Dodsonboyette0638

We find an exact series solution for the steady-state probability distribution of a harmonically trapped active Brownian particle in two dimensions in the presence of translational diffusion. This series solution allows us to efficiently explore the behavior of the system in different parameter regimes. Identifying "active" and "passive" regimes, we predict a surprising re-entrant active-to-passive transition with increasing trap stiffness. Our numerical simulations validate this finding. We discuss various interesting limiting cases wherein closed-form expressions for the distributions can be obtained.Dyson has shown an equivalence between infinite-range Coulomb gas models and classical random matrix ensembles for the study of eigenvalue statistics. In this paper, we introduce finite-range Coulomb gas models as a generalization of the Dyson models with a finite range of eigenvalue interactions. As the range of interaction increases, there is a transition from Poisson statistics to classical random matrix statistics. These models yield distinct universality classes of random matrix ensembles. They also provide a theoretical framework to study banded random matrices, and dynamical systems the matrix representation of which can be written in the form of banded matrices.Positron annihilation lifetime spectroscopy has been used to study 4-hexyl-4'-isothiocyanatobiphenyl. Changes of the orthopositronium lifetime parameters with temperature have been observed for the supercooled smectic-E phase. The measurements confirm that positronium is created and annihilates in a layer of a lower electron density containing alkyl chains of molecules. The two-state bond-lattice model of glass transition explains the thermal activation of the centers where orthopositronium is created and annihilates when the glass of the smectic-E phase softens. However, the subsequent cold crystallization of the softened regions also influences the orthopositronium lifetime and intensity, which complicates the picture seen by positrons. The measurements during isothermal crystallization suggest that it progresses in two stages. The first stage can be described by the Avrami equation with the Avrami exponent close to unity, which indicates low-dimensional crystallization. Similarly to liquid n alkanes, the application of pressure is equivalent to temperature lowering with the similar equivalence relationship between pressure and temperature, which seems to confirm the structure of the smectic-E phase with sublayers containing alkyl chains in a molten state. The dependence of the orthopositronium lifetime on pressure for the smectic-E phase may be described by the bubble model where the positronium bubble is approximated with a finite square potential well with the depth of U=1.45eV.Bistable nonequilibrium systems are realized in catalytic reaction-diffusion processes, biological transport and regulation, spatial epidemics, etc. check details Behavior in spatially continuous formulations, described at the mean-field level by reaction-diffusion type equations (RDEs), often mimics that of classic equilibrium van der Waals type systems. When accounting for noise, similarities include a discontinuous phase transition at some value, p_eq, of a control parameter, p, with metastability and hysteresis around p_eq. For each p, there is a unique critical droplet of the more stable phase embedded in the less stable or metastable phase which is stationary (neither shrinking nor growing), and with size diverging as p→p_eq. Spatially discrete analogs of these mean-field formulations, described by lattice differential equations (LDEs), are more appropriate for some applications, but have received less attention. It is recognized that LDEs can exhibit richer behavior than RDEs, specifically propagation failure for planar interphases separating distinct phases. We show that this feature, together with an orientation dependence of planar interface propagation also deriving from spatial discreteness, results in the occurrence of entire families of stationary droplets. The extent of these families increases approaching the transition and can be infinite if propagation failure is realized. In addition, there can exist a regime of generic two-phase coexistence where arbitrarily large droplets of either phase always shrink. Such rich behavior is qualitatively distinct from that for classic nucleation in equilibrium and spatially continuous nonequilibrium systems.We demonstrate that fluid mechanical systems arising from large fluctuations of one-dimensional statistical processes generically exhibit solitons and nonlinear waves. We derive the explicit form of these solutions and examine their properties for the specific cases of the Kipnis-Marchioro-Presutti model (KMP) and the symmetric exclusion process (SEP). We show that the two fluid systems are related by a nonlinear transformation but still have markedly different properties. In particular, the KMP fluid has a nontrivial sound wave spectrum exhibiting birefringence, whereas sound waves for the SEP fluid are essentially trivial. The appearance of sound waves and soliton configurations in the KMP model is related to the onset of instabilities.Currently there is considerable interest in creating scalable laboratory plasmas to study the mechanisms behind the formation and evolution of astrophysical phenomena such as Herbig-Haro objects and supernova remnants. Laboratory-scaled experiments can provide a well diagnosed and repeatable supplement to direct observations of these extraterrestrial objects if they meet similarity criteria demonstrating that the same physics govern both systems. Here, we present a study on the role of collision and cooling rates on shock formation using colliding jets from opposed conical wire arrays on a compact pulsed-power driver. These diverse conditions were achieved by changing the wire material feeding the jets, since the ion-ion mean free path (λ_mfp-ii) and radiative cooling rates (P_rad) increase with atomic number. Low Z carbon flows produced smooth, temporally stable shocks. Weakly collisional, moderately cooled aluminum flows produced strong shocks that developed signs of thermal condensation instabilities and turbulence.