Search results for "equation"
showing 10 items of 4219 documents
The reaction enthalpy of hydrogen dissociation calculated with the Small System Method from simulation of molecular fluctuations.
2014
We show how we can find the enthalpy of a chemical reaction under non-ideal conditions using the Small System Method to sample molecular dynamics simulation data for fluctuating variables. This method, created with Hill's thermodynamic analysis, is used to find properties in the thermodynamic limit, such as thermodynamic correction factors, partial enthalpies, volumes, heat capacities and compressibility. The values in the thermodynamic limit at (T,V, μj) are then easily transformed into other ensembles, (T,V,Nj) and (T,P,Nj), where the last ensemble gives the partial molar properties which are of interest to chemists. The dissociation of hydrogen from molecules to atoms was used as a conve…
Non-linear systems under impulsive parametric input
1999
In this paper the problem of the response of non-linear systems excited by an impulsive parametric input is treated. For such systems the response exhibits a jump depending on the amplitude of the impulse as well as on the value of the state variables immediately before the impulse occurrence. Recently, the jump prediction has been obtained in a series form. Here the incremental rule for any scalar real valued function is obtained in an analytical form involving the jump of the state variables. It is also shown that the formulation for the jump evaluation is also able to give a new step-by-step integration technique.
Analysis of multi degree of freedom systems with fractional derivative elements of rational order
2014
In this paper a novel method based on complex eigenanalysis in the state variables domain is proposed to uncouple the set of rational order fractional differential equations governing the dynamics of multi-degree-of-freedom system. The traditional complex eigenanalysis is appropriately modified to be applicable to the coupled fractional differential equations. This is done by expanding the dimension of the problem and solving the system in the state variable domain. Examples of applications are given pertaining to multi-degree-of-freedom systems under both deterministic and stochastic loads.
Magnus and Fer expansions for matrix differential equations: the convergence problem
1998
Approximate solutions of matrix linear differential equations by matrix exponentials are considered. In particular, the convergence issue of Magnus and Fer expansions is treated. Upper bounds for the convergence radius in terms of the norm of the defining matrix of the system are obtained. The very few previously published bounds are improved. Bounds to the error of approximate solutions are also reported. All results are based just on algebraic manipulations of the recursive relation of the expansion generators.
Application of the theory of naturally curved and twisted bars to designing Gorlov's helical turbine 1. System of governing equations
1998
The method of designing a new type of turbine used in flows of various kinds is discussed. Static, kinematic, and constitutive equations for transversely isotropic naturally curved and twisted bars are given, and the hypotheses used are discussed. The statement of the problem is linear and corresponds to small displacements. A method for solving the statically indeterminate problem is proposed. The objectives of numerical calculations, which will comprise the content of the second part of the investigation, are formulated.
Ornstein-Zernike equation and Percus-Yevick theory for molecular crystals
2004
We derive the Ornstein-Zernike equation for molecular crystals of axially symmetric particles and apply the Percus-Yevick approximation to this system. The one-particle orientational distribution function has a nontrivial dependence on the orientation and is needed as an input. Despite some differences, the Ornstein-Zernike equation for molecular crystals has a similar structure as for liquids. We solve both equations for hard ellipsoids on a sc lattice. Compared to molecular liquids, the tensorial orientational correlators exhibit less structure. However, depending on the lengths a and b of the rotation axis and the perpendicular axes of the ellipsoids, different behavior is found. For obl…
$L_2$-variation of L\'{e}vy driven BSDEs with non-smooth terminal conditions
2016
We consider the $L_2$-regularity of solutions to backward stochastic differential equations (BSDEs) with Lipschitz generators driven by a Brownian motion and a Poisson random measure associated with a L\'{e}vy process $(X_t)_{t\in[0,T]}$. The terminal condition may be a Borel function of finitely many increments of the L\'{e}vy process which is not necessarily Lipschitz but only satisfies a fractional smoothness condition. The results are obtained by investigating how the special structure appearing in the chaos expansion of the terminal condition is inherited by the solution to the BSDE.
One-dimensional random walks with self-blocking immigration
2017
We consider a system of independent one-dimensional random walkers where new particles are added at the origin at fixed rate whenever there is no older particle present at the origin. A Poisson ansatz leads to a semi-linear lattice heat equation and predicts that starting from the empty configuration the total number of particles grows as $c \sqrt{t} \log t$. We confirm this prediction and also describe the asymptotic macroscopic profile of the particle configuration.
Statistics of nonlinear stochastic dynamical systems under Lévy noises by a convolution quadrature approach
2010
This paper describes a novel numerical approach to find the statistics of the non-stationary response of scalar non-linear systems excited by L\'evy white noises. The proposed numerical procedure relies on the introduction of an integral transform of Wiener-Hopf type into the equation governing the characteristic function. Once this equation is rewritten as partial integro-differential equation, it is then solved by applying the method of convolution quadrature originally proposed by Lubich, here extended to deal with this particular integral transform. The proposed approach is relevant for two reasons: 1) Statistics of systems with several different drift terms can be handled in an efficie…
Weighted bounded mean oscillation applied to backward stochastic differential equations
2015
Abstract We deduce conditional L p -estimates for the variation of a solution of a BSDE. Both quadratic and sub-quadratic types of BSDEs are considered, and using the theory of weighted bounded mean oscillation we deduce new tail estimates for the solution ( Y , Z ) on subintervals of [ 0 , T ] . Some new results for the decoupling technique introduced in Geiss and Ylinen (2019) are obtained as well and some applications of the tail estimates are given.