An isotropic magnetoelastic phase-field-crystal model to study the relation between morphological structure and magnetic properties of pure ferromagnetic solids is introduced. Analytic calculations in two dimensions were used to determine the phase diagram and obtain the relationship between elastic strains and magnetization. Time-dependent numerical simulations in two dimensions were used to demonstrate the effect of grain boundaries on the formation of magnetic domains. It was shown that the grain boundaries act as nucleating sites for domains of reverse magnetization. Finally, we derive a relation for coercivity versus grain misorientation in the isotropic limit.

Using acoustic resonators, we have studied the occurrence and the magnitude of partial slip between glass spheres and polymer surfaces. The measurement relies on the shifts of resonance frequency and bandwidth, Δ$f$ and ΔΓ, induced by the contact as well as the dependence of Δ$f$ and ΔΓ on the amplitude of oscillation. One often finds a decrease of Δ$f$ at elevated amplitudes, which goes back to partial slip (also “microslip”). Building on two different models of partial slip, we derive the frequency-amplitude relation from the force-displacement relation. In accordance with both models, the bandwidth is found to increase with amplitude in the partial slip regime. For the highest amplitudes and largest spheres investigated, one observes a decrease of bandwidth with amplitude, which is interpreted as a transition to gross slip. Deviating from both models of partial slip, Δ$f$ is sometimes found to be independent of amplitude in the low-amplitude range. Constant Δ$f$ implies linear force-displacement relations. The critical amplitude for the onset of partial slip depends on the contact radius, where partial slip is more pronounced for larger contacts. This finding can be explained by a smooth stress profile at the edge of the contact with no singularity. The stress at the edge might be lowered by nanoscale roughness, by capillary forces, or by the inability of the two surfaces to reestablish a sticking contact at the turning point of the oscillation.

We discuss the cholesteric-nematic transition induced by an external field in a cell in the shape of a slab of finite thickness whose anchoring energy is infinitely strong on one surface and negligible on the other. The case where the surface orientations of the cholesteric director are parallel in the ground state is considered. In a sample of thickness $\ell$, multiple of the natural periodicity of the system $\Lambda$, the number of complete twists in the cholesteric liquid crystal is reduced by increasing the strength of the external distorting field. The sequence of the field values for expelling complete twists accumulate as the strength of the field approaches a critical value. Beyond this critical value the system assumes an unwinding configuration going toward a uniform structure, corresponding to nematic phase. Generalization of the results to the weak-weak anchoring cell case is also discussed. In our analysis the anisotropic part of the surface energy is assumed or very large or very small with respect to the total energy per unit surface due to the bulk distortion induced by the magnetic field.

Using density-functional theory in the restricted-orientation approximation, we analyze the liquid-crystal patterns and phase behavior of a fluid of hard rectangular particles confined in a two-dimensional square nanocavity of side length $H$ composed of hard inner walls. Patterning in the cavity is governed by surface-induced order as well as capillary and frustration effects and depends on the relative values of the particle aspect ratio $\kappa \equiv L/\sigma$, with $L$ the length and $\sigma$ the width of the rectangles ($L\ge \sigma$), and cavity size $H$. Ordering may be very different from bulk ($H\to \infty$) behavior when $H$ is a few times the particle length $L$ (nanocavity). Bulk and confinement properties are obtained for the cases $\kappa =1$, 3, and 6. In bulk the isotropic phase is always stable at low packing fractions $\eta =L\sigma {\rho }_0$ (with ${\rho }_0$ the average density) and nematic, smectic, columnar, and crystal phases can be stabilized at higher $\eta$ depending on $\kappa$: For increasing $\eta$ the sequence of isotropic to columnar is obtained for $\kappa =1$ and 3, whereas for $\kappa =6$ we obtain isotropic to nematic to smectic (the crystal being unstable in all three cases for the density range explored). In the confined fluid surface-induced frustration leads to fourfold symmetry breaking in all phases (which become twofold symmetric). Since no director distortion can arise in our model by construction, frustration in the director orientation is relaxed by the creation of domain walls (where the director changes by ${90}^{\circ }$); this configuration is necessary to stabilize periodic phases. For $\kappa =1$ the crystal becomes stable with commensurate transitions taking place as $H$ is varied. These transitions involve structures with different number of peaks in the local density. In the case $\kappa =3$ the commensurate transitions involve columnar phases with different number of columns. In the case $\kappa =6$ the high-density region of the phase diagram is dominated by commensurate transitions between smectic structures; at lower densities there is a symmetry-breaking isotropic to nematic transition exhibiting nonmonotonic behavior with cavity size. Apart from the present application in a confinement setup, our model could be used to explore the bulk region near close packing in order to elucidate the possible existence of disordered phases at close packing.

Short double-stranded DNA molecules exhibit a softening transition under large bending which is quantitatively described by a critical bending torque ${\tau }_c$ at which the molecule develops a kink. Through equilibrium measurements of the elastic energy of short (∼10 nm), highly stressed DNA molecules with a nick at the center we determine ${\tau }_c$ for different sequences around the nick. We find that ${\tau }_c$ is a robust materials parameter essentially independent of sequence. The measurements also show that, at least for nicked DNA, the local structure at the origin of the softening transition is not a single-stranded “bubble.”

Herein we provide a closed form perturbative solution to a general $M$-node network susceptible-infected-susceptible (SIS) model using the transport rates between nodes as a perturbation parameter. We separate the dynamics into a short-time regime and a medium-to-long-time regime. We solve the short-time dynamics of the system and provide a limit before which our explicit, analytical result of the first-order perturbation for the medium-to-long-time regime is to be employed. These stitched calculations provide an approximation to the full temporal dynamics for rather general initial conditions. To further corroborate our results, we solve the mean-field equations numerically for an infectious SIS outbreak in New Zealand (NZ, Aotearoa) recomposed into 23 subpopulations where the virus is spread to different subpopulations via (documented) air traffic data, and the country is internationally quarantined. We demonstrate that our analytical predictions compare well to the numerical solution.

Small regulatory RNAs (srRNAs) are important regulators of gene expression in eukaryotes and prokaryotes. A common motif containing srRNA is a bistable two-gene motif where one gene codes for a transcription factor (TF) which represses the transcription of the second gene, whose transcript is a srRNA which targets the first gene's transcript. Here, we investigate the properties of this motif in a stochastic model which takes the low copy numbers of the RNA components into account. First, we examine the conditions for stability of the two “noisy attractors.” We find that for realistic low copy numbers, extreme, but within realistic intervals, mutual repression strengths are required to compensate for the variability of the RNA numbers and thus, achieve long-term bistability. Second, the promoter initiation kinetics is found to strongly influence the bistability of the switch. Super-Poissonian RNA production disrupts the ability of the srRNA to silence its target, though sub-Poissonian RNA production does not rule out the need for strong mutual repression. Finally, we show that asymmetry between the two interactions forming the switch allows an external input to induce the transition from “high srRNA” to “‘high TF” more easily (i.e., with a shorter input) than in the opposite direction. We hypothesize that this asymmetric switching property allows these circuits to be more sensitive to one external input, without sacrificing the stability of one of the noisy attractors.

Although the community structure organization is an important characteristic of real-world networks, most of the traditional network models fail to reproduce the feature. Therefore, the models are useless as benchmark graphs for testing community detection algorithms. They are also inadequate to predict various properties of real networks. With this paper we intend to fill the gap. We develop an exponential random graph approach to networks with community structure. To this end we mainly built upon the idea of blockmodels. We consider both the classical blockmodel and its degree-corrected counterpart and study many of their properties analytically. We show that in the degree-corrected blockmodel, node degrees display an interesting scaling property, which is reminiscent of what is observed in real-world fractal networks. A short description of Monte Carlo simulations of the models is also given in the hope of being useful to others working in the field.

We investigate the scaling behavior in the statistical properties of Barkhausen noise in ferromagnetic films. We apply the statistical treatment usually employed for bulk materials in experimental Barkhausen noise time series measured with the traditional inductive technique in polycrystalline ferromagnetic films having different thickness from 100 to 1000 nm and determine the scaling exponents. Based on this procedure, we group the samples in a single universality class, since the scaling behavior of Barkhausen avalanches is characterized by exponents $\tau \sim 1.5$, $\alpha \sim 2.0$, and $1/\sigma \nu z\sim \vartheta \sim 2.0$ for all the films. We interpret these results in terms of theoretical models and provide experimental evidence that a well-known mean-field model for the dynamics of a ferromagnetic domain wall in three-dimensional ferromagnets can be extended for films. We identify that the films present an universal three-dimensional magnetization dynamics, governed by long-range dipolar interactions, even at the smallest thicknesses, indicating that the two-dimensional magnetic behavior commonly verified for films cannot be generalized for all thickness ranges.

We study dynamics of a serial array of spin-torque oscillators with a parallel inductor-capacitor-resistor ($LCR$) load. In a large range of parameters the fully synchronous regime, where all the oscillators have the same state and the output field is maximal, is shown to be stable. However, not always such a robust complete synchronization develops from a random initial state; in many cases nontrivial clustering is observed, with a partial synchronization resulting in a quasiperiodic or chaotic mean-field dynamics.

Numerically, we study the time fluctuations of few-body observables after relaxation in isolated dynamical quantum systems of interacting particles. Our results suggest that they decay exponentially with system size in both regimes, integrable and chaotic. The integrable systems considered are solvable with the Bethe ansatz and have a highly nondegenerate spectrum. This is in contrast with integrable Hamiltonians mappable to noninteracting ones. We show that the coefficient of the exponential decay depends on the level of delocalization of the initial state with respect to the energy shell.

The effect of a weak source of noise on the chaotic scattering is relevant to situations of physical interest. We investigate how a weak source of additive uncorrelated Gaussian noise affects both the dynamics and the topology of a paradigmatic chaotic scattering problem as the one taking place in the open nonhyperbolic regime of the Hénon-Heiles Hamiltonian system. We have found long transients for the time escape distributions for critical values of the noise intensity for which the particles escape slower as compared with the noiseless case. An analysis of the survival probability of the scattering function versus the Gaussian noise intensity shows a smooth curve with one local maximum and with one local minimum which are related to those long transients and with the basin structure in phase space. On the other hand, the computation of the exit basins in phase space shows a quadratic curve for which the basin boundaries lose their fractal-like structure as noise turned on.

Here, we capture the consequences of solvent-mediated nonelectrostatic ion-ion interactions, coupled with the considerations of finite-sized effects of the ionic species, on electrokinetic transport in narrow fluidic confinements. We consider pressure-driven flow in microchannels and nanochannels in the presence of electrical double layer effects and analyze the establishment of a streaming potential as mediated by a Yukawa-like pair potential that integrates the ion specificity with the governing nonelectrostatic interactions. We bring out the influences of these interactions on electroviscous effects manifested due to the establishment of the streaming potential. Our considerations provide a plausible explanation for the gross overestimation of electrokinetic energy conversion efficiencies as predicted by classical electrical double layer theories that ignore nonelectrostatic interactions between the ionic species.

The intersection between a network of polygonal fractures and a cubic cavity is numerically studied. Several probabilities are defined and particular attention is paid to the probabilities of intersection or not of the percolating cluster with the cavity; they depend on the size of the domain, on the fracture density, and on the relative size of the fractures and of the cavity. These probabilities are extrapolated to infinite domains. Analytical approximations are proposed which are in good agreement with the numerical data for sufficiently large densities. Some extensions of practical and theoretical interests are given in the concluding remarks.

It is shown numerically that a rotating inviscid liquid ring has a temporally oscillating state, where the radius of the ring varies periodically because of the competition between the centrifugal force and the centripetal force caused by the surface tension. Stability analysis reveals that an enlarging or shrinking ring is unstable to a varicose-type mode, which is affected by both the radial velocity and the radius ratio between the cross section and the ring. Furthermore, uniform rotation of a ring leads to a traveling unstable mode, whose frequency is determined by a simple sinuous mode, while the surface shape is modulated by the varicose mode and twisted by the rotation-induced Coriolis force.

The physics of miscible flow displacements with unfavorable mobility ratios through horizontal layered heterogeneous media is investigated. The flow model is solved numerically, and the effects of various physical parameters such as the injection velocity, diffusion, viscosity, and the heterogeneity length scale and variance are examined. The flow instability is characterized qualitatively through concentration contours as well as quantitatively through the mixing zone length and the breakthrough time. This characterization allowed us to identify four distinct regimes that govern the flow displacement. Furthermore, a scaling of the model resulted in generalized curves of the mixing zone length for any flow scenario in which the first three regimes of diffusion, channeling, and lateral dispersion superpose into a single unifying curve and allowed us to clearly identify the onset of the fourth regime. A critical effective Péclet number $w_c^{*}$ based on the layers’ width is proposed to identify flows where heterogeneity effects are expected to be important and those where the flow can be safely treated as homogeneous. A similar scaling of the breakthrough time was obtained and allowed us to identify two optimal effective Péclet numbers $w_{\mathrm{opt}}^{*}$ that result in the longest and shortest breakthrough times for any flow displacement.

Thermophysical properties of hydrogen, helium, and hydrogen-helium mixtures have been investigated in the warm dense matter regime at electron number densities ranging from $6.02\times {10}^{29}\sim 2.41\times {10}^{30}$ m${}^{-3}$ and temperatures from 4000 to $20000$ K via quantum molecular dynamics simulations. We focus on the dynamical properties such as the equation of states, diffusion coefficients, and viscosity. Mixing rules (density matching, pressure matching, and binary ionic mixing rules) have been validated by checking composite properties of pure species against that of the fully interacting mixture derived from quantum molecular dynamics simulations. These mixing rules reproduce pressures within 10% accuracy, while it is 75% and 50% for the diffusion and viscosity, respectively. The binary ionic mixing rule moves the results into better agreement. Predictions from one component plasma model are also provided and discussed.

The divergence that occurs at large impact parameters in Stark collision operators is examined for low-density hydrogen plasmas. In a previous work [J. Rosato, H. Capes, and R. Stamm, Phys. Rev. E 86, 046407 (2012)], we showed that the correlations between a radiating atom and the charged particles surrounding it affect the mean evolution of the atom, resulting in a mitigation of the Stark broadening near the line center. In this work, we examine the physical mechanism underlying this mitigation with an approach inspired from the standard semiclassical impact model. Our approach accounts for the atom-perturber correlations in a simple fashion, through a cutoff at large impact parameters, and embraces the impact model in the weakly coupled plasma limit. Comparisons with numerical simulations are performed and indicate a good agreement.

In this article we study numerically the final state of the two-dimensional ferromagnetic critical Ising model after a quench to zero temperature. Beginning from equilibrium at $T_c$, the system can be blocked in a variety of infinitely long lived stripe states in addition to the ground state. Similar results have already been obtained for an infinite temperature initial condition and an interesting connection to exact percolation crossing probabilities has emerged. Here we complete this picture by providing an example of stripe states precisely related to initial crossing probabilities for various boundary conditions. We thus show that this is not specific to percolation but rather that it depends on the properties of spanning clusters in the initial state.