Search results for "Solutions"
showing 10 items of 757 documents
On the critical behavior for inhomogeneous wave inequalities with Hardy potential in an exterior domain
2021
Abstract We study the wave inequality with a Hardy potential ∂ t t u − Δ u + λ | x | 2 u ≥ | u | p in ( 0 , ∞ ) × Ω , $$\begin{array}{} \displaystyle \partial_{tt}u-{\it\Delta} u+\frac{\lambda}{|x|^2}u\geq |u|^p\quad \mbox{in } (0,\infty)\times {\it\Omega}, \end{array}$$ where Ω is the exterior of the unit ball in ℝ N , N ≥ 2, p > 1, and λ ≥ − N − 2 2 2 $\begin{array}{} \displaystyle \left(\frac{N-2}{2}\right)^2 \end{array}$ , under the inhomogeneous boundary condition α ∂ u ∂ ν ( t , x ) + β u ( t , x ) ≥ w ( x ) on ( 0 , ∞ ) × ∂ Ω , $$\begin{array}{} \displaystyle \alpha \frac{\partial u}{\partial \nu}(t,x)+\beta u(t,x)\geq w(x)\quad\mbox{on } (0,\infty)\times \partial{\it\Omega}, \e…
Location of transition states and stable intermediates by MINIMAX/MINIMI optimization of synchronous transit pathways
1983
The MINIMAX/MINIMI concept for the location of transition states and/or stable intermediates of chemical reactions is introduced, based on the synchronous transit method. According to this strategy, minimization of quadratic synchronous transit path maxima or minima is achieved by constrained exhaustive optimization of internal coordinates. The method and its efficiency are demonstrated for two-dimensional model surfaces as well as for thermally allowed electrocyclic interconversions of cyclopropyl-/allyl-cation and cyclobutene-/butadiene (gauche) within the framework of MNDO-SCF calculations. Thus, in both cases a direct comparison with the exact solution determined by minimization of the …
The fifth order Peregrine breather and its eight-parameters deformations solutions of the NLS equation.
2013
We construct here explicitly new deformations of the Peregrine breather of order 5 with 8 real parameters. This gives new families of quasi-rational solutions of the NLS equation and thus one can describe in a more precise way the phenomena of appearance of multi rogue waves. With this method, we construct new patterns of different types of rogue waves. We get at the same time, the triangular configurations as well as rings isolated. Moreover, one sees appearing for certain values of the parameters, new configurations of concentric rings.
Final State Interaction Effects in 3He(e ,e'p)
2003
Abstract Asymmetries in quasi-elastic 3 He ( e → , e ′ p ) have been measured at a momentum transfer of 0.67 (GeV/ c ) 2 and are compared to a calculation which takes into account relativistic kinematics in the final state and a relativistic one-body current operator. With an exact solution of the Faddeev equation for the 3 He -ground state and an approximate treatment of final state interactions in the continuum good agreement is found with the experimental data.
Three-body Coulomb interaction effects in the final state of thePb208(B8,Be7p)Pb208Coulomb breakup reaction
2005
The photodissociation reaction $^{8}\mathrm{B}+\ensuremath{\gamma}\ensuremath{\rightarrow}^{7}\mathrm{Be}+p$ is used to provide information on the astrophysical ${S}_{17}$ factor of the inverse radiative capture reaction, knowledge of which is crucial for an estimation of the high-energy neutrino flux from the sun. Since, at present, the Coulomb field of a fully stripped nucleus serves as the source of the photons, an adequate analysis requires a genuine three-body treatment of this reaction. Among the uncertainties still affecting present analyses, the possible modification of the dissociation cross section by the post-decay acceleration of the fragments $^{7}\mathrm{Be}$ and p in the targ…
Three-Body Coulomb Final-State Interaction Effects in the Coulomb Breakup of Light Nuclei
2005
Coulomb breakup of a projectile in the Coulomb field of a fully stripped heavy nucleus is at present one of the most popular experimental methods to obtain information on reactions of interest in nuclear astrophysics. Its theoretical interpretation presents, however, considerable difficulties, due to the three-body nature and the infinite range of the Coulomb forces involved. Among the uncertainties affecting present analyses, the possible modification of the dissociation cross section by three-body Coulomb final-state interactions plays a major role. Various methods which have been proposed to deal with it are briefly reviewed. However, none of them is based on a consistent and mathematica…
Tensor Network Annealing Algorithm for Two-Dimensional Thermal States
2019
Tensor network methods have become a powerful class of tools to capture strongly correlated matter, but methods to capture the experimentally ubiquitous family of models at finite temperature beyond one spatial dimension are largely lacking. We introduce a tensor network algorithm able to simulate thermal states of two-dimensional quantum lattice systems in the thermodynamic limit. The method develops instances of projected entangled pair states and projected entangled pair operators for this purpose. It is the key feature of this algorithm to resemble the cooling down of the system from an infinite temperature state until it reaches the desired finite-temperature regime. As a benchmark we …
Exact solutions for the mutual inductance of circular coils and elliptic coils
2012
An exact solution is presented for the mutual inductance between general noncoaxial thin circular and elliptic coils with parallel axes. The thin coil solution is given as an angular integral of an elliptic integral expression. In addition, for the coaxial case, an exact solution is given for the mutual inductance of a thick circular coil and a thick elliptic coil. The elliptic coil is such that the coil thickness is the same along both elliptic semi-axes. The thick coil solution is given as an integral of an expression involving Bessel and Struve functions. Extensive numerical results for sample geometries are given for both solutions, which are cross checked against each other in the limi…
Collision-model-based approach to non-Markovian quantum dynamics
2013
We present a theoretical framework to tackle quantum non-Markovian dynamics based on a microscopic collision model (CM), where the bath consists of a large collection of initially uncorrelated ancillas. Unlike standard memoryless CMs, we endow the bath with memory by introducing inter-ancillary collisions between next system-ancilla interactions. Our model interpolates between a fully Markovian dynamics and the continuous interaction of the system with a single ancilla, i.e., a strongly non-Markovian process. We show that in the continuos limit one can derive a general master equation, which while keeping such features is guaranteed to describe an unconditionally completely positive and tra…
Scale-free relaxation of a wave packet in a quantum well with power-law tails
2013
We propose a setup for which a power-law decay is predicted to be observable for generic and realistic conditions. The system we study is very simple: A quantum wave packet initially prepared in a potential well with (i) tails asymptotically decaying like ~ x^{-2} and (ii) an eigenvalues spectrum that shows a continuous part attached to the ground or equilibrium state. We analytically derive the asymptotic decay law from the spectral properties for generic, confined initial states. Our findings are supported by realistic numerical simulations for state-of-the-art expansion experiments with cold atoms.