Geometric Algebra Techniques for General Relativity

Geometric (Clifford) algebra provides an efficient mathematical language for describing physical problems. We formulate general relativity in this language. The resulting formalism combines the efficiency of differential forms with the straightforwardness of coordinate methods. We focus our attention on orthonormal frames and the associated connection bivector, using them to find the Schwarzschild and Kerr solutions, along with a detailed exposition of the Petrov types for the Weyl tensor.Comment: 34 pages, 0 figures; submitted to Annals of Physic

Matrix exponential via Clifford algebras

We use isomorphism $\varphi$ between matrix algebras and simple orthogonal Clifford algebras \cl(Q) to compute matrix exponential ${e}^{A}$ of a real, complex, and quaternionic matrix A. The isomorphic image $p=\varphi(A)$ in \cl(Q), where the quadratic form $Q$ has a suitable signature $(p,q),$ is exponentiated modulo a minimal polynomial of $p$ using Clifford exponential. Elements of \cl(Q) are treated as symbolic multivariate polynomials in Grassmann monomials. Computations in \cl(Q) are performed with a Maple package `CLIFFORD'. Three examples of matrix exponentiation are given

Nonlinear [Ca2+] signaling in dendrites and spines caused by activity-dependent depression of Ca2+ extrusion

Spine Ca2+ triggers the induction of synaptic plasticity and other adaptive neuronal responses. The amplitude and time course of Ca2+ signals specify the activation of the signaling pathways that trigger different forms of plasticity such as long-term potentiation and depression. The shapes of Ca2+ signals are determined by the dynamics of Ca2+ sources, Ca2+ buffers, and Ca2+ extrusion mechanisms. Here we show in rat CA1 pyramidal neurons that plasma membrane Ca2+ pumps (PMCAs) and Na+/Ca2+ exchangers are the major Ca2+ extrusion pathways in spines and small dendrites. Surprisingly, we found that Ca2+ extrusion via PMCA and Na+/Ca2+ exchangers slows in an activity-dependent manner, mediated by intracellular Na+ and Ca2+ accumulations. This activity-dependent depression of Ca2+ extrusion is, in part, attributable to Ca2+-dependent inactivation of PMCAs. Ca2+ extrusion recovers from depression with a time constant of 0.5 s. Depression of Ca2+ extrusion provides a positive feedback loop, converting small differences in stimuli into large differences in Ca2+ concentration. Depression of Ca2+ extrusion produces Ca2+ concentration dynamics that depend on the history of neuronal activity and therefore likely modulates the induction of synaptic plasticity

Risk of climate-induced damage in historical textiles

Eleven wool and silk historic textiles and two modern artist's canvases were examined to determine their water vapour adsorption, moisture dimensional response and tensile behaviour. All the textiles showed a similar general pattern of moisture response. A rise in ambient relative humidity (RH) from dry conditions produced expansion of a textile until a certain critical RH level after which a contraction occurred to a greater or lesser degree depending on the yarn crimp and the weave geometry. The largest expansion recorded between the dry state and 80% RH was 1.2 and 0.9% for wool and silk textiles, respectively. The largest shrinkage of 0.8% at high RH range was experienced by a modern linen canvas. Two potential damage mechanisms related to the moisture response of the textiles—stress building as a result of shrinkage of the textile restrained in its dimensional response and the fretting fatigue when yarns move with friction one against another—were found insignificant in typical textile display environments unless the textiles are severely degraded or excessively strained in their mounting

Initial report from the ICFA Neutrino Panel

In July 2013 ICFA established the Neutrino Panel with the mandate "To promote international cooperation in the development of the accelerator-based neutrino-oscillation program and to promote international collaboration in the development a neutrino factory as a future intense source of neutrinos for particle physics experiments". This, the Panel's Initial Report, presents the conclusions drawn by the Panel from three regional "Town Meetings" that took place between November 2013 and February 2014. After a brief introduction and a short summary of the status of the knowledge of the oscillation parameters, the report summarises the approved programme and identifies opportunities for the development of the field. In its conclusions, the Panel recognises that to maximise the discovery potential of the accelerator-based neutrino-oscillation programme it will be essential to exploit the infrastructures that exist at CERN, FNAL and J-PARC and the expertise and resources that reside in laboratories and institutes around the world. Therefore, in its second year, the Panel will consult with the accelerator-based neutrino-oscillation community and its stakeholders to: develop a road-map for the future accelerator-based neutrino-oscillation programme that exploits the ambitions articulated at CERN, FNAL and J-PARC and includes the programme of measurement and test-beam exposure necessary to ensure the programme is able to realise its potential; develop a proposal for a coordinated "Neutrino RD" programme, the accelerator and detector R&D programme required to underpin the next generation of experiments; and to explore the opportunities for the international collaboration necessary to realise the Neutrino Factory.Comment: ICFA Neutrino Panel 2014(01

Wroclaw neutrino event generator

A neutrino event generator developed by the Wroclaw Neutrino Group is described. The physical models included in the generator are discussed and illustrated with the results of simulations. The considered processes are quasi-elastic scattering and pion production modelled by combining the $\Delta$ resonance excitation and deep inelastic scattering.Comment: Talk given at 2nd Scandanavian Neutrino Workshop (SNOW 2006), Stockholm, Sweden, 2-6 May 2006. 3 pages, 6 figure

Statistics of non-linear stochastic dynamical systems under L\'evy noises by a convolution quadrature approach

This paper describes a novel numerical approach to find the statistics of the non-stationary response of scalar non-linear systems excited by L\'evy white noises. The proposed numerical procedure relies on the introduction of an integral transform of Wiener-Hopf type into the equation governing the characteristic function. Once this equation is rewritten as partial integro-differential equation, it is then solved by applying the method of convolution quadrature originally proposed by Lubich, here extended to deal with this particular integral transform. The proposed approach is relevant for two reasons: 1) Statistics of systems with several different drift terms can be handled in an efficient way, independently from the kind of white noise; 2) The particular form of Wiener-Hopf integral transform and its numerical evaluation, both introduced in this study, are generalizations of fractional integro-differential operators of potential type and Gr\"unwald-Letnikov fractional derivatives, respectively.Comment: 20 pages, 5 figure

Information dynamics: Temporal behavior of uncertainty measures

We carry out a systematic study of uncertainty measures that are generic to dynamical processes of varied origins, provided they induce suitable continuous probability distributions. The major technical tool are the information theory methods and inequalities satisfied by Fisher and Shannon information measures. We focus on a compatibility of these inequalities with the prescribed (deterministic, random or quantum) temporal behavior of pertinent probability densities.Comment: Incorporates cond-mat/0604538, title, abstract changed, text modified, to appear in Cent. Eur. J. Phy

Final State Interactions Effects in Neutrino-Nucleus Interactions

Final State Interactions effects are discussed in the context of Monte Carlo simulations of neutrino-nucleus interactions. A role of Formation Time is explained and several models describing this effect are compared. Various observables which are sensitive to FSI effects are reviewed including pion-nucleus interaction and hadron yields in backward hemisphere. NuWro Monte Carlo neutrino event generator is described and its ability to understand neutral current $\pi^0$ production data in $\sim 1$ GeV neutrino flux experiments is demonstrated.Comment: 13 pages, 16 figure