Search results for "equation"

Modified Landau levels, damped harmonic oscillator and two-dimensional pseudo-bosons

2010

In a series of recent papers one of us has analyzed in some details a class of elementary excitations called {\em pseudo-bosons}. They arise from a special deformation of the canonical commutation relation $[a,a^\dagger]=\1$, which is replaced by $[a,b]=\1$, with $b$ not necessarily equal to $a^\dagger$. Here, after a two-dimensional extension of the general framework, we apply the theory to a generalized version of the two-dimensional Hamiltonian describing Landau levels. Moreover, for this system, we discuss coherent states and we deduce a resolution of the identity. We also consider a different class of examples arising from a classical system, i.e. a damped harmonic oscillator.

1993

The viscosities of moderately concentrated solutions of poly(butyl methacrylate)—Mw = 1820 kg/mol–in the thermodynamically good solvent toluene and in the theta solvent 2-propanol were measured up to pressures of 2000 bar as a function of shear rate in the temperature interval from 40 to 70°C. Both systems obey Graessley's equation so that it is possible to obtain the following rheological parameters in addition to the zero-shear viscosity η0 from the dependences . η can be split into an entanglement part ηent plus a frictional contribution ηfric, and the characteristic viscometric relaxation time τ0 becomes accessible. The present results demonstrate that the application of pressure raises…

Space‐time dynamical models

2008

Purpose – The purpose is to present a new formal approach based on a partial integro‐differential equation, the space‐time state transition equation (STSTE), and on a set of general equations with which space‐time dynamical models of complex systems, such as social systems and ecosystems, can be built.Design/methodology/approach – The STSTE provides the partial derivative of the density of a state‐variable with regard to time as a sum of time rates and space‐time rates. Time rates describe the dynamics of the system for each space‐point irrespectively of the other points, whilst space‐time rates describe this evolution as a consequence of the relation of each space‐point with a given set of…

Covariant Operator Formalism for Quantized Superfields

1988

The Takahashi-Umezawa method of deriving the free covariant quantization relations from the linear equations of motion is extended to superfields. The Cauchy problem for free superfields is solved, and an expression for the time independent scalar product is given. For the case of interacting fields, we give the general Kallen-Lehmann spectral representation for the two-point superfield Green functions and, after the introduction of the asymptotic condition for superfields, we give the superfield extension of the Yang-Feldman equation. The case of the D = 2 real scalar superfield and the case of the D = 4 chiral superfield are discussed in detail.

The Tan 2Θ Theorem in fluid dynamics

2017

We show that the generalized Reynolds number (in fluid dynamics) introduced by Ladyzhenskaya is closely related to the rotation of the positive spectral subspace of the Stokes block-operator in the underlying Hilbert space. We also explicitly evaluate the bottom of the negative spectrum of the Stokes operator and prove a sharp inequality relating the distance from the bottom of its spectrum to the origin and the length of the first positive gap.

30 years of finite-gap integration theory

2007

The method of finite-gap integration was created to solve the periodic KdV initial problem. Its development during last 30 years, combining the spectral theory of differential and difference operators with periodic coefficients, the algebraic geometry of compact Riemann surfaces and their Jacobians, the Riemann theta functions and inverse problems, had a strong impact on the evolution of modern mathematics and theoretical physics. This article explains some of the principal historical points in the creation of this method during the period 1973–1976, and briefly comments on its evolution during the last 30 years.

Self-Assembly of Polymeric Particles in Poiseuille Flow: A Hybrid Lattice Boltzmann/External Potential Dynamics Simulation Study

2017

We present a hybrid simulation method which allows one to study the dynamical evolution of self-assembling (co)polymer solutions in the presence of hydrodynamic interactions. The method combines an established dynamic density functional theory for polymers that accounts for the nonlocal character of chain dynamics at the level of the Rouse model, the external potential dynamics (EPD) model, with an established Navier–Stokes solver, the Lattice Boltzmann (LB) method. We apply the method to study the self-assembly of nanoparticles and vesicles in two-dimensional copolymer solutions in a typical microchannel Poiseuille flow profile. The simulations start from fully mixed systems which are sudd…

Determinants of dynamic inspiratory muscle strength in healthy trained elderly.

2021

Background: The S-Index assessed by means of electronic devices is a measure of Inspiratory Muscle Strength (IMS) that highly correlates with the maximal inspiratory pressure (MIP). The variables involved when using regression models for the prediction of IMS/MIP depend on both the sample characteristics and the device or protocol used. In light of the scarce information on the influence of physical activity (PA) on IMS in healthy older adults (OA), together with the incorporation of new assessment devices, the objectives of this research are: 1) to determine which factors influence the IMS in a group of trained OA, using a portable electronic device; and 2) to propose a regression model to…

Zur numerischen Lösung gewöhnlicher Differential-gleichungen mit Splines in einem Sonderfall

1980

In an earlier paper [1] a general procedure has been presented to obtain polynomial spline approximations for the solution of the initial value problem for ordinary differential equations. In this paper the general procedure is described by an equivalent one step method. Furthermore two convergence theorems are proved for a special case which is not included in the general convergence or divergence theory given in [1].

Block-Based Inversion of the Heat Equations

2014

This chapter presents robust methods, which refine the algorithms, in Sect. 7.2, for inversion of the heat equations. The idea behind the algorithms is to solve the inversion problem separately in different frequency bands. This is achieved by using spline wavelet packets. The solutions that minimize some parameterized quadratic functionals, are derived as linear combinations of the wavelet packets. Choice of parameters, which is performed automatically, determines the trade-off between the solution regularity and the initial data approximation. The Spline Harmonic Analysis (SHA) technique provides a unified computational scheme for the fast implementation of the algorithm and an explicit r…