Search results for " Operator"
showing 10 items of 931 documents
From classical to operatorial models
2023
Mathematical models for the collective dynamics of interacting and spatially distributed populations find applications in several contexts (biology, ecology, social sciences). Their formulation depends primarily on the (continuous or discrete) description of the space. Reaction-diffusion equations have been widely used in bioecology (morphogenesis, migration of biological species, tumor growth, neuro-degenerative diseases) and in the social sciences (diffusion of opinions or decisionmaking processes), and exhibit complex behaviors (propagation of oscillatory phenomena, pattern formation caused by instability). A reaction–diffusion system exhibits diffusion-driven instability, sometimes call…
Revealing non-classical behaviours in the oscillatory motion of a trapped ion
2003
The possibility of revealing non-classical behaviours in the dynamics of a trapped ion via measurements of the mean value of suitable operators is reported. In particular we focus on the manifestation known as `` Parity Effect\rq\rq which may be observed \emph{directly measuring} the expectation value of an appropriate correlation operator. The experimental feasibility of our proposal is discussed.
Exact Coulomb cutoff technique for supercell calculations in two dimensions
2009
We present a reciprocal space technique for the calculation of the Coulomb integral in two dimensions in systems with reduced periodicity, i.e., finite systems, or systems that are periodic only in one dimension. The technique consists in cutting off the long-range part of the interaction by modifying the expression for the Coulomb operator in reciprocal space. The physical result amounts in an effective screening of the spurious interactions originated by the presence of ghost periodic replicas of the system. This work extends a previous report [C. A. Rozzi et al., Phys. Rev. B 73, 205119 (2006)], where three-dimensional systems were considered. We show that the use of the cutoffs dramatic…
Minimal unit vector fields
2002
We compute the first variation of the functional that assigns each unit vector field the volume of its image in the unit tangent bundle. It is shown that critical points are exactly those vector fields that determine a minimal immersion. We also find a necessary and sufficient condition that a vector field, defined in an open manifold, must fulfill to be minimal, and obtain a simpler equivalent condition when the vector field is Killing. The condition is fulfilled, in particular, by the characteristic vector field of a Sasakian manifold and by Hopf vector fields on spheres.
A WAVELET OPERATOR ON THE INTERVAL IN SOLVING MAXWELL'S EQUATIONS
2011
In this paper, a differential wavelet-based operator defined on an interval is presented and used in evaluating the electromagnetic field described by Maxwell's curl equations, in time domain. The wavelet operator has been generated by using Daubechies wavelets with boundary functions. A spatial differential scheme has been performed and it has been applied in studying electromagnetic phenomena in a lossless medium. The proposed approach has been successfully tested on a bounded axial-symmetric cylindrical domain.
The exterior derivative as a Killing vector field
1996
Among all the homogeneous Riemannian graded metrics on the algebra of differential forms, those for which the exterior derivative is a Killing graded vector field are characterized. It is shown that all of them are odd, and are naturally associated to an underlying smooth Riemannian metric. It is also shown that all of them are Ricci-flat in the graded sense, and have a graded Laplacian operator that annihilates the whole algebra of differential forms.
Adaptive rational interpolation for cell-average
2020
Abstract In this paper, we extend the rational interpolation introduced by G. Ramponi et al. (1997, 1998, 1996, 1995) to the cell average setting. We propose a new family of non linear interpolation operator. It consists on constructing new approximations using a non linear weighted combination of polynomials of degree 1 or 2 to obtain new interpolations of degree 2 or 4 respectively. New weights are proposed and analyzed. Gibbs phenomenon is studied and some experiments are performed comparing the new methods with classical linear and non linear interpolation as Weighted Essentially Non-Oscillatory (WENO).
Heisenberg Uncertainty Relation in Quantum Liouville Equation
2009
We consider the quantum Liouville equation and give a characterization of the solutions which satisfy the Heisenberg uncertainty relation. We analyze three cases. Initially we consider a particular solution of the quantum Liouville equation: the Wigner transformf(x,v,t) of a generic solutionψ(x;t) of the Schrödinger equation. We give a representation ofψ(x,t) by the Hermite functions. We show that the values of the variances ofxandvcalculated by using the Wigner functionf(x,v,t) coincide, respectively, with the variances of position operatorX^and conjugate momentum operatorP^obtained using the wave functionψ(x,t). Then we consider the Fourier transform of the density matrixρ(z,y,t) =ψ∗(z,t)…
Alternative Methods of Sterilization in Dental Practices Against COVID-19
2020
SARS-CoV-2, and several other microorganisms, may be present in nasopharyngeal and salivary secretions in patients treated in dental practices, so an appropriate clinical behavior is required in order to avoid the dangerous spread of infections. COVID-19 could also be spread when patients touches a contaminated surface with infected droplets and then touch their nose, mouth, or eyes. It is time to consider a dental practice quite similar to a hospital surgery room, where particular attention should be addressed to problems related to the spreading of infections due to air and surface contamination. The effectiveness of conventional cleaning and disinfection procedures may be limited by seve…
Positive solutions for a discrete two point nonlinear boundary value problem with p-Laplacian
2017
Abstract In the framework of variational methods, we use a two non-zero critical points theorem to obtain the existence of two positive solutions to Dirichlet boundary value problems for difference equations involving the discrete p -Laplacian operator.