Negative energy densities in integrable quantum field theories at one-particle level

We study the phenomenon of negative energy densities in quantum field theories with self-interaction. Specifically, we consider a class of integrable models (including the sinh-Gordon model) in which we investigate the expectation value of the energy density in one-particle states. In this situation, we classify the possible form of the stress-energy tensor from first principles. We show that one-particle states with negative energy density generically exist in non-free situations, and we establish lower bounds for the energy density (quantum energy inequalities). Demanding that these inequalities hold reduces the ambiguity in the stress-energy tensor, in some situations fixing it uniquely. Numerical results for the lowest spectral value of the energy density allow us to demonstrate how negative energy densities depend on the coupling constant and on other model parameters

Entropy continuity for interval maps with holes

We study the dependence of the topological entropy of piecewise monotonic maps with holes under perturbations, for example sliding a hole of fixed size at uniform speed or expanding a hole with uniform expansion. We show that under suitable conditions the topological entropy varies locally Hoelder continuously with the local Hoelder exponent depending itself on the value of the topological entropy.Comment: 23 pages; section 6 has been considerably simplified following suggestions of a referee; to appear in Ergodic Theory and Dynamical System

Temperature dependence of ESR intensity for the nanoscale molecular magnet V15

The electron spin resonance (ESR) of nanoscale molecular magnet ${\rm V}_{15}$ is studied. Since the Hamiltonian of ${\rm V}_{15}$ has a large Hilbert space and numerical calculations of the ESR signal evaluating the Kubo formula with exact diagonalization method is difficult, we implement the formula with the help of the random vector technique and the Chebyshev polynominal expansion, which we name the double Chebyshev expansion method. We calculate the temperature dependence of the ESR intensity of ${\rm V}_{15}$ and compare it with the data obtained in experiment. As another complementary approach, we also implement the Kubo formula with the subspace iteration method taking only important low-lying states into account. We study the ESR absorption curve below $100{\rm K}$ by means of both methods. We find that side peaks appear due to the Dzyaloshinsky-Moriya interaction and these peaks grows as temperature decreases.Comment: 9 pages, 4 figures. To appear in J. Phys. Soc. Jpn. Supp

Efficient Recursion Method for Inverting Overlap Matrix

A new O(N) algorithm based on a recursion method, in which the computational effort is proportional to the number of atoms N, is presented for calculating the inverse of an overlap matrix which is needed in electronic structure calculations with the the non-orthogonal localized basis set. This efficient inverting method can be incorporated in several O(N) methods for diagonalization of a generalized secular equation. By studying convergence properties of the 1-norm of an error matrix for diamond and fcc Al, this method is compared to three other O(N) methods (the divide method, Taylor expansion method, and Hotelling's method) with regard to computational accuracy and efficiency within the density functional theory. The test calculations show that the new method is about one-hundred times faster than the divide method in computational time to achieve the same convergence for both diamond and fcc Al, while the Taylor expansion method and Hotelling's method suffer from numerical instabilities in most cases.Comment: 17 pages and 4 figure

Computing the lower and upper bounds of Laplace eigenvalue problem: by combining conforming and nonconforming finite element methods

This article is devoted to computing the lower and upper bounds of the Laplace eigenvalue problem. By using the special nonconforming finite elements, i.e., enriched Crouzeix-Raviart element and extension $Q_1^{\rm rot}$, we get the lower bound of the eigenvalue. Additionally, we also use conforming finite elements to do the postprocessing to get the upper bound of the eigenvalue. The postprocessing method need only to solve the corresponding source problems and a small eigenvalue problem if higher order postprocessing method is implemented. Thus, we can obtain the lower and upper bounds of the eigenvalues simultaneously by solving eigenvalue problem only once. Some numerical results are also presented to validate our theoretical analysis.Comment: 19 pages, 4 figure

A Jacobi-Davidson type method with a correction equation tailored for integral operators

The final publication is available at Springer via http://dx.doi.org/10.1007/s11075-012-9656-9We propose two iterative numerical methods for eigenvalue computations of large dimensional problems arising from finite approximations of integral operators, and describe their parallel implementation. A matrix representation of the problem on a space of moderate dimension, defined from an infinite dimensional one, is computed along with its eigenpairs. These are taken as initial approximations and iteratively refined, by means of a correction equation based on the reduced resolvent operator and performed on the moderate size space, to enhance their quality. Each refinement step requires the prolongation of the correction equation solution back to a higher dimensional space, defined from the infinite dimensional one. This approach is particularly adapted for the computation of eigenpair approximations of integral operators, where prolongation and restriction matrices can be easily built making a bridge between coarser and finer discretizations. We propose two methods that apply a Jacobi–Davidson like correction: Multipower Defect-Correction (MPDC), which uses a single-vector scheme, if the eigenvalues to refine are simple, and Rayleigh–Ritz Defect-Correction (RRDC), which is based on a projection onto an expanding subspace. Their main advantage lies in the fact that the correction equation is performed on a smaller space while for general solvers it is done on the higher dimensional one. We discuss implementation and parallelization details, using the PETSc and SLEPc packages. Also, numerical results on an astrophysics application, whose mathematical model involves a weakly singular integral operator, are presented.This work was partially supported by European Regional Development Fund through COMPETE, FCT-Fundacao para a Ciencia e a Tecnologia through CMUP-Centro de Matematica da Universidade do Porto and Spanish Ministerio de Ciencia e Innovacion under projects TIN2009-07519 and AIC10-D-000600.Vasconcelos, PB.; D'almeida, FD.; Román Moltó, JE. (2013). A Jacobi-Davidson type method with a correction equation tailored for integral operators. Numerical Algorithms. 64(1):85-103. doi:10.1007/s11075-012-9656-9S85103641Absil, P.A., Mahony, R., Sepulchre, R., Dooren, P.V.: A Grassmann–Rayleigh quotient iteration for computing invariant subspaces. SIAM Rev. 44(1), 57–73 (2002)Ahues, M., Largillier, A., Limaye, B.V.: Spectral Computations with Bounded Operators. Chapman and Hall, Boca Raton (2001)Ahues, M., d’Almeida, F.D., Largillier, A., Titaud, O., Vasconcelos, P.: An L 1 refined projection approximate solution of the radiation transfer equation in stellar atmospheres. J. Comput. Appl. Math. 140(1–2), 13–26 (2002)Ahues, M., d’Almeida, F.D., Largillier, A., Vasconcelos, P.B.: Defect correction for spectral computations for a singular integral operator. Commun. Pure Appl. Anal. 5(2), 241–250 (2006)Bai, Z., Demmel, J., Dongarra, J., Ruhe, A., van der Vorst, H. (eds.): Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide. Society for Industrial and Applied Mathematics, Philadelphia (2000)Balay, S., Buschelman, K., Eijkhout, V., Gropp, W.D., Kaushik, D., Knepley, M., McInnes, L.C., Smith, B.F., Zhang, H.: PETSc Users Manual. Tech. Rep. ANL-95/11 - Revision 3.1, Argonne National Laboratory (2010)Chatelin, F.: Spectral Approximation of Linear Operators. SIAM, Philadelphia (2011)d’Almeida, F.D., Vasconcelos, P.B.: Convergence of multipower defect correction for spectral computations of integral operators. Appl. Math. Comput. 219(4), 1601–1606 (2012)Falgout, R.D., Yang, U.M.: Hypre: A library of high performance preconditioners. In: Sloot, P.M.A., Tan, C.J.K., Dongarra, J., Hoekstra, A.G. (eds.) Computational Science - ICCS 2002, International Conference, Amsterdam, The Netherlands, April 21–24, 2002. Proceedings, Part III, Lecture Notes in Computer Science, vol. 2331, pp. 632–641. Springer (2002)Henson, V.E., Yang, U.M.: BoomerAMG: A parallel algebraic multigrid solver and preconditioner. Appl. Numer. Math. 41(1), 155–177 (2002)Hernandez, V., Roman, J.E., Vidal, V.: SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems. ACM Trans. Math. Softw. 31(3), 351–362 (2005)Hernandez, V., Roman, J.E., Tomas, A., Vidal, V.: SLEPc Users Manual. Tech. Rep. DSIC-II/24/02 - Revision 3.1, D. Sistemas Informáticos y Computación, Universidad Politécnica de Valencia (2010)Saad, Y.: Iterative methods for sparse linear systems, 2nd edn. Society for Industrial and Applied Mathematics, Philadelphia (2003)Simoncini, V., Eldén, L.: Inexact Rayleigh quotient-type methods for eigenvalue computations. BIT 42(1), 159–182 (2002)Sleijpen, G.L.G., van der Vorst, H.A.: A Jacobi–Davidson iteration method for linear eigenvalue problems. SIAM Rev. 42(2), 267–293 (2000)Sorensen, D.C.: Implicit application of polynomial filters in a k-step Arnoldi method. SIAM J. Matrix Anal. Appl. 13, 357–385 (1992)Stewart, G.W.: A Krylov–Schur algorithm for large eigenproblems. SIAM J. Matrix Anal. Appl. 23(3), 601–614 (2001

Asymptotic Expansions for Stationary Distributions of Perturbed Semi-Markov Processes

New algorithms for computing of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes are presented. The algorithms are based on special techniques of sequential phase space reduction, which can be applied to processes with asymptotically coupled and uncoupled finite phase spaces.Comment: 83 page

Sequence Defined Disulfide-Linked Shuttle for Strongly Enhanced Intracellular Protein Delivery

Intracellular protein transduction technology is opening the door for a promising alternative to gene therapy. Techniques have to address all critical steps, like efficient cell uptake, endolysosomal escape, low toxicity, while maintaining full functional activity of the delivered protein. Here, we present the use of a chemically precise, structure defined three-arm cationic oligomer carrier molecule for protein delivery. This carrier of exact and low molecular weight combines good cellular uptake with efficient endosomal escape and low toxicity. The protein cargo is covalently attached by a bioreversible disulfide linkage. Murine 3T3 fibroblasts could be transduced very efficiently with cargo nlsEGFP, which was tagged with a nuclear localization signal. We could show subcellular delivery of the nlsEGFP to the nucleus, confirming cytosolic delivery and expected subsequent subcellular trafficking. Transfection efficiency was concentration-dependent in a directly linear mode and 20-fold higher in comparison with HIV-TAT-nlsEGFP containing a functional TAT transduction domain. Furthermore, β-galactosidase as a model enzyme cargo, modified with the carrier oligomer, was transduced into neuroblastoma cells in enzymatically active form

Cognition based bTBI mechanistic criteria; a tool for preventive and therapeutic innovations

Blast-induced traumatic brain injury has been associated with neurodegenerative and neuropsychiatric disorders. To date, although damage due to oxidative stress appears to be important, the specific mechanistic causes of such disorders remain elusive. Here, to determine the mechanical variables governing the tissue damage eventually cascading into cognitive deficits, we performed a study on the mechanics of rat brain under blast conditions. To this end, experiments were carried out to analyse and correlate post-injury oxidative stress distribution with cognitive deficits on a live rat exposed to blast. A computational model of the rat head was developed from imaging data and validated against in vivo brain displacement measurements. The blast event was reconstructed in silico to provide mechanistic thresholds that best correlate with cognitive damage at the regional neuronal tissue level, irrespectively of the shape or size of the brain tissue types. This approach was leveraged on a human head model where the prediction of cognitive deficits was shown to correlate with literature findings. The mechanistic insights from this work were finally used to propose a novel helmet design roadmap and potential avenues for therapeutic innovations against blast traumatic brain injury