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Sequential impingement channels can reduce the adverse effect of crossflow in narrow impingement channels, as well as increase the cooling efficiency. In this work, sequential impingement channels are experimentally investigated using the transient liquid ...
The explicit split-operator algorithm is often used for solving the linear and nonlinear time-dependent Schrödinger equations. However, when applied to certain nonlinear time-dependent Schrödinger equations, this algorithm loses time reversibility and seco ...
Multiply excited states in semiconductor quantum dots feature intriguing physics and play a crucial role in nanocrystal-based technologies. While photoluminescence provides a natural probe to investigate these states, room-temperature single-particle spect ...
The null controllability of the heat equation is known for decades [21, 25, 34]. The finite time stabilizability of the one dimensional heat equation was proved by Coron-Nguyên [15], while the same question for high dimensional spaces remained widely open. ...
We study the regularity of the probability density function of the supremum of the solution to the linear stochastic heat equation. Using a general criterion for the smoothness of densities for locally nondegenerate random variables, we establish the smoot ...
We study the formation of singularities for cylindrical symmetric solutions to the Gross-Pitaevskii equation describing a Dipolar Bose-Einstein condensate. We prove that solutions arising from initial data with energy below the energy of the Ground State a ...
Heat conduction in dielectric crystals originates from the dynamics of atomic vibrations, whose evolution is well described by the linearized Boltzmann transport equation for the phonon populations. Recently, it was shown that thermal conductivity can be r ...
We establish a sharp estimate on the negative moments of the smallest eigenvalue of the Malliavin matrix gamma z of Z := (u(s, y), u(t , x) - u(s, y)), where u is the solution to a system of d non-linear stochastic heat equations in spatial dimension k >= ...
Since the 20th century, the rate of urbanization in the world has been increasing exponentially and will reach 68% in 2050. In parallel with this expansion, the size and activities of cities are also greatly growing. As a result, cities are depleting avail ...
We develop a comprehensive mathematical framework for polynomial jump-diffusions in a semimartingale context, which nest affine jump-diffusions and have broad applications in finance. We show that the polynomial property is preserved under polynomial trans ...
