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In this paper, we account for the many critical exponents derived from the studies of the electrical conductivity in porous media by applying analysis of the well-known relation known as Archie's law. In spite of its seeming simplicity this law is considered to be "poorly understood," and the question that was and still is debated in the literature is whether there is some "hidden physics" in this law, or if it is "strictly a parametrization use for curve fitting with a priori no physical meaning." Our solution to the corresponding long-debated 78 years old puzzle is based on the classical percolation theory, but it also involves a principle that is based on continuum percolation. This principle is that the electrical properties of a percolation system are determined by the interplay between the connectivity of the conducting objects in that system, and the connectivity of the intersections between pairs of them. We thus propose a general concept that we call an electrically affected connectivity, and we predfrom Archie's-law data, within the framework of the percolation phase transition, is expected to open a new direction in the understanding and the applications of this law.A variety of theoretical models have been proposed to calculate the stopping power of charged particles in matter, which is a fundamental issue in many fields. However, the approximation adopted in these theories will be challenged under warm dense matter conditions. Molecular dynamics (MD) simulation is a good way to validate the effectiveness of these models. We investigate the stopping power of warm dense hydrogen for electrons with projectile energies ranging from 400-10000 eV by means of an electron force field (eFF) method, which can effectively avoid the Coulomb catastrophe in conventional MD calculations. It is found that the stopping power of warm dense hydrogen decreases with increasing temperature of the sample at those high projectile velocities. This phenomenon could be explained by the effect of electronic structure dominated by bound electrons, which is further explicated by a modified random phase approximation (RPA) model based on local density approximation proper to inhomogeneous media. Most of the models extensively accepted by the plasma community, e.g., Landau-Spitzer model, Brown-Preston-Singleton model and RPA model, cannot well address the effect caused by bound electrons so that their predictions of stopping power contradict our result. Therefore, the eFF simulations of this paper reveals the important role played by the bound electrons on stopping power in warm dense plasmas.Gene transcription is a complex multistep biochemical process, which can create memory between individual reaction events. On the other hand, many inducible genes, when activated by external cues, are often coregulated by several competitive pathways with crosstalk. This raises an unexplored question how do molecular memory and crosstalk together affect gene expressions? To address this question, we introduce a queuing model of stochastic transcription, where two crossing signaling pathways are used to direct gene activation in response to external signals and memory functions to model multistep reaction processes involved in transcription. We first establish, based on the total probability principle, the chemical master equation for this queuing model, and then we derive, based on the binomial moment approach, exact expressions for statistical quantities (including distributions) of mRNA, which provide insights into the roles of crosstalk and memory in controlling the mRNA level and noise. We find that molecular memory of gene activation decreases the mRNA level but increases the mRNA noise, and double activation pathways always reduce the mRNA noise in contrast to a single pathway. In addition, we find that molecular memory can make the mRNA bimodality disappear.The stochastic dynamics of an electron in counterpropagating linearly polarized laser beams is analyzed using a recently developed 3/2-dimensional Hamiltonian approach. It is shown that perpendicular canonical momenta suppress stochasticity, helping to explain the results from recently reported numerical studies of stochastic dynamics in a similar setting. The stochasticity in a perpendicular polarization setup is demonstrated. Lastly, the impact of radiation friction effects is considered, and shown to be negligible in the classical radiation reaction limit.The Fluctuation-Dissipation Theorem (FDT) is a powerful tool to estimate the thermal noise of physical systems in equilibrium. In general, however, thermal equilibrium is an approximation or cannot be assumed at all. A more general formulation of the FDT is then needed to describe the behavior of the fluctuations. In our experiment we study a microcantilever brought out of equilibrium by a strong heat flux generated by the absorption of the light of a laser. While the base is kept at cryogenic temperatures, the tip is heated up to the melting point, thus creating the highest temperature difference the system can sustain. We independently estimate the temperature profile of the cantilever and its mechanical fluctuations as well as its dissipation. We then demonstrate how the thermal fluctuations of all the observed degrees of freedom, though increasing with the heat flux, are much lower than what is expected from the average temperature of the system. We interpret these results using a minimal extension of the FDT this dearth of thermal noise arises from a dissipation shared between clamping losses and distributed damping.We study discrete-time random walks on arbitrary networks with first-passage resetting processes. To the end, a set of nodes are chosen as observable nodes, and the walker is reset instantaneously to a given resetting node whenever it hits either of observable nodes. Epacadostat mw We derive exact expressions of the stationary occupation probability, the average number of resets in the long time, and the mean first-passage time between arbitrary two nonobservable nodes. We show that all the quantities can be expressed in terms of the fundamental matrix Z=(I-Q)^-1, where I is the identity matrix and Q is the transition matrix between nonobservable nodes. Finally, we use ring networks, two-dimensional square lattices, barbell networks, and Cayley trees to demonstrate the advantage of first-passage resetting in global search on such networks.Detailed understanding of the couplings between fluid flow and solid deformation in porous media is crucial for the development of novel technologies relating to a wide range of geological and biological processes. A particularly challenging phenomenon that emerges from these couplings is the transition from fluid invasion to fracturing during multiphase flow. Previous studies have shown that this transition is highly sensitive to fluid flow rate, capillarity, and the structural properties of the porous medium. However, a comprehensive characterization of the relevant fluid flow and material failure regimes does not exist. Here, we used our newly developed multiphase Darcy-Brinkman-Biot framework to examine the transition from drainage to material failure during viscously stable multiphase flow in soft porous media in a broad range of flow, wettability, and solid rheology conditions. We demonstrate the existence of three distinct material failure regimes controlled by nondimensional numbers that quantify the balance of viscous, capillary, and structural forces in the porous medium, in agreement with previous experiments and granular simulations. To the best of our knowledge, this study is the first to effectively decouple the effects of viscous and capillary forces on fracturing mechanics. Last, we examine the effects of consolidation or compaction on said dimensional numbers and the system's propensity to fracture.We investigate the evolution of the interface separating two Newtonian fluids of different viscosities in two-dimensional Stokes flow driven by suction or injection. A second-order, mode-coupling theory is used to explore key morphological aspects of the emerging interfacial patterns in the stage of the flow that bridges the purely linear and fully nonlinear regimes. In the linear regime, our analysis reveals that an injection-driven expanding interface is stable, while a contracting motion driven by suction is unstable. Moreover, we find that the linear growth rate associated with this suction-driven instability is independent of the viscosity contrast between the fluids. However, second-order results tell a different story, and show that the viscosity contrast is crucial in determining the morphology of the interface. Our theoretical description is applicable to the entire range of viscosity contrasts, and provides insights on the formation of near-cusp pattern-forming structures. Reproduction of fully nonlinear, n-fold symmetric near-cuspidal shapes previously obtained through conformal mapping techniques substantiates the validity of our mode-coupling approach.We report Brownian dynamics simulation results for the relative permittivity of electrorheological (ER) fluids in an applied electric field. The relative permittivity of an ER fluid can be calculated from the Clausius-Mosotti (CM) equation in the small applied field limit. When a strong field is applied, however, the ER spheres are organized into chains and assemblies of chains in which case the ER spheres are polarized not only by the external field but by each other. This manifests itself in an enhanced dielectric response, e.g., in an increase in the relative permittivity. The correction to the relative permittivity and the time dependence of this correction is simulated on the basis of a model in which the ER particles are represented as polarizable spheres. In this model, the spheres are also polarized by each other in addition to the applied field. Our results are qualitatively similar to those obtained by Horváth and Szalai experimentally [Phys. Rev. E 86, 061403 (2012)PLEEE81539-375510.1103/PhysRevE.86.061403]. We report characteristic time constants obtained from biexponential fits that can be associated with the formation of pairs and short chains as well as with the aggregation of chains. The electric field dependence of the induced dielectric increment reveals the same qualitative behavior that experiments did three regions with different slopes corresponding to different aggregation processes are identified.Network dismantling aims at breaking a network into disconnected components and attacking vertices that intersect with many loops has proven to be a most efficient strategy. Yet existing loop-focusing methods do not distinguish the short loops within densely connected local clusters (e.g., cliques) from the long loops connecting different clusters, leading to lowered performance of these algorithms. Here we propose a new solution framework for network dismantling based on a two-scale bipartite factor-graph representation, in which long loops are maintained while local dense clusters are simplistically represented as individual factor nodes. A mean-field spin-glass theory is developed for the corresponding long-loop feedback vertex set problem. The framework allows for the advancement of various existing dismantling algorithms; we developed the new version of two benchmark algorithms BPD (which uses the message-passing equations of the spin-glass theory as the solver) and CoreHD (which is fastest among well-performing algorithms).