Composition methods are methods for the integration of ordinary differential equations arising from differential geometry, or more precisely, Lie algebra theory. We apply them here to the simulation of arrays of Chua’s circuits. In these methods, we split the vector field of the array of Chua’s circuits into its linear part and its nonlinear part. We then solve the elementary differential equat...

In this paper the Levy-Leblond procedure for linearizing the Schrödinger equation to obtain the Pauli equation for one particle is generalized to obtain an N -particle equation with spin. This is achieved by using the more universal matrix factorization, GG̃ = |G|I = (−K)lI. Here the square matrix G is linear in the total energy E and all momenta, G̃ is the matrix adjoint of G, I is the identity ...

The Lie splitting algorithm is frequently used when splitting stiff ODEs or, more generally, dissipative evolution equations. It is unconditionally stable and is considered to be a robust choice of method in most settings. However, it possesses a rather unfavorable local error structure. This gives rise to order reductions if the evolution equation does not satisfy extra compatibility assumptio...

— A new splitting is proposed for solving the Vlasov–Maxwell system. This splitting is based on a decomposition of the Hamiltonian of the Vlasov–Maxwell system and allows for the construction of arbitrary high order methods by composition (independent of the specific deterministic method used for the discretization of the phase space). Moreover, we show that for a spectral method in space this ...

We present a nested splitting conjugate gradient iteration method for solving large sparse continuous Sylvester equation, in which both coefficient matrices are (non-Hermitian) positive semi-definite, and at least one of them is positive definite. This method is actually inner/outer iterations, which employs the Sylvester conjugate gradient method as inner iteration to approximate each outer it...

This talk discusses the relative impact of running-coupling and other higher-order corrections on the small-x gluon-gluon splitting function. Comments are made on similarities with some aspects of the Balitsky-Kovchegov equation, which arise because of the presence of an effective infrared cutoff in both cases. It is emphasised that, at least in the splitting-function case, the asymptotic small...

Climate warming and atmospheric nitrogen (N) deposition are known to influence ecosystem structure and functioning. However, our understanding of the interactive effect of these global changes on ecosystem functioning is relatively limited, especially when it concerns the responses of soils and soil organisms. We conducted a field experiment to study the interactive effects of warming and N add...

In this paper we study the splitting of separatrices phenomenon which arises when one considers a Hamiltonian System of one degree of freedom with a fast periodic or quasiperiodic and meromorphic in the state variables perturbation. The obtained results are different from the previous ones in the literature, which mainly assume algebraic or trigonometric polynomial dependence on the state varia...

A linear vector equation is considered defined in terms of idempotent mathematics. To solve the equation, we apply an approach that is based on the analysis of distances between vectors in idempotent vector spaces and reduces the solution of the equation to that of a tropical optimization problem. Based on the approach, existence and uniqueness conditions are established for the solution, and a...

Thermodynamical properties and phase diagram of asymmetric strange quark matter using the Polyakov chiral $$\text {SU(3)}$$ mean field (PCQMF) model at finite temperature chemical potential have been investigated. Within PCQMF model, are calculated through scalar fields $$\sigma $$ , $$\zeta $$\delta $$\chi vector $$\omega $$\rho $$\phi loop $$\Phi $$\bar{\Phi }$$ . The isospin splitting consti...