A nonlinear Schrödinger equation that includes two terms with power-law nonlinearity and external potential modulated both on time and on the spatial coordinates is considered. The model appears in various branches of contemporary physics, especially in the case of lower values of the nonlinearity power. A significant generalization of the similarity transformations approach to construct explicit localized solutions for the model with arbitrary power-law nonlinearities is introduced. We obtain the exact analytical bright and kink soliton solutions of the governing equation for different nonlinearities and potentials that are of particular interest in applications to Bose-Einstein condensates and nonlinear optics. Necessary conditions on the physical parameters for propagating envelope formation are presented. The obtained results can be straightforwardly applied to a large variety of nonlinear Schrödinger models and hence would be of value to understand nonlinear phenomena in a diversity of nonlinear media.

The response of a traveling pulse to a local external stimulus is considered numerically for a modified three-component Oregonator, which is a model system for the photosensitive Belousov-Zhabotinsky (BZ) reaction. The traveling pulse is traced and constantly stimulated, with the distance between the pulse and the stimulus being kept constant. We are interested in the minimal strength of the spatially localized stimulus in order to eliminate the pulse. The use of a stimulus of small width allows us to detect the point in the pulse most sensitive to the external stimulus, referred to as the “Achilles' heel” of the traveling pulse, at which minimal strength of stimulus causes a collapse of the pulse. Our findings are demonstrated experimentally as well with the photosensitive BZ reaction.

Simplicial complexes describe collaboration networks, protein interaction networks, and brain networks and in general network structures in which the interactions can include more than two nodes. In real applications, often simplicial complexes are weighted. Here we propose a nonequilibrium model for weighted growing simplicial complexes. The proposed dynamics is able to generate weighted simplicial complexes with a rich interplay between weights and topology emerging not just at the level of nodes and links, but also at the level of faces of higher dimension.

We study a $q$-voter model with stochastic driving on a complete graph with $q$ being a random variable described by probability density function $P\left(q\right)$, instead of a constant value. We investigate two types of $P\left(q\right)$: (1) artificial with the fixed expected value $\langle q\rangle$, but a changing variance and (2) empirical of freely forming groups in informal places. We investigate also two types of stochasticity that can be interpreted as different kinds of nonconformity (anticonformity or independence) to answer the question about differences observed at the macroscopic level between these two types of nonconformity in real social systems. Moreover, we ask the question if the behavior of a system depends on the average value of the group size $q$ or rather on probability distribution function $P\left(q\right)$.

Current models for opinion dynamics typically utilize a Poisson process for speaker selection, making the waiting time between events exponentially distributed. Human interaction tends to be bursty though, having higher probabilities of either extremely short waiting times or long periods of silence. To quantify the burstiness effects on the dynamics of social models, we place in competition two groups exhibiting different speakers' waiting-time distributions. These competitions are implemented in the binary naming game and show that the relevant aspect of the waiting-time distribution is the density of the head rather than that of the tail. We show that even with identical mean waiting times, a group with a higher density of short waiting times is favored in competition over the other group. This effect remains in the presence of nodes holding a single opinion that never changes, as the fraction of such committed individuals necessary for achieving consensus decreases dramatically when they have a higher head density than the holders of the competing opinion. Finally, to quantify differences in burstiness, we introduce the expected number of small-time activations and use it to characterize the early-time regime of the system.

Many cell signaling pathways involve the diffusion of messengers that bind and unbind to and from intracellular components. Quantifying their net transport rate under different conditions then requires having separate estimates of their free diffusion coefficient and binding or unbinding rates. In this paper, we show how performing sets of fluorescence correlation spectroscopy (FCS) experiments under different conditions, it is possible to quantify free diffusion coefficients and on and off rates of reaction-diffusion systems. We develop the theory and present a practical implementation for the case of the universal second messenger, calcium (${\mathrm{Ca}}^{2+}$) and single-wavelength dyes that increase their fluorescence upon ${\mathrm{Ca}}^{2+}$ binding. We validate the approach with experiments performed in aqueous solutions containing ${\mathrm{Ca}}^{2+}$ and Fluo4 dextran (both in its high and low affinity versions). Performing FCS experiments with tetramethylrhodamine-dextran in Xenopus laevis oocytes, we infer the corresponding free diffusion coefficients in the cytosol of these cells. Our approach can be extended to other physiologically relevant reaction-diffusion systems to quantify biophysical parameters that determine the dynamics of various variables of interest.

We perform experiments where air is injected at a constant overpressure $P_{\text{in}}$, ranging from 5 to 250 kPa, into a dry granular medium confined within a horizontal linear Hele-Shaw cell. The setup allows us to explore compacted configurations by preventing decompaction at the outer boundary, i.e., the cell outlet has a semipermeable filter such that beads are stopped while air can pass. We study the emerging patterns and dynamic growth of channels in the granular media due to fluid flow, by analyzing images captured with a high speed camera (1000 images/s). We identify four qualitatively different flow regimes, depending on the imposed overpressure, ranging from no channel formation for $P_{\text{in}}$ below 10 kPa, to large thick channels formed by erosion and fingers merging for high $P_{\text{in}}$ around 200 kPa. The flow regimes where channels form are characterized by typical finger thickness, final depth into the medium, and growth dynamics. The shape of the finger tips during growth is studied by looking at the finger width $w$ as function of distance $d$ from the tip. The tip profile is found to follow $w\left(d\right)\propto d^{\beta }$, where $\beta =0.68$ is a typical value for all experiments, also over time. This indicates a singularity in the curvature $d^{2}d/d{w}^2\sim \kappa \sim d^{1-2\beta }$, but not of the slope $dw/dd\sim d^{\beta -1}$, i.e., more rounded tips rather than pointy cusps, as they would be for the case $\beta >1$. For increasing $P_{\text{in}}$, the channels generally grow faster and deeper into the medium. We show that the channel length along the flow direction has a linear growth with time initially, followed by a power-law decay of growth velocity with time as the channel approaches its final length. A closer look reveals that the initial growth velocity $v_0$ is found to scale with injection pressure as $v_0\propto P_{\mathrm{in}}^{\frac{3}{2}}$, while at a critical time $t_c$ there is a cross-over to the behavior $v\left(t\right)\propto t^{-\alpha }$, where $\alpha$ is close to 2.5 for all experiments. Finally, we explore the fractal dimension of the fully developed patterns. For example, for patterns resulting from intermediate $P_{\text{in}}$ around 100–150 kPa, we find that the box-counting dimensions lie within the range $D_B\in [1.53,1.62]$, similar to viscous fingering fractals in porous media.

We theoretically study how the electro-osmotic fluid velocity in a charged cylindrical nanopore in a thin solid state membrane depends on the pore's geometry, membrane charge, and electrolyte concentration. We find that when the pore's length is comparable to its diameter, the velocity profile develops a concave shape with a minimum along the pore axis unlike the situation in very long nanopores with a maximum velocity along the central pore axis. This effect is attributed to the induced pressure along the nanopore axis due to the fluid flow expansion and contraction near the exit or entrance to the pore and to the reduction of electric field inside the nanopore. The induced pressure is maximal when the pore's length is about equal to its diameter while decreasing for both longer and shorter nanopores. A model for the fluid velocity incorporating these effects is developed and shown to be in a good agreement with numerically computed results.

General methods for solving simultaneous nonlinear equations work by generating a sequence of approximate solutions that successively improve a measure of the total error. However, if the total error function has a narrow curved valley, the available techniques tend to find the solution after a very large number of steps, if ever. The solver first converges rapidly to the valley, but once there it converges extremely slowly to the solution. In this paper we show that in the specific physically important case where these valleys are the result of a softly broken symmetry, the solution can often be found much more quickly by adding the generators of the softly broken symmetry as auxiliary variables. This makes the number of variables more than the equations and hence there will be a family of solutions, any one of which would be acceptable. We present a procedure for finding solutions in this case and apply it to several simple examples and an important problem in the physics of false vacuum decay. We also provide a Mathematica package that implements Powell's hybrid method with the generalization to allow more variables than equations.

Shifting our electricity generation from fossil fuel to renewable energy sources introduces large fluctuations to the power system. Here, we demonstrate how increased fluctuations, reduced damping, and reduced intertia may undermine the dynamical robustness of power grid networks. Focusing on fundamental noise models, we derive analytic insights into which factors limit the dynamic robustness and how fluctuations may induce a system escape from an operating state. Moreover, we identify weak links in the grid that make it particularly vulnerable to fluctuations. These results thereby not only contribute to a theoretical understanding of how fluctuations act on distributed network dynamics, they may also help designing future renewable energy systems to be more robust.

The interplay between quenched disorder provided by a random field (RF) and network connectivity in the Blume-Capel (BC) model is the subject of this paper. The replica method is used to average over the network randomness. It offers an alternative analytic route to both numerical simulations and standard mean field approaches. The results reveal a rich thermodynamic scenario with multicritical points that are strongly dependent on network connectivity. In addition, we also demonstrate that the RF has a deep effect on the inverse melting transition. This highly nontrivial type of phase transition has been proposed to exist in the BC model as a function of network topology. Our results confirm that the topological mechanism can lead to an inverse melting transition. Nevertheless, our results also show that as the RF becomes stronger, the paramagnetic phase is affected in such way that the topological mechanism for inverse melting is disabled.

We propose a set of general coupling conditions to select a coupling profile (a set of coupling matrices) from the linear flow matrix of dynamical systems for realizing global stability of complete synchronization (CS) in identical systems and robustness to parameter perturbation. The coupling matrices define the coupling links between any two oscillators in a network that consists of a conventional diffusive coupling link (self-coupling link) as well as a cross-coupling link. The addition of a selective cross-coupling link in particular plays constructive roles that ensure the global stability of synchrony and furthermore enables robustness of synchrony against small to nonsmall parameter perturbation. We elaborate the general conditions for the selection of coupling profiles for two coupled systems, three- and four-node network motifs analytically as well as numerically using benchmark models, the Lorenz system, the Hindmarsh-Rose neuron model, the Shimizu-Morioka laser model, the Rössler system, and a Sprott system. The role of the cross-coupling link is, particularly, exemplified with an example of a larger network, where it saves the network from a breakdown of synchrony against large parameter perturbation in any node. The perturbed node in the network transits from CS to generalized synchronization (GS) when all the other nodes remain in CS. The GS is manifested by an amplified response of the perturbed node in a coherent state.

Recent investigations on the Hamiltonian of excitons by Schweiner et al.. [Phys. Rev. Lett. 118, 046401 (2017)] revealed that the combined presence of a cubic band structure and external fields breaks all antiunitary symmetries. The nearest-neighbor spacing distribution of magnetoexcitons can exhibit Poissonian statistics, the statistics of a Gaussian orthogonal ensemble (GOE), or a Gaussian unitary ensemble (GUE) depending on the system parameters. Hence, magnetoexcitons are an ideal system to investigate the transitions between these statistics. Here we investigate the transitions between GOE and GUE statistics and between Poissonian and GUE statistics by changing the angle of the magnetic field with respect to the crystal lattice and by changing the scaled energy known from the hydrogen atom in external fields. Comparing our results with analytical formulas for these transitions derived with random matrix theory, we obtain a very good agreement and thus confirm the Wigner surmise for the exciton system.

We consider the Wright-Fisher model of the finite population evolution on a fitness landscape defined in the sequence space by a path of nearly neutral mutations. We study a specific structure of the fitness landscape: One of the intermediate mutations on the mutation path results in either a large fitness value (climbing up a fitness hill) or a low fitness value (crossing a fitness canyon), the rest of the mutations besides the last one are neutral, and the last sequence has much higher fitness than any intermediate sequence. We derive analytical formulas for the first arrival time of the mutant with two point mutations. For the first arrival problem for the further mutants in the case of canyon crossing, we analytically deduce how the mean first arrival time scales with the population size and fitness difference. The location of the canyon on the path of sequences has a crucial role. If the canyon is at the beginning of the path, then it significantly prolongs the first arrival time; otherwise it just slightly changes it. Furthermore, the fitness hill at the beginning of the path strongly prolongs the arrival time period; however, the hill located near the end of the path shortens it. We optimize the first arrival time by applying a nonzero selection to the intermediate sequences. We extend our results and provide a scaling for the valley crossing time via the depth of the canyon and population size in the case of a fitness canyon at the first position. Our approach is useful for understanding some complex evolution systems, e.g., the evolution of cancer.

Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on modeling the phenomenology of these stochastic dynamics has predominantly focused on one model, geometric Brownian motion (GBM), which can be described as the solution of a Langevin equation with linear drift and linear multiplicative noise. Using recent experimental results on stochastic exponential growth of individual bacterial cell sizes, we motivate the need for a more general class of phenomenological models of stochastic exponential growth, which are consistent with the observation that the mean-rescaled distributions are approximately stationary at long times. We show that this behavior is not consistent with GBM, instead it is consistent with power-law multiplicative noise with positive fractional powers. Therefore, we consider this general class of phenomenological models for stochastic exponential growth, provide analytical solutions, and identify the important dimensionless combination of model parameters, which determines the shape of the mean-rescaled distribution. We also provide a prescription for robustly inferring model parameters from experimentally observed stochastic growth trajectories.

We demonstrate an internal breakup mechanism for high Weber number drop impact on superhydrophobic surfaces uniformly patterned with submillimeter-scale textures, in which the liquid film ruptures from both interior and rim. The employment of submillimeter-scale posts could help decrease the critical Weber number of internal rupture, due to the small solid fraction and the large dimension ratio between primary structures and droplets. The internal rupture is found to promote more rapid drop bouncing than conventional rebound and rim breakup on superhydrophobic surfaces with small roughness, with a 10%–50% reduction of contact time. The internal rupture results from the film instability inside and the jet instability outside.

In this work, we introduce the Kaiser-Bessel interpolation basis for the particle-mesh interpolation in the fast Ewald method. A reliable a priori error estimate is developed to measure the accuracy of the force computation in correlated charge systems, and is shown to be effective in optimizing the shape parameter of the Kaiser-Bessel basis in terms of accuracy. By comparing the optimized Kaiser-Bessel basis with the traditional $B$-spline basis, we demonstrate that the former is more accurate than the latter in part of the working parameter space, say, a relatively small real-space cutoff, a relatively small reciprocal space mesh, and a relatively large truncation of basis. In some cases, the Kaiser-Bessel basis is found to be more than one order of magnitude more accurate.

Thermodynamic systems can be defined as composed by many identical interacting subsystems. Here it is shown how the dynamics of relaxation toward equilibrium of a thermodynamic system is closely related to the symmetry group of the Hamiltonian of the subsystems of which it is composed. The transitions between states driven by the interactions between identical subsystems correspond to elements of the root system associated to the symmetry group of their Hamiltonian. This imposes constraints on the relaxation dynamics of the complete thermodynamic system, which allow formulating its evolution toward equilibrium as a system of linear differential equations in which the variables are the thermodynamic forces of the system. The trajectory of a thermodynamic system in the space of thermodynamic forces corresponds to the negative gradient of a potential function, which depends on the symmetry group of the Hamiltonian of the individual interacting subsystems.

Photosynthesis is the basic process used by plants to convert light energy in reaction centers into chemical energy. The high efficiency of this process is not yet understood today. Using the formalism for the description of open quantum systems by means of a non-Hermitian Hamilton operator, we consider initially the interplay of gain (acceptor) and loss (donor). Near singular points it causes fluctuations of the cross section which appear without any excitation of internal degrees of freedom of the system. This process occurs therefore very quickly and with high efficiency. We then consider the excitation of resonance states of the system by means of these fluctuations. This second step of the whole process takes place much slower than the first one, because it involves the excitation of internal degrees of freedom of the system. The two-step process as a whole is highly efficient, and the decay is biexponential. We provide, if possible, the results of analytical studies, otherwise characteristic numerical results. The similarities of the obtained results to light harvesting in photosynthetic organisms are discussed.