Search results for "Equations"
showing 10 items of 955 documents
Variable time amplitude amplification and quantum algorithms for linear algebra problems
2012
Quantum amplitude amplification is a method of increasing a success probability of an algorithm from a small epsilon>0 to Theta(1) with less repetitions than classically. In this paper, we generalize quantum amplitude amplification to the case when parts of the algorithm that is being amplified stop at different times. We then apply the new variable time amplitude amplification to give two new quantum algorithms for linear algebra problems. Our first algorithm is an improvement of Harrow et al. algorithm for solving systems of linear equations. We improve the running time of the algorithm from O(k^2 log N) to O(k log^3 k log N) where k is the condition number of the system of equations. …
Asymptotic behavior of global solutions of aerotaxis equations
2019
Abstract We study asymptotic behavior of global solutions of one-dimensional aerotaxis model proposed in Knosalla and Nadzieja (2015) [9] .
A multilayer model for self-propagating high-temperature synthesis of inter-metallic compounds
2007
International audience; Self-propagating high-temperature synthesis of intermetallic compounds is of wide interest. We consider reactions in a binary system in which the rise and fall of the temperature during the reaction is such that one of the reacting metals melts but not the other. For such a system, using the phase diagram of the binary system, we present a general theory that describes the reaction taking place in a single solid particle of one component surrounded by the melt of the second component. The theory gives us a set of kinetic equations that describe the propagation of the phase interfaces in the solid particle and the change in composition of the melt that surrounds it. I…
Electromagnetically induced switching of ferroelectric thin films
2007
We analyze the interaction of an electromagnetic spike (one cycle) with a thin layer of ferroelectric medium with two equilibrium states. The model is the set of Maxwell equations coupled to the undamped Landau-Khalatnikov equation, where we do not assume slowly varying envelopes. From linear-scattering theory, we show that low-amplitude pulses can be completely reflected by the medium. Large-amplitude pulses can switch the ferroelectric. Using numerical simulations and analysis, we study this switching for long and short pulses, estimate the switching times, and provide useful information for experiments.
Communication: multireference equation of motion coupled cluster: a transform and diagonalize approach to electronic structure.
2014
The novel multireference equation-of-motion coupled-cluster (MREOM-CC) approaches provide versatile and accurate access to a large number of electronic states. The methods proceed by a sequence of many-body similarity transformations and a subsequent diagonalization of the transformed Hamiltonian over a compact subspace. The transformed Hamiltonian is a connected entity and preserves spin- and spatial symmetry properties of the original Hamiltonian, but is no longer Hermitean. The final diagonalization spaces are defined in terms of a complete active space (CAS) and limited excitations (1h, 1p, 2h, …) out of the CAS. The methods are invariant to rotations of orbitals within their respective…
Introducing Memory in Coarse-Grained Molecular Simulations
2021
[Image: see text] Preserving the correct dynamics at the coarse-grained (CG) level is a pressing problem in the development of systematic CG models in soft matter simulation. Starting from the seminal idea of simple time-scale mapping, there have been many efforts over the years toward establishing a meticulous connection between the CG and fine-grained (FG) dynamics based on fundamental statistical mechanics approaches. One of the most successful attempts in this context has been the development of CG models based on the Mori–Zwanzig (MZ) theory, where the resulting equation of motion has the form of a generalized Langevin equation (GLE) and closely preserves the underlying FG dynamics. In…
Boulder coastal deposits at Favignana Island rocky coast (Sicily, Italy): Litho-structural and hydrodynamic control
2018
Boulders are frequently dislodged from rock platforms, transported and deposited along coastal zones by high-magnitude storm waves or tsunamis. Their size and shape are often controlled by the thickness of bedding planes as well as by high-angle to bedding fracture network. We investigate these processes along two coastal areas of Favignana Island by integrating geological data for 81 boulders, 49 rupture surfaces (called sockets) and fracture orientation and spacing with four radiocarbon dates, numerical hydrodynamic analysis, and hindcast numerical simulation data. Boulders are scattered along the carbonate platform as isolated blocks or in small groups, which form, as a whole, a disconti…
Controlled time integration for the numerical simulation of meteor radar reflections
2016
We model meteoroids entering the Earth[U+05F3]s atmosphere as objects surrounded by non-magnetized plasma, and consider efficient numerical simulation of radar reflections from meteors in the time domain. Instead of the widely used finite difference time domain method (FDTD), we use more generalized finite differences by applying the discrete exterior calculus (DEC) and non-uniform leapfrog-style time discretization. The computational domain is presented by convex polyhedral elements. The convergence of the time integration is accelerated by the exact controllability method. The numerical experiments show that our code is efficiently parallelized. The DEC approach is compared to the volume …
Stochastic Galerkin method for cloud simulation
2018
AbstractWe develop a stochastic Galerkin method for a coupled Navier-Stokes-cloud system that models dynamics of warm clouds. Our goal is to explicitly describe the evolution of uncertainties that arise due to unknown input data, such as model parameters and initial or boundary conditions. The developed stochastic Galerkin method combines the space-time approximation obtained by a suitable finite volume method with a spectral-type approximation based on the generalized polynomial chaos expansion in the stochastic space. The resulting numerical scheme yields a second-order accurate approximation in both space and time and exponential convergence in the stochastic space. Our numerical results…
Ray optics for absorbing particles with application to ice crystals at near-infrared wavelengths
2018
Abstract Light scattering by particles large compared to the wavelength of incident light is traditionally solved using ray optics which considers absorption inside the particle approximately, along the ray paths. To study the effects rising from this simplification, we have updated the ray-optics code SIRIS to take into account the propagation of light as inhomogeneous plane waves inside an absorbing particle. We investigate the impact of this correction on traditional ray-optics computations in the example case of light scattering by ice crystals through the extended near-infrared (NIR) wavelength regime. In this spectral range, ice changes from nearly transparent to opaque, and therefore…