The consequences of small scale-length precursor plasmas on high-intensity laser-driven relativistic electrons are studied via experiments and simulations. Longer scale-length plasmas are shown to dramatically increase the efficiency of electron acceleration, yet, if too long, they reduce the coupling of these electrons into the solid target. Evidence for the existence of an optimal plasma scale-length is presented and estimated to be from 1 to $5\mu \mathrm{m}$. Experiments on the Trident laser $\left(I=5\times {10}^{19}\mathrm{W}/{\mathrm{cm}}^2\right)$ diagnosed via $\mathrm{K}\alpha$ emission from Cu wires attached to Au cones are quantitively reproduced using 2D particle-in-cell simulations that capture the full temporal and spatial scale of the nonlinear laser interaction and electron transport. The simulations indicate that $32\%\pm 8\%(6.5\%\pm 2\%)$ of the laser energy is coupled into electrons of all energies (1–3 MeV) reaching the inner cone tip and that, with an optimized scale-length, this could increase to 35% (9%).

Temperature gradients polarize water, a nonequilibrium effect that may result in significant electrostatic fields for strong thermal gradients. Using nonequilibrium molecular dynamics simulations, we show that the thermal polarization features a significant dependence with temperature that ultimately leads to an inversion phenomenon, whereby the polarization field reverses its sign at a specific temperature. Temperature inversion effects have been reported before in the Soret coefficient of aqueous solutions, where the solution changes from thermophobic to thermophilic at specific temperatures. We show that a similar inversion behavior is observed in pure water. Microscopically, the inversion is the result of a balance of dipolar and quadrupolar contributions and the strong temperature dependence of the quadrupolar contribution, which is determined by the thermal expansion of the liquid.

The pinch off of heterogeneous ferrofluid drops at a nozzle in air was experimentally investigated with a magnetic field (downward or upward) and without a magnetic field. Compared to homogeneous drops, the self-similarity and universal scaling law were verified through modifying the initial conditions, such as the nozzle diameter, flow rate, and magnitude and direction of the magnetic fields. Two pinch-off points were observed, and the two consecutive pinch-off dynamics were characterized through scaling laws. Here our scaling exponent remains within the scope of (0.70–0.80) for the primary whereas it remains within the scope of (0.60–0.70) for the secondary pinch off, respectively, comparable to the classic range from 2/3 to 1 for homogeneous drops. The gravity-compensating and gravity-superimposing magnetic fields display a negligible effect on the exponent but determine the sequence of double pinch offs. The universal character of the self-similar pinch off is extended to a heterogeneous fluid.

Markov processes restarted or reset at random times to a fixed state or region in space have been actively studied recently in connection with random searches, foraging, and population dynamics. Here we study the large deviations of time-additive functions or observables of Markov processes with resetting. By deriving a renewal formula linking generating functions with and without resetting, we are able to obtain the rate function of such observables, characterizing the likelihood of their fluctuations in the long-time limit. We consider as an illustration the large deviations of the area of the Ornstein-Uhlenbeck process with resetting. Other applications involving diffusions, random walks, and jump processes with resetting or catastrophes are discussed.

For a fixed-energy (FE) Manna sandpile model in one dimension, we investigate the critical behavior for regular initial conditions in which activities are distributed at regular intervals on average. The FE Manna model conserves the density $\rho$ of total particles and undergoes an absorbing phase transition at a critical ${\rho }_c$. For the regular initial conditions, we show via extensive simulations that the dynamical scaling behaviors differ from those of the random and the natural initial conditions. Off-critical scaling exponents $\beta$ and ${\nu }_{\perp }$ are also measured and shown to agree well with the values of the directed percolation (DP) class as reported by Basu et al. [Phys. Rev. Lett. 109, 015702 (2012)]. Our results suggest that the dynamical scaling behaviors depend on the characteristics of initial conditions, but the off-critical scaling behaviors in the steady state are independent of initial conditions and belong to the DP class.

Gas invasion in liquid-saturated sands exhibits different morphologies and dynamics. For mobile beds, the repeated rise of gas through the layer leads to the growth of a fluidized zone, which reaches a stationary shape. Here, we present experimental results characterizing the evolution of the fluidized region as a function of the gas-flow rate and grain size. We introduce a new observable, the flow density, which quantifies the motion of the grains in the system. The growth of the fluidized zone is characterized by a spatiotemporal analysis, which provides the stabilization time, ${\tau }_s$. In the stationary regime, we report two main contributions to motion in the fluidized region: the central gas rise and a convective granular motion. Interestingly, a static model with a fixed porous network accounts for the final shape of the invasion zone. We propose an explanation where the initial gas invasion weakens the system and fixes since the early stage the morphology of the fluidized zone.

An approach to predicting critical transitions from time series is introduced. A nonstationary low-order stochastic dynamical model of appropriate complexity to capture the transition mechanism under consideration is estimated from data. In the simplest case, the model is a one-dimensional effective Langevin equation, but also higher-dimensional dynamical reconstructions based on time-delay embedding and local modeling are considered. Integrations with the nonstationary models are performed beyond the learning data window to predict the nature and timing of critical transitions. The technique is generic, not requiring detailed a priori knowledge about the underlying dynamics of the system. The method is demonstrated to successfully predict a fold and a Hopf bifurcation well beyond the learning data window.

We perform a numerical investigation of the Lyapunov spectra of chaotic dynamics in lattices of classical spins in the vicinity of second-order ferromagnetic and antiferromagnetic phase transitions. On the basis of this investigation, we identify a characteristic of the shape of the Lyapunov spectra, the “$G$-index,” which exhibits a sharp peak as a function of temperature at the phase transition, provided the order parameter is capable of sufficiently strong dynamic fluctuations. As part of this work, we also propose a general numerical algorithm for determining the temperature in many-particle systems, where kinetic energy is not defined.

We explore the possibility of controlling the wake and drag of a spherical object independently of each other, using radial distributions of permeability in the Brinkman-Stokes formalism. By discretizing a graded-permeability shell into discrete, macroscopically homogeneous layers, we are able to sample the entire functional space of spherically-symmetric permeabilities and observe quick convergence to a certain manifold in the wake-drag coordinates. Monte Carlo samplings with ${10}^4–{10}^5$ points have become possible thanks to our new algorithm, which is based on exact analytical solutions for the Stokes flow through an arbitrary multilayer porous sphere. The algorithm is not restricted to the Brinkman-Stokes equation and can be modified to account for other types of scattering problems for spherically-symmetric systems with arbitrary radial complexity. Our main practical finding for Stokes flow is that it is possible to reduce a certain measure of wake of a spherical object without any energy penalty and without active (power-consuming) force generation.

As a key mechanism of submicron particle capture in wet deposition and wet scrubbing processes, thermophoresis is influenced by the flow and temperature fields. Three-dimensional direct numerical simulations were conducted to quantify the characteristics of the flow and temperature fields around a droplet at three droplet Reynolds numbers (Re) that correspond to three typical boundary-layer-separation flows (steady axisymmetric, steady plane-symmetric, and unsteady plane-symmetric flows). The thermophoretic motion of submicron particles was simulated in these cases. Numerical results show that the motion of submicron particles around the droplet and the deposition distribution exhibit different characteristics under three typical flow forms. The motion patterns of particles are dependent on their initial positions in the upstream and flow forms. The patterns of particle motion and deposition are diversified as Re increases. The particle motion pattern, initial position of captured particles, and capture efficiency change periodically, especially during periodic vortex shedding. The key effects of flow forms on particle motion are the shape and stability of the wake behind the droplet. The drag force of fluid and the thermophoretic force in the wake contribute jointly to the deposition of submicron particles after the boundary-layer separation around a droplet.

We study nonisothermal diffusion transport of a weakly soluble substance in a liquid-saturated porous medium in contact with a reservoir of this substance. The surface temperature of the porous medium half-space oscillates in time, which results in a decaying solubility wave propagating deep into the porous medium. In this system, zones of saturated solution and nondissolved phase coexist with ones of undersaturated solution. The effect is first considered for the case of annual oscillation of the surface temperature of water-saturated ground in contact with the atmosphere. We reveal the phenomenon of formation of a near-surface bubbly horizon due to temperature oscillation. An analytical theory of the phenomenon is developed. Further, the treatment is extended to the case of higher frequency oscillations and the case of weakly soluble solids and liquids.

We report charge inversion using Monte Carlo calculations for a negatively charged surface in aqueous solutions involving coions of different charges and monovalent counterions. It is shown that a rise in the valence of coions at moderate concentrations can substantially promote charge inversion for the surface charge values of biological relevance, regardless of the representation of surface charges but dependent in a nontrivial way on polarization effects resulting from dielectric discontinuity. These obtained characteristics challenge the traditional belief that the coions are generally considered to suppress charge inversion and expose the important role of coions of higher valence in tailoring the effective interactions of biomolecules with the cell membrane.

We study the thermostatistics of a damped bimodal particle, i.e., a particle of mass $m$ subject to a work reservoir that is analytically represented by the telegraph noise. Because of the colored nature of the noise, it does not fit the Lévy-Itô class of stochastic processes, making this system an instance of a nonequilibrium system in contact with a non-Gaussian external reservoir. We obtain the statistical description of the position and velocity, namely in the stationary state, as well as the (time-dependent) statistics of the energy fluxes in the system considering no constraints on the telegraph noise features. With that result we are able to give an account of the statistical properties of the large deviations of the injected and dissipated power that can change from sub-Gaussianity to super-Gaussianity depending on the color of the noise. By properly defining an effective temperature for this system, $\mathcal{T}$, we are capable of obtaining an equivalent entropy production-exchange rate equal to the ratio between the dissipation of the medium, $\gamma$, and the mass of the particle, $m$, a relation that concurs with the case of a standard thermal reservoir at temperature, $T=\mathcal{T}$.

We argue that a non-Markovian random walk on a fractal can be treated as a Markovian process in a fractional dimensional space with a suitable metric. This allows us to define the fractional dimensional space allied to the fractal as the $\nu$-dimensional space $F^{\nu }$ equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal ($\nu$) and fractal dimensionalities is deduced. The intrinsic time of random walk in $F^{\nu }$ is inferred. The Laplacian operator in $F^{\nu }$ is constructed. This allows us to map physical problems on fractals into the corresponding problems in $F^{\nu }$. In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.

We numerically demonstrate the dynamic stabilization of a strongly interacting many-body bosonic system which can be realized by coupled ultracold atom-molecule gases. The system is initialized to an unstable equilibrium state corresponding to a saddle point in the classical phase space, where subsequent free evolution gives rise to atom-molecule conversion. To control and stabilize the system, periodic modulation is applied that suddenly shifts the relative phase between the atomic and the molecular modes and limits their further interconversion. The stability diagram for the range of modulation amplitudes and periods that stabilize the dynamics is given. The validity of the phase diagram obtained from the time-average calculation is discussed by using the orbit tracking method, and the difference in contrast with the maximum absolute deviation analysis is shown as well. A brief quantum analysis shows that quantum fluctuations can put serious limitations on the applicability of the mean-field results.

Hydrofracturing to recover natural gas and oil relies on the creation of a fracture network with pressurized water. We analyze the creation of the network in two ways. First, we assemble a collection of analytical estimates for pressure-driven crack motion in simple geometries, including crack speed as a function of length, energy dissipated by fluid viscosity and used to break rock, and the conditions under which a second crack will initiate while a first is running. We develop a pseudo-three-dimensional numerical model that couples fluid motion with solid mechanics and can generate branching crack structures not specified in advance. One of our main conclusions is that the typical spacing between fractures must be on the order of a meter, and this conclusion arises in two separate ways. First, it arises from analysis of gas production rates, given the diffusion constants for gas in the rock. Second, it arises from the number of fractures that should be generated given the scale of the affected region and the amounts of water pumped into the rock.

We examine the ejection of an initially strongly confined flexible polymer from a spherical capsid through a nanoscale pore. We use molecular dynamics for unprecedentedly high initial monomer densities. We show that the time for an individual monomer to eject grows exponentially with the number of ejected monomers. By measurements of the force at the pore we show this dependence to be a consequence of the excess free energy of the polymer due to confinement growing exponentially with the number of monomers initially inside the capsid. This growth relates closely to the divergence of mixing energy in the Flory-Huggins theory at large concentration. We show that the pressure inside the capsid driving the ejection dominates the process that is characterized by the ejection time growing linearly with the lengths of different polymers. Waiting time profiles would indicate that the superlinear dependence obtained for polymers amenable to computer simulations results from a finite-size effect due to the final retraction of polymers' tails from capsids.

The dynamics of solitons is considered in the framework of an extended nonlinear Schrödinger equation (NLSE), which is derived from a Zakharov-type model for wind-driven high-frequency surface waves in the ocean, coupled to damped low-frequency internal waves. The drive gives rise to a convective (but not absolute) instability in the system. The resulting NLSE includes a pseudo-stimulated-Raman-scattering (pseudo-SRS) term, which is a spatial-domain counterpart of the SRS term, a well-known ingredient of the temporal-domain NLSE in optics. Analysis of the field-momentum balance and direct simulations demonstrates that wave-number downshift by the pseudo-SRS may be compensated by the upshift induced by the wind traction, thus maintaining robust bright solitons in both stationary and oscillatory forms; in particular, they are not destroyed by the underlying convective instability. Analytical soliton solutions are found in an approximate form and are verified by numerical simulations. Solutions for soliton pairs are obtained in the numerical form.

Hydrodynamic interactions between a pair of capsules in simple shear are numerically investigated using a front-tracking finite difference method. The membrane of the capsule is modeled using different hyperelastic constitutive relations. We also compare the pair interactions between drops to those between capsules. An increased viscosity ratio leads to a reduced net cross-stream separation between capsules as well as drops after collision. At low viscosity ratios, for the same capillary number drop-pairs show higher cross-stream separation than those for capsule-pairs, while substantially large viscosity ratios result in almost the same value for both cases. We investigate pair-collisions between two heterogeneous capsules ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ with two different capillary numbers. The maximum deformation of ${\mathrm{C}}_1$ was seen to increase with increasing stiffness (decreasing capillary number) of ${\mathrm{C}}_2$, even though the stiffness of ${\mathrm{C}}_1$ was kept fixed. The findings are similar for a drop-pair, however, with a smaller maximum deformation for the same combinations of capillary numbers. The final cross-stream drift of the trajectory of ${\mathrm{C}}_1$ decreases with the increasing stiffness of ${\mathrm{C}}_2$, but the relative trajectory between the capsules remains unchanged. The maximum deformation and the cross-stream drift of the trajectory of ${\mathrm{C}}_1$ are shown to approximately vary with power-law functions of the ratio of the capillary numbers of ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$. An analytical explanation of the dependence on the two capillary numbers is offered. Different membrane constitutive laws result in similar deformation and drift in trajectory.