Search results for "Nonlinear"
showing 10 items of 3684 documents
Noise delayed decay of unstable states: theory versus numerical simulations
2004
We study the noise delayed decay of unstable nonequilibrium states in nonlinear dynamical systems within the framework of the overdamped Brownian motion model. We give the exact expressions for the decay times of unstable states for polynomial potential profiles and obtain nonmonotonic behavior of the decay times as a function of the noise intensity for the unstable nonequilibrium states. The analytical results are compared with numerical simulations.
A Temperature Dependent Non-Linear Inductor Model for a DC/DC Boost Converter
2018
This paper is focused on the use of non-linear inductors in DC/DC switching converters, as well as their behaviour due to changes in current and temperature. The model of an inductor is set up on the basis of experimental data, which are automatically acquired by a virtual instrument; from those data, a polynomial curve describing the inductance variations is obtained. The analysis of the converter, performed by including the proposed model, is validated by experimental tests.
On the Leibniz bracket, the Schouten bracket and the Laplacian
2003
International audience; The Leibniz bracket of an operator on a (graded) algebra is defined and some of its properties are studied. A basic theorem relating the Leibniz bracket of the commutator of two operators to the Leibniz bracket of them is obtained. Under some natural conditions, the Leibniz bracket gives rise to a (graded) Lie algebra structure. In particular, those algebras generated by the Leibniz bracket of the divergence and the Laplacian operators on the exterior algebra are considered, and the expression of the Laplacian for the product of two functions is generalized for arbitrary exterior forms.
A direct method to find solutions of some type of coupled Korteweg-de Vries equations using hyperelliptic functions of genus two
2008
Abstract We suggest how one can obtain exact solutions of some type of coupled Korteweg–de Vries equations by means of hyperelliptic functions of genus two.
Nilpotence of orbits under monodromy and the length of Melnikov functions
2021
Abstract Let F ∈ ℂ [ x , y ] be a polynomial, γ ( z ) ∈ π 1 ( F − 1 ( z ) ) a non-trivial cycle in a generic fiber of F and let ω be a polynomial 1-form, thus defining a polynomial deformation d F + e ω = 0 of the integrable foliation given by F . We study different invariants: the orbit depth k , the nilpotence class n , the derivative length d associated with the couple ( F , γ ) . These invariants bind the length l of the first nonzero Melnikov function of the deformation d F + e ω along γ . We analyze the variation of the aforementioned invariants in a simple but informative example, in which the polynomial F is defined by a product of four lines. We study as well the relation of this b…
Maximal slicings in spherical symmetry: Local existence and construction
2011
We show that any spherically symmetric spacetime locally admits a maximal spacelike slicing and we give a procedure allowing its construction. The construction procedure that we have designed is based on purely geometrical arguments and, in practice, leads to solve a decoupled system of first order quasi-linear partial differential equations. We have explicitly built up maximal foliations in Minkowski and Friedmann spacetimes. Our approach admits further generalizations and efficient computational implementation. As by product, we suggest some applications of our work in the task of calibrating Numerical Relativity complex codes, usually written in Cartesian coordinates.
Multiparticle breathers for a chain with double-quadratic on-site potential
1999
We investigate the existence and properties of multiparticle breathers for a one-dimensional model with harmonic nearest neighbor interactions where a group of r particles $(r=1,2,3,\dots{})$ perform interwell oscillations between both wells of a double-quadratic on-site potiential. We find two types of such breathers. For the first type the breather frequency $\ensuremath{\Omega}$ is within the single-particle oscillator spectrum, and the ``residence'' time of each breather particle in the left and right well is about the same. For the second breather $\ensuremath{\Omega}$ is below that spectrum, and the ratio ${\ensuremath{\tau}}_{L}/{\ensuremath{\tau}}_{R}$ of the residence time in the l…
Dynamics of breather modes in a nonlinear “helicoidal” model of DNA
1991
Via a recent model with an additional helicoidal coupling, the dynamics of breathers modes in DNA are studied analytically and with the use of numerical simulations. It is shown that these excitations are longlived and can match experimentally observed fluctuational openings.
Entanglement between two superconducting qubits via interaction with nonclassical radiation
2003
We propose a scheme to physically interface superconducting nano-circuits and quantum optics. We address the transfer of quantum information between systems having different physical natures and defined in Hilbert spaces of different dimensions. In particular, we investigate the transfer of the entanglement initially in a non-classical state of a continuous-variable system to a pair of superconducting charge qubits. This set-up is able to drive an initially separable state of the qubits into an almost pure, highly entangled state suitable for quantum information processing.
Generalized Bloch spheres form-qubit states
2006
m-Qubit states are imbedded in $\mathfrak{Cl}_{2^m}$ Clifford algebras. Their probability spectra then depend on $O(2m)$ or $O(2m+1)$ invariants. Parameter domains for $O(2m(+1))-$ vector and tensor configurations, generalizing the notion of a Bloch sphere, are derived.