相关论文: Ostwald Ripening on Nanoscale

A renormalization group theory for a system consisting of coupled superconducting layers as a model for typical high-temperature superconducters is developed. In a first step the electromagnetic interaction over infinitely many layers is…

The classical theorems about singular perturbation reduction (due to Tikhonov and Fenichel) are concerned with convergence on a compact time interval (in slow time) as a small parameter approaches zero. For unbounded time intervals…

Generative adversarial networks (GANs) are so complex that the existing learning theories do not provide a satisfactory explanation for why GANs have great success in practice. The same situation also remains largely open for deep neural…

In spite of their original discrepancy, both dark energy and modified theory of gravity can be parameterized by the effective equation of state (EOS) $\omega$ for the expansion history of the Universe. A useful model independent approach to…

We study the weighted averages of resonance clusters for the hydrogen atom with a Stark electric field in the weak field limit. We prove a semiclassical Szego-type theorem for resonance clusters showing that the limiting distribution of the…

The isothermal compressibility of a general crystal is analyzed within classical density functional theory. Our approach can be used for homogeneous and unstrained crystals containing an arbitrarily high density of local defects. We start…

In this paper, we systematically study the regularity theory of the linear system of nearly incompressible elasticity. In the setting of stochastic homogenization, we develop new techniques to establish the large-scale estimates of…

The physical and chemical properties of metal nanoparticles differ significantly from those of free metal atoms as well as from the properties of bulk metals, and therefore, they may be viewed as a transition regime between the two physical…

A two-variable stochastic model for diffusion-limited nucleation is developed using a formalism derived from fluctuating hydrodynamics. The model is a direct generalization of the standard Classical Nucleation Theory. The nucleation rate…

Nucleation is an out-of-equilibrium process, which can be strongly affected by the presence of external fields. In this letter, we report a simple extension of classical nucleation theory to systems submitted to an homogeneous shear flow.…

We prove a converse Lyapunov theorem for boundedness of reachability sets for a general class of control systems whose flow is Lipschitz continuous on compact intervals with respect to trajectory-dominated inputs. We show that this…

The classical Gaussian concentration inequality for Lipschitz functions is adapted to a setting where the classical assumptions (i.e. Lipschitz and Gaussian) are not met. The theory is more direct than much of the existing theory designed…

We investigate the spherical collapse model and the abundance of galaxy clusters in a class of degenerate higher-order scalar--tensor (DHOST) theories in which gravitational waves do not decay into scalar perturbations and which are…

We establish a margin based data dependent generalization error bound for a general family of deep neural networks in terms of the depth and width, as well as the Jacobian of the networks. Through introducing a new characterization of the…

We study the scaling properties of the clusters grown by the Wolff algorithm on seven different Sierpinski-type fractals of Hausdorff dimension $1 < d_f \le 3$ in the framework of the Ising model. The mean absolute value of the surface…

Phase separation is not only ubiquitous in diverse physical systems, but also plays an important organizational role inside biological cells. However, experimental studies of intracellular condensates (drops with condensed concentrations of…

We discuss the theoretical interpretation of observational data concerning the clustering of galaxies at high redshifts. Building on the theoretical machinery developed by Matarrese et al. (1997), we make detailed quantitative predictions…

We use the recently proposed generalised on-shell representation for scattering amplitudes and a consistency test to explore the space of tree-level consistent couplings in four-dimensional Minkowski spacetime. The extension of the…

Many convolutional neural networks (CNNs) have a feed-forward structure. In this paper, a linear program that estimates the Lipschitz bound of such CNNs is proposed. Several CNNs, including the scattering networks, the AlexNet and the…

In a recent paper, Struwe considered the Cauchy problem for a class of nonlinear wave and Scr\"odinger equations. Under some assumptions on the nonlinearities, it was shown that uniqueness of classical solutions can be obtained in the much…