Stochastic Komatu–Loewner evolutions and BMD domain constant

For Komatu–Loewner equation on a standard slit domain, we randomize the Jordan arc in a manner similar to that of Schramm (2000) to find the SDEs satisfied by the induced motion $\xi \left(t\right)$ on $?\mathbb{H}$ and the slit motion $\mathbf{s}\left(t\right)$. The diffusion coefficient $\alpha$ and drift coefficient $b$ of such SDEs are homogeneous functions.Next with solutions of such SDEs, we study the corresponding stochastic Komatu–Loewner evolution, denoted as ${\mathrm{SKLE}}_{\alpha ,b}$. We introduce a function $b_{\mathrm{BMD}}$ measuring the discrepancy of a standard slit domain from $\mathbb{H}$ relative to BMD. We show that ${\mathrm{SKLE}}_{\sqrt{6},?b_{\mathrm{BMD}}}$ enjoys a locality property.     

Non-linear Relaxation of the Photo-induced High Spin State in Spin-Crossover Solids: Effect of Correlations

We investigate a microscopic model based on the pair approximation, for the dynamical properties of the photo-induced high-spin state in spin-crossover solids at low temperature. The model uses the Ising-like hamiltonian and combines long- and short-range interactions. The stochastic treatment of the latter provides a set of two coupled differential equations for the macroscopic short- and long-range order parameters, which reproduce successfully the main features of the experimental relaxation curves.     

Benchmarking the accuracy of coverage-dependent models: adsorption and desorption of benzene on Pt (1 1 1) and Pt3Sn (1 1 1) from first principles

Bimetallic catalysts have demonstrated properties favorable for upgrading biofuel through catalytic hydrodeoxygenation. However, the design and optimization of such bimetallic catalysts requires the ability to construct accurate, predictive models of these systems. To generate a model that predicts the kinetic behavior of benzene adsorbed on Pt (1 1 1) and a Pt₃Sn (1 1 1) surface alloy (Pt₃Sn (1 1 1)), the adsorption of benzene was studied for a wide range of benzene coverages on both surfaces using density functional theory (DFT) calculations. The adsorption energy of benzene was found to correlate linearly with benzene coverage on Pt (1 1 1) and Pt₃Sn (1 1 1); both surfaces exhibited net repulsive lateral interactions. Through an analysis of the d-band properties of the metal surface, it was determined that the coverage dependence is a consequence of the electronic interactions between benzene and the surface. The linear coverage dependence of the adsorption energy allowed us to quantify the influence of the lateral interactions on the heat of adsorption and temperature programmed desorption (TPD) spectra using a mean-field model. A comparison of our simulated TPD to experiment showed that this mean-field model adequately reproduces the desorption behavior of benzene on Pt (1 1 1) and Pt₃Sn (1 1 1). In particular, the TPD correctly exhibits a broadening desorption peak as the initial coverage of benzene increases on Pt (1 1 1) and a low temperature desorption peak on Pt₃Sn (1 1 1). However, due to the sensitivity of the TPD peak temperature to the desorption energy, precise alignment of experimental and theoretical TPD spectra demands an accurate calculation of the adsorption energy. Therefore, an analysis of the effect of the exchange-correlation functional on TPD modeling is presented. Through this work, we show the necessity of incorporating lateral interactions into theoretical models in order to correctly predict experimental behavior.     

Theories and Applications of Mixed Quantum-Classical Non-adiabatic Dynamics

Electronically non-adiabatic processes are essential parts of photochemical process, collisions of excited species, electron transfer processes, and quantum information processing. Various non-adiabatic dynamics methods and their numerical implementation have been developed in the last decades. This review summarizes the most significant development of mixed quantum-classical methods and their applications which mainly include the Liouville equation, Ehrenfest mean-field, trajectory surface hopping, and multiple spawning methods. The recently developed quantum trajectory mean-field method that accounts for the decoherence corrections in a parameter-free fashion is discussed in more detail.     

Regularity of strong solutions of one-dimensional SDE’s with discontinuous and unbounded drift

In this paper we develop a method for constructing strong solutions of one-dimensional Stochastic Differential Equations where the drift may be discontinuous and unbounded. The driving noise is the Brownian Motion and we show that the solution is Sobolev-differentiable in the initial condition and Malliavin differentiable. This method is not based on a pathwise uniqueness argument. We will apply these results to the stochastic transport equation. More specifically, we obtain a continuously differentiable solution of the stochastic transport equation when the driving function is a step function.     

Mean-field properties of impurity in Bose gas with three-body forces

We exactly analyze, on the mean-field level, the low-momentum properties of a single impurity atom loaded in the dilute one-dimensional Bose gas with two- and three-body short-range interactions. Particularly the Bose polaron binding energy and the quasiparticle residue are calculated for the considered system in the broad region of parameters change. We also explore the generic mean-field formula for the polaron effective mass which was shown to depend on the density profile of bath particles with a motionless impurity immersed.     

An implicit-gradient-enhanced incremental-secant mean-field homogenization scheme for elasto-plastic composites with damage

This paper presents an incremental-secant mean-field homogenization (MFH) procedure for composites made of elasto-plastic constituents exhibiting damage. During the damaging process of one phase, the proposed method can account for the resulting unloading of the other phase, ensuring an accurate prediction of the scheme. When strain softening of materials is involved, classical finite element formulations lose solution uniqueness and face the strain localization problem. To avoid this issue the model is formulated in a so-called implicit gradient-enhanced approach, with a view toward macro-scale simulations. The method is then used to predict the behavior of composites whose matrix phases exhibit strain softening, and is shown to be accurate compared to unit cell simulations and experimental results. Then the convergence of the method upon strain softening, with respect to the mesh size, is demonstrated on a notched composite ply. Finally, applications consisting in a stacking plate, successively without and with a hole, are given as illustrations of the possibility of the method to be used in a multiscale framework.     

Mean-field limit for the stochastic Vicsek model

We consider the continuous version of the Vicsek model with noise, proposed as a model for collective behaviour of individuals with a fixed speed. We rigorously derive the kinetic mean-field partial differential equation satisfied when the number N of particles tends to infinity, quantifying the convergence of the law of one particle to the solution of the PDE. For this we adapt a classical coupling argument to the present case in which both the particle system and the PDE are defined on a surface rather than on the whole space R^d. As part of the study we give existence and uniqueness results for both the particle system and the PDE.