相关论文: Nonlinear Accelerator Problems via Wavelets: 8. In…
We present applications of variational -- wavelet approach to nonlinear (rational) rms envelope dynamics. We have the solution as a multiresolution (multiscales) expansion in the base of compactly supported wavelet basis.
We develop a general notion of orthogonal wavelets `centered' on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. We develop efficient algorithms to implement these…
When proving invariance properties of a program, we face two problems. The first problem is related to the necessity of proving tautologies of considered assertion language, whereas the second manifests in the need of finding sufficiently…
Non-linear effects in accelerator physics are important for both successful operation of accelerators and during the design stage. Since both of these aspects are closely related, they will be treated together in this overview. Some of the…
We present the application of the variational-wavelet analysis to the analysis of quantum ensembles in Wigner framework. (Naive) deformation quantization, the multiresolution representations and the variational approach are the key points.…
We consider an application of modification of our variational-wavelet approach to some nonlinear collective model of beam/plasma physics: Vlasov/Boltzmann-like reduction from general BBGKY hierachy related to modeling of propagation of…
We consider an approach to the analysis of nonstationary processes based on the application of wavelet basis sets constructed using segments of the analyzed time series. The proposed method is applied to the analysis of time series…
We present applications of variational -- wavelet approach to different forms of nonlinear (rational) rms envelope equations. We have the representation for beam bunch oscillations as a multiresolution (multiscales) expansion in the base of…
Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…
For describing the probability distribution of the positions and times of particles performing anomalous motion, fractional PDEs are derived from the continuous time random walk models with waiting time distribution having divergent first…
Capturing solution near the singular point of any nonlinear SBVPs is challenging because coefficients involved in the differential equation blow up near singularities. In this article, we aim to construct a general method based on…
We consider Quantum Chromodynamics with external vector, axial-vector, scalar and pseudo-scalar currents and compute three-loop corrections to the corresponding vertex function taking into account massive quarks. We consider all non-singlet…
We present the application of the variational-wavelet approach to the construction and analysis of solutions of Wigner/von Neumann/Moyal and related equations corresponding to the nonlinear (polynomial) dynamical problems. (Naive)…
We propose a nonlinear, wavelet based signal representation that is translation invariant and robust to both additive noise and random dilations. Motivated by the multi-reference alignment problem and generalizations thereof, we analyze the…
We use a one-scale similarity analysis which gives specific relations between the velocity, amplitude and width of localized solutions of nonlinear differential equations, whose exact solutions are generally difficult to obtain. We also…
This paper presents a novel framework for high-dimensional nonlinear quantum computation that exploits tensor products of amplified vector and matrix encodings to efficiently evaluate multivariate polynomials. The approach enables the…
Wavelets are a useful basis for constructing solutions of the integral and differential equations of scattering theory. Wavelet bases efficiently represent functions with smooth structures on different scales, and the matrix representation…
Ensuring software correctness remains a fundamental challenge in formal program verification. One promising approach relies on finding polynomial invariants for loops. Polynomial invariants are properties of a program loop that hold before…
Recently, algorithms for calculation of 3-loop propagator diagrams in HQET and on-shell QCD with a heavy quark have been constructed and implemented. These algorithms (based on integration by parts recurrence relations) reduce an arbitrary…
The evaluation of loop amplitudes via differential equations and harmonic polylogarithms is discussed at an introductory level. The method is based on evolution equations in the masses or in the external kinematical invariants and on a…