McKean-Vlasov SDEs and SPDEs with Locally Monotone Coefficients

In this paper we mainly investigate the strong and weak well-posedness of a class of McKean-Vlasov stochastic (partial) differential equations. The main existence and uniqueness results state that we only need to impose some local assumptions on the coefficients, i.e. locally monotone condition both in state variable and distribution variable, which cause some essential difficulty since the coefficients of McKean-Vlasov stochastic equations typically are nonlocal. Furthermore, the large deviation principle is also derived for the McKean-Vlasov stochastic equations under those weak assumptions. The wide applications of main results are illustrated by various concrete examples such as the Granular media equations, Kinetic equations, distribution dependent porous media equations and Navier-Stokes equations, moreover, we could remove or relax some typical assumptions previously imposed on those models.Comment: 53 page

Supersymmetric Solutions in Four-Dimensional Off-Shell Curvature-Squared Supergravity

Off-shell formulations of supergravities allow one to add closed-form higher-derivative super-invariants that are separately supersymmetric to the usual lower-derivative actions. In this paper we study four-dimensional off-shell N=1 supergravity where additional super-invariants associated with the square of the Weyl tensor and the square of the Ricci scalar are included. We obtain a variety of solutions where the metric describes domain walls, Lifshitz geometries, and also solutions of a kind known as gyratons. We find that in some cases the solutions can be supersymmetric for appropriate choices of the parameters. In some solutions the auxiliary fields may be imaginary. One may reinterpret these as real solutions in an analytically-continued theory. Since the supersymmetry transformation rules now require the gravitino to be complex, the analytically-continued theory has a "fake supersymmetry" rather than a genuine supersymmetry. Nevertheless, the concept of pseudo-supersymmetric solutions is a useful one, since the Killing spinor equations provide first-order equations for the bosonic fields.Comment: 28 page

DC Conductivities from Non-Relativistic Scaling Geometries with Momentum Dissipation

We consider a gravitational theory with two Maxwell fields, a dilatonic scalar and spatially dependent axions. Black brane solutions to this theory are Lifshitz-like and violate hyperscaling. Working with electrically charged solutions, we calculate analytically the holographic DC conductivities when both gauge fields are allowed to fluctuate. We discuss some of the subtleties associated with relating the horizon to the boundary data, focusing on the role of Lifshitz asymptotics and the presence of multiple gauge fields. The axionic scalars lead to momentum dissipation in the dual holographic theory. Finally, we examine the behavior of the DC conductivities as a function of temperature, and comment on the cases in which one can obtain a linear resistivity.Comment: 32 pages, 3 figures. Figures and references added. Discussion modifie

Study on Fire Smoke Distribution and Smoke Control in Extra-long Double-hole Tunnel

Abstract： Construction of tunnels, as one of the main methods to solve physical traffic barriers, However, It vulnerable to the threat of fire during the process of tunnel operation period. In response to such situation, this article explores the smoke distribution of extra-long double-tube tunnel and its impact on evacuation in the event of a fire. This paper take the Jieling tunnel as an example, and applies Accident Tree Analysis (ATA) method combined with Fires Dynamics Simulator (FDS）simulation software to study the changes of harmful factors such as tunnel smoke. According to the research, when a fire occurs in an extra-long double-tube tunnel, It is concluded that people are supposed to be guided to leave via the nearest cross-passages as soon as possible, In the end analysis the roles that air curtains could play in the control of smoke. It is recommended to open the air curtain so that in such condition people away from the cross-passages have enough time to escape

3-Hydr­oxy-3-phenyl­isoindolin-1-one 0.33-hydrate

The asymmetric unit of the title compound, C14H11NO2·0.33H2O, contains three 3-hydr­oxy-3-phenyl­isoindolin-1-one (HPIO) mol­ecules and one water mol­ecule. The three independent HPIO mol­ecules differ in the orientations of hydr­oxy and phenyl groups substituted at the 3-position with respect to the planar [r.m.s. deviations of 0.0173, 0.0170 and 0.0102 Å] dihydro­isoindolin-1-one ring system. In the crystal structure, mol­ecules are linked into a three-dimensional network by O—H⋯O, N—H⋯O and C—H⋯O hydrogen bonds

Entanglement dynamics of two-qubit system in different types of noisy channels

In this paper, we study entanglement dynamics of a two-qubit extended Werner-like state locally interacting with independent noisy channels, i.e., amplitude damping, phase damping and depolarizing channels. We show that the purity of initial entangled state has direct impacts on the entanglement robustness in each noisy channel. That is, if the initial entangled state is prepared in mixed instead of pure form, the state may exhibit entanglement sudden death (ESD) and/or be decreased for the critical probability at which the entanglement disappear.Comment: 11 pages, 6 figure