Search results for "Operator"
showing 10 items of 1427 documents
An upper bound for nonlinear eigenvalues on convex domains by means of the isoperimetric deficit
2010
We prove an upper bound for the first Dirichlet eigenvalue of the p-Laplacian operator on convex domains. The result implies a sharp inequality where, for any convex set, the Faber-Krahn deficit is dominated by the isoperimetric deficit.
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…
Calculation of frequency-dependent polarizabilities using general coupled-cluster models
2006
Abstract An analytic scheme for the calculation of frequency-dependent polarizabilities within a response-theory approach has been implemented for the use within general coupled-cluster (CC) models with arbitrary excitations in the cluster operator. Calculations for CH + and CN demonstrate the fast convergence of the coupled-cluster approach when successively higher excitations are considered. Quadruple excitation effects on the frequency-dependent polarizabilities are found to be rather small except close to the poles.
Pilot applications of internally contracted multireference coupled cluster theory, and how to choose the cluster operator properly.
2011
The internally contracted multireference coupled cluster (icMRCC) method allows a highly accurate description of both static and dynamic correlation with a computational scaling similar to single reference coupled cluster theory. The authors show that the method can lose its orbital invariance and size consistency when no special care is taken in the elimination of redundant excitations. Using the BeH(2) model system, four schemes are compared which differ in their treatment of linear dependencies between excitations of different rank (such as between singles and doubles). While the energy curves agree within tens of μE(h) when truncating the cluster operator at double excitations (icMRCCSD…
Spin-orbit coupling constants from coupled-cluster response theory
2000
A scheme for the calculation of spin-orbit coupling constants using coupled-cluster (CC) electronic structure methods is described based on response-theory expressions for transition properties. An implementation is reported for singlet–triplet transitions within the coupled-cluster singles and doubles (CCSD) approximation. An atomic mean-field representation of the spin-orbit interaction is used to simplify the calculation of spin-orbit coupling constants. Sample calculations are presented for spin-orbit couplings for the 11Σ+→13Π transitions for BH and AlH and for the 11A′→13A″ and the 13A″→11A″ transitions for the silylenes HSiX, X=F, Cl, Br, and are compared to results obtained from ful…
Communication: spin-orbit splittings in degenerate open-shell states via Mukherjee's multireference coupled-cluster theory: a measure for the couplin…
2012
We propose a generally applicable scheme for the computation of spin-orbit (SO) splittings in degenerate open-shell systems using multireference coupled-cluster (MRCC) theory. As a specific method, Mukherjee's version of MRCC (Mk-MRCC) in conjunction with an effective mean-field SO operator is adapted for this purpose. An expression for the SO splittings is derived and implemented using Mk-MRCC analytic derivative techniques. The computed SO splittings are found to be in satisfactory agreement with experimental data. Due to the symmetry properties of the SO operator, SO splittings can be considered a quality measure for the coupling between reference determinants in Jeziorski-Monkhorst base…
Machine learning risk prediction of mortality for patients undergoing surgery with perioperative SARS-CoV-2: the COVIDSurg mortality score
2021
The British journal of surgery 108(11), 1274-1292 (2021). doi:10.1093/bjs/znab183
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.