Search results for "Mathematical physics"

The ATLAS Level-1 Calorimeter Trigger: PreProcessor implementation and performance

2012

The PreProcessor system of the ATLAS Level-1 Calorimeter Trigger (L1Calo) receives about 7200 analogue signals from the electromagnetic and hadronic components of the calorimetric detector system. Lateral division results in cells which are pre-summed to so-called Trigger Towers of size 0.1 × 0.1 along azimuth (phi) and pseudorapidity (η). The received calorimeter signals represent deposits of transverse energy. The system consists of 124 individual PreProcessor modules that digitise the input signals for each LHC collision, and provide energy and timing information to the digital processors of the L1Calo system, which identify physics objects forming much of the basis for the full ATLAS fi…

Readout system of the ALICE Fast Interaction Trigger

2020

Upgrade of the ATLAS Central Trigger for LHC Run-2

2015

The increased energy and luminosity of the LHC in the run-2 data taking period requires a more selective trigger menu in order to satisfy the physics goals of ATLAS. Therefore the electronics of the central trigger system is upgraded to allow for a larger variety and more sophisticated trigger criteria. In addition, the software controlling the central trigger processor (CTP) has been redesigned to allow the CTP to accommodate three freely configurable and separately operating sets of sub detectors, each independently using the almost full functionality of the trigger hardware. This new approach and its operational advantages are discussed as well as the hardware upgrades.

Peiffer product and peiffer commutator for internal pre-crossed modules

2017

In this work we introduce the notions of Peiffer product and Peiffer commutator of internal pre-crossed modules over a fixed object B, extending the corresponding classical notions to any semi-abelian category C. We prove that, under mild additional assumptions on C, crossed modules are characterized as those pre-crossed modules X whose Peiffer commutator 〈X, X〉 is trivial. Furthermore we provide suitable conditions on C (fulfilled by a large class of algebraic varieties, including among others groups, associative algebras, Lie and Leibniz algebras) under which the Peiffer product realizes the coproduct in the category of crossed modules over B.

The Heisenberg dynamics of spin systems: A quasi*‐algebras approach

1996

The problem of the existence of the thermodynamical limit of the algebraic dynamics for a class of spin systems is considered in the framework of a generalized algebraic approach in terms of a special class of quasi*-algebras, called CQ*-algebras. Physical applications to (almost) mean-field models and to bubble models are discussed. © 1996 American Institute of Physics.

Discrete KP Equation and Momentum Mapping of Toda System

2003

Abstract A new approach to discrete KP equation is considered, starting from the Gelfand-Zakhharevich theory for the research of Casimir function for Toda Poisson pencil. The link between the usual approach through the use of discrete Lax operators, is emphasized. We show that these two different formulations of the discrete KP equation are equivalent and they are different representations of the same equations. The relation between the two approaches to the KP equation is obtained by a change of frame in the space of upper truncated Laurent series and translated into the space of shift operators.

Everywhere differentiability of viscosity solutions to a class of Aronsson's equations

2017

For any open set $\Omega\subset\mathbb R^n$ and $n\ge 2$, we establish everywhere differentiability of viscosity solutions to the Aronsson equation $$ =0 \quad \rm in\ \ \Omega, $$ where $H$ is given by $$H(x,\,p)==\sum_{i,\,j=1}^na^{ij}(x)p_i p_j,\ x\in\Omega, \ p\in\mathbb R^n, $$ and $A=(a^{ij}(x))\in C^{1,1}(\bar\Omega,\mathbb R^{n\times n})$ is uniformly elliptic. This extends an earlier theorem by Evans and Smart \cite{es11a} on infinity harmonic functions.

Statistical Thermodynamics of Polymer Quantum Systems

2011

Polymer quantum systems are mechanical models quantized similarly as loop quantum gravity. It is actually in quantizing gravity that the polymer term holds proper as the quantum geometry excitations yield a reminiscent of a polymer material. In such an approach both non-singular cosmological models and a microscopic basis for the entropy of some black holes have arisen. Also important physical questions for these systems involve thermodynamics. With this motivation, in this work, we study the statistical thermody- namics of two one dimensional polymer quantum systems: an ensemble of oscillators that describe a solid and a bunch of non-interacting particles in a box, which thus form an ideal…

Anisotropic elliptic equations with gradient-dependent lower order terms and L^1 data

2023

<abstract><p>We prove the existence of a weak solution for a general class of Dirichlet anisotropic elliptic problems such as $ \mathcal Au+\Phi(x, u, \nabla u) = \mathfrak{B}u+f $ in $ \Omega $, where $ \Omega $ is a bounded open subset of $ \mathbb R^N $ and $ f\in L^1(\Omega) $ is arbitrary. The principal part is a divergence-form nonlinear anisotropic operator $ \mathcal A $, the prototype of which is $ \mathcal A u = -\sum_{j = 1}^N \partial_j(|\partial_j u|^{p_j-2}\partial_j u) $ with $ p_j > 1 $ for all $ 1\leq j\leq N $ and $ \sum_{j = 1}^N (1/p_j) > 1 $. As a novelty in this paper, our lower order terms involve a new class of operators $ \mathfrak B $ such…

Nambu-Poisson manifolds and associated n-ary Lie algebroids

2001

We introduce an n-ary Lie algebroid canonically associated with a Nambu-Poisson manifold. We also prove that every Nambu-Poisson bracket defined on functions is induced by some differential operator on the exterior algebra, and characterize such operators. Some physical examples are presented.