the simulation of the doubly periodic shear layer is performed with a Reynolds number ranging from ${10}^4$ to ${10}^6$, and where a thorough analysis of the case at $\text{Re}=3\times {10}^4$ is conducted. In the latter, results obtained using both regularization steps are compared against the Bhatnagar-Gross-Krook LBM for standard (D2Q9) and high-order (D2V17 and D2V37) lattice structures, confirming the tremendous increase of stability range of the proposed approach. Further comparisons on thermal and fully compressible flows, using the general extension of this procedure, are then conducted through the numerical simulation of Sod shock tubes with the D2V37 lattice. They confirm the stability increase induced by the recursive approach as compared with the standard one.

This paper consists in the description and application of a method called wavelet-induced mode extraction (WIME) in the context of time-frequency analysis. WIME aims to extract the oscillating components that build amplitude modulated-frequency modulated signals. The essence of this technique relies on the successive extractions of the dominant ridges of wavelet-based time-frequency representations of the signal under consideration. Our tests on simulated examples indicate strong decomposition and reconstruction skills, trouble-free handling of crossing trajectories in the time-frequency plane, sharp performances in frequency detection in the case of mode-mixing problems, and a natural tolerance to noise. These results are compared with those obtained with empirical mode decomposition. We also show that WIME still gives meaningful results with real-life data, namely, the Oceanic Niño Index.

Single cell stimulation in vivo is a powerful tool to investigate the properties of single neurons and their functionality in neural networks. We present a method to determine a cell-specific stimulus that reliably evokes a prescribed spike train with high temporal precision of action potentials. We test the performance of this stimulus in simulations for two different stochastic neuron models. For a broad range of parameters and a neuron firing with intermediate firing rates (20–40 Hz) the reliability in evoking the prescribed spike train is close to its theoretical maximum that is mainly determined by the level of intrinsic noise.

We consider a quasistatic quantum Otto cycle using two effectively two-level systems with degeneracy in the excited state. The systems are coupled through isotropic exchange interaction of strength $J>0$, in the presence of an external magnetic field $B$ which is varied during the cycle. We prove the positive work condition and show that level degeneracy can act as a thermodynamic resource, so that a larger amount of work can be extracted than in the nondegenerate case, both with and without coupling. We also derive an upper bound for the efficiency of the cycle. This bound is the same as derived for a system of coupled spin-1/2 particles [G. Thomas and R. S. Johal, Phys. Rev. E 83, 031135 (2011)], i.e., without degeneracy, and depends only on the control parameters of the Hamiltonian, being independent of the level degeneracy and the reservoir temperatures.

The role of nonlinear dissipation in vibrational resonance (VR) is investigated in an inhomogeneous system characterized by a symmetric and spatially periodic potential and subjected to nonuniform state-dependent damping and a biharmonic driving force. The contributions of the parameters of the high-frequency signal to the system's effective dissipation are examined theoretically in comparison to linearly damped systems, for which the parameter of interest is the effective stiffness in the equation of slow vibration. We show that the VR effect can be enhanced by varying the nonlinear dissipation parameters and that it can be induced by a parameter that is shared by the damping inhomogeneity and the system potential. Furthermore, we have apparently identified the origin of the nonlinear-dissipation-enhanced response: We provide evidence of its connection to a Hopf bifurcation, accompanied by monotonic attractor enlargement in the VR regime.

Ecological diversity is ubiquitous despite the restrictions imposed by competitive exclusion and apparent competition. To explain the observed richness of species in a given habitat, food-web theory has explored nonlinear functional responses, self-interaction, or spatial structure and dispersal—model ingredients that have proven to promote stability and diversity. We return instead here to classical Lotka-Volterra equations, where species-species interaction is characterized by a simple product and spatial restrictions are ignored. We quantify how this idealization imposes constraints on coexistence and diversity for many species. To this end, we introduce the concept of free and controlled species and use this to demonstrate how stable food webs can be constructed by the sequential addition of species. The resulting food webs can reach dozens of species and generally yield nonrandom degree distributions in accordance with the constraints imposed through the assembly process. Our model thus serves as a formal starting point for the study of sustainable interaction patterns between species.

We measure experimentally and analyze the resisting force exerted by a bidimensional packing of small disks on a larger intruder disk dragged horizontally at constant velocity $V_0$. Depending on the vibration level of the packing that leads to a granular “cold” or “hot” packing, two force regimes are observed. At low vibration level (“cold” granular medium), the drag force $F$ does not depend on $V_0$, whereas for high vibrations (“hot” granular medium), the drag force increases linearly with $V_0$. Both regimes can be understood by the balance of two “granular temperatures” that can be defined in the system: a bulk temperature $T_b$ imposed by the external vibration to the overall packing and a local temperature $T_0$ induced by the own motion of the intruder disk in its vicinity. All experimental data obtained for different sizes and velocities of the intruder disk are shown to be governed by the temperature ratio $T_0/T_b$. A critical velocity $V_{0c}$, above which the system switches from “hot” to “cold,” can be obtained in this frame. Finally, we discuss how these two “viscous” regimes should be followed by an inertial regime where the drag force $F$ should increase as ${V_0}^2$ at high enough velocity values, for $V_0$ greater than a critical value $V_{0i}$ corresponding to high enough Reynolds or Froude number.

Massively parallel simulations of transport equation systems call for a paradigm change in algorithm development to achieve efficient scalability. Traditional approaches require time synchronization of processing elements (PEs), which severely restricts scalability. Relaxing synchronization requirement introduces error and slows down convergence. In this paper, we propose and develop a novel “proxy equation” concept for a general transport equation that (i) tolerates asynchrony with minimal added error, (ii) preserves convergence order and thus, (iii) expected to scale efficiently on massively parallel machines. The central idea is to modify a priori the transport equation at the PE boundaries to offset asynchrony errors. Proof-of-concept computations are performed using a one-dimensional advection (convection) diffusion equation. The results demonstrate the promise and advantages of the present strategy.

The escape of two harmonically coupled Brownian particles across the fluctuating barrier of a bistable potential is investigated with correlated additive and multiplicative fluctuations. Positive correlations enhance the rate of escape across the barrier when the coupling is effective, whereas for weakly coupled particles, escape becomes difficult. It is found that the system exhibits the phenomenon of resonant activation when the rate of barrier fluctuations is comparable to the relaxation time in the bistable potential. Using a decoupling ansatz, we derive the Markovian limit of the problem in the steady state, under the constraint that the barriers fluctuate on a time scale faster than the relative oscillation of the two particles. Adiabatic elimination of the fast variable of the dynamical system is discussed in appropriate limits.

We investigate the coexistence of low- and high-frequency oscillations in a delayed optoelectronic oscillator. We identify two nearby Hopf bifurcation points exhibiting low and high frequencies and demonstrate analytically how they lead to stable solutions. We then show numerically that these two branches of solutions undergo higher order instabilities as the feedback rate is increased but remain separated in the bifurcation diagram. The two bifurcation routes can be followed independently by either progressively increasing or decreasing the bifurcation parameter.

The speed and stability of fronts near a weakly subcritical steady-state bifurcation are studied, focusing on the transition between pushed and pulled fronts in the bistable Ginzburg-Landau equation. Exact nonlinear front solutions are constructed and their stability properties investigated. In some cases, the exact solutions are stable but are not selected from arbitrary small amplitude initial conditions. In other cases, the exact solution is unstable to modulational instabilities which select a distinct front. Chaotic front dynamics may result and is studied using numerical techniques.

Bilayers of chiral molecules can self-assemble into twisted and tubular structures, as was recently shown with chiral molecular constituents such as ssDNA-amphiphiles. I show that the dynamics of the transition between these topologies is driven by a nucleation mechanism that bears a striking formal similarity to that encountered in first-order wetting and dewetting transitions. Exploiting this analogy enables the critical nuclei of the transition to be calculated.

We report on an experimental investigation of craters generated by explosions at the surface of a model granular bed. Following the initial blast, a pressure wave propagates through the bed, producing high-speed ejecta of grains and ultimately a crater. We analyzed the crater morphology in the context of large-scale explosions and other cratering processes. The process was analyzed in the context of large-scale explosions, and the crater morphology was compared with those resulting from other cratering processes in the same energy range. From this comparison, we deduce that craters formed through different mechanisms can exhibit fine surface features depending on their origin, at least at the laboratory scale. Moreover, unlike laboratory-scale craters produced by the impact of dense spheres, the diameter and depth do not follow a $1/4$-power-law scaling with energy, rather the exponent observed herein is approximately 0.30, as has also been found in large-scale events. Regarding the ejecta curtain of grains, its expansion obeys the same time dependence followed by shock waves produced by underground explosions. Finally, from experiments in a two-dimensional system, the early cavity growth is analyzed and compared to a recent study on explosions at the surface of water.

In this paper we use a formal discrete-to-continuum procedure to derive a continuum variational model for two chains of atoms with slightly incommensurate lattices. The chains represent a cross section of a three-dimensional system consisting of a graphene sheet suspended over a substrate. The continuum model recovers both qualitatively and quantitatively the behavior observed in the corresponding discrete model. The numerical solutions for both models demonstrate the presence of large commensurate regions separated by localized incommensurate domain walls.

We compute the free energy of the planar monomer-dimer model. Unlike the classical planar dimer model, an exact solution is not known in this case. Even the computation of the low-density power series expansion requires heavy and nontrivial computations. Despite the exponential computational complexity, we compute almost three times more terms than were previously known. Such an expansion provides both lower and upper bounds for the free energy and makes it possible to obtain more accurate numerical values than previously possible. We expect that our methods can be applied to other similar problems.