Search results for "init"

Ultrafast decay of the excited singlet states of thioxanthone by internal conversion and intersystem crossing.

2010

The experimental ultrafast photophysics of thioxanthone in several aprotic organic solvents at room temperature is presented, measured using femtosecond transient absorption together with high-level ab initio CASPT2 calculations of the singlet- and triplet-state manifolds in the gas phase, including computed state minima and conical intersections, transition energies, oscillator strengths, and spin-orbit coupling terms. The initially populated singlet pi pi* state is shown to decay through internal conversion and intersystem crossing processes via intermediate n pi* singlet and triplet states, respectively. Two easily accessible conical intersections explain the favorable internal conversio…

From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture

2020

Abstract In this paper we study the joint convexity/concavity of the trace functions Ψ p , q , s ( A , B ) = Tr ( B q 2 K ⁎ A p K B q 2 ) s , p , q , s ∈ R , where A and B are positive definite matrices and K is any fixed invertible matrix. We will give full range of ( p , q , s ) ∈ R 3 for Ψ p , q , s to be jointly convex/concave for all K. As a consequence, we confirm a conjecture of Carlen, Frank and Lieb. In particular, we confirm a weaker conjecture of Audenaert and Datta and obtain the full range of ( α , z ) for α-z Renyi relative entropies to be monotone under completely positive trace preserving maps. We also give simpler proofs of many known results, including the concavity of Ψ p…

2014

This paper investigates the finite-time distributedL2–L∞consensus control problem of multiagent systems with parameter uncertainties. The relative states of neighboring agents are used to construct the control law and some agents know their own states. By substituting the control input into multiagent systems, an augmented closed-loop system is obtained. Then, we analyze its finite-time boundedness (FTB) and finite-timeL2–L∞performance. A sufficient condition for the existence of the designed controller is given with the form of linear matrix inequalities (LMIs). Finally, simulation results are described.

Elementary Newtonian Mechanics

2010

This chapter deals with the kinematics and the dynamics of a finite number of mass points that are subject to internal, and possibly external, forces, but whose motions are not further constrained by additional conditions on the coordinates. Constraints such as requiring some mass points to follow given curves in space, to keep their relative distance fixed, or the like, are introduced in Chap. 2. Unconstrained mechanical systems can be studied directly by means of Newton’s equations and do not require the introduction of new, generalized coordinates that incorporate the constraints and are dynamically independent. This is what is meant by “elementary” in the heading of this chapter — thoug…

High Order Extrapolation Techniques for WENO Finite-Difference Schemes Applied to NACA Airfoil Profiles

2017

Finite-difference WENO schemes are capable of approximating accurately and efficiently weak solutions of hyperbolic conservation laws. In this context high order numerical boundary conditions have been proven to increase significantly the resolution of the numerical solutions. In this paper a finite-difference WENO scheme is combined with a high order boundary extrapolation technique at ghost cells to solve problems involving NACA airfoil profiles. The results obtained are comparable with those obtained through other techniques involving unstructured meshes.

Flux-gradient and source-term balancing for certain high resolution shock-capturing schemes

2009

Abstract We present an extension of Marquina’s flux formula, as introduced in Fedkiw et al. [Fedkiw RP, Merriman B, Donat R, Osher S. The penultimate scheme for systems of conservation laws: finite difference ENO with Marquina’s flux splitting. In: Hafez M, editor. Progress in numerical solutions of partial differential equations, Arcachon, France; July 1998], for the shallow water system. We show that the use of two different Jacobians at cell interfaces prevents the scheme from satisfying the exact C -property [Bermudez A, Vazquez ME. Upwind methods for hyperbolic conservation laws with source terms. Comput Fluids 1994;23(8):1049–71] while the approximate C -property is satisfied for high…

Large time behavior for a porous medium equation in a nonhomogeneous medium with critical density

2014

Abstract We study the large time behavior of solutions to the Cauchy problem for the porous medium equation in nonhomogeneous media with critical singular density | x | − 2 ∂ t u = Δ u m , in R N × ( 0 , ∞ ) , where m > 1 and N ≥ 3 , with nonnegative initial condition u ( x , 0 ) = u 0 ( x ) ≥ 0 . The asymptotic behavior proves to have some interesting and striking properties. We show that there are different asymptotic profiles for the solutions, depending on whether the continuous initial data u 0 vanishes at x = 0 or not. Moreover, when u 0 ( 0 ) = 0 , we show the convergence towards a peak-type profile presenting a jump discontinuity, coming from an interesting asymptotic simplification…

Numerical propagator method solutions for the linear parabolic initial boundary-value problems

2007

On the base of our numerical propagator method a new finite volume difference scheme is proposed for solution of linear initial-boundary value problems. Stability of the scheme is investigated taking into account the obtained analytical solution of the initial-boundary value problems. It is shown that stability restrictions for the propagator scheme become weaker in comparison to traditional semi-implicit difference schemes. There are some regions of coefficients, for which the elaborated propagator difference scheme becomes absolutely stable. It is proven that the scheme is unconditionally monotonic. Analytical solutions, which are consistent with solubility conditions of the problem are f…

Long-range cohesive interactions of non-local continuum faced by fractional calculus

2008

Abstract A non-local continuum model including long-range forces between non-adjacent volume elements has been studied in this paper. The proposed continuum model has been obtained as limit case of two fully equivalent mechanical models: (i) A volume element model including contact forces between adjacent volumes as well as long-range interactions, distance decaying, between non-adjacent elements. (ii) A discrete point-spring model with local springs between adjacent points and non-local springs with distance-decaying stiffness connecting non-adjacent points. Under the assumption of fractional distance-decaying interactions between non-adjacent elements a fractional differential equation in…

An optimality test for semi-infinite linear programming

1992

In this paper we present a test to characterize the optimal solutions for the continuous semi-infinite linear programming problem. This optimality characterization is a condition of Kuhn–Tucker type. The resolution of a linear program permits to check the optimality of a feasible point,to detect the unboundedness of the problem and to find descent directions. We give some illustrative examples. We show that the local Mangasarian–Fromovitz constraint qualification is almost equivalent to Slater qualification for this problem. Furthermore, it follows from our study that this optimality condition is always necessary for a wide class of semi-infinite linear programming problems