Search results for "Mathematical physics"
showing 10 items of 2687 documents
High Spin Phenomena in the Mass 100-200 Region Seen Through the Crystal Ball
1983
The average properties of the gamma ray entry region and the decay from it are studied systematically, for 49 nuclear systems, in the spin spectrometer. Preliminary results are given for the mass the neutron number dependence of the gamma ray fold distribution and of unresolved γ spectra. The possibility of gating simultaneously on narrow regions of fold and excitation energy is exploited.
Thermodynamics of Toda lattice models: application to DNA
1993
Abstract Our generalised Bethe ansatz method is used to formulate the statistical mechanics of the classical Toda lattice in terms of a set of coupled integral equations expressed in terms of appropriate action-angle variables. The phase space as coordinatised by these action-angle variables is constrained; and both the soliton number density and the soliton contribution to the free energy density can be shown to decouple from the phonon degrees of freedom and to depend only on soliton-soliton interactions. This makes it possible to evaluate the temperature dependence of the soliton number density which, to leading order, is found to be proportional to T 1 3 .
Semipredictable dynamical systems
2015
A new class of deterministic dynamical systems, termed semipredictable dynamical systems, is presented. The spatiotemporal evolution of these systems have both predictable and unpredictable traits, as found in natural complex systems. We prove a general result: The dynamics of any deterministic nonlinear cellular automaton (CA) with $p$ possible dynamical states can be decomposed at each instant of time in a superposition of $N$ layers involving $p_{0}$, $p_{1}$,... $p_{N-1}$ dynamical states each, where the $p_{k\in \mathbb{N}}$, $k \in [0, N-1]$ are divisors of $p$. If the divisors coincide with the prime factors of $p$ this decomposition is unique. Conversely, we also prove that $N$ CA w…
BEM-Based Magnetic Field Reconstruction by Ensemble Kálmán Filtering
2022
Abstract Magnetic fields generated by normal or superconducting electromagnets are used to guide and focus particle beams in storage rings, synchrotron light sources, mass spectrometers, and beamlines for radiotherapy. The accurate determination of the magnetic field by measurement is critical for the prediction of the particle beam trajectory and hence the design of the accelerator complex. In this context, state-of-the-art numerical field computation makes use of boundary-element methods (BEM) to express the magnetic field. This enables the accurate computation of higher-order partial derivatives and local expansions of magnetic potentials used in efficient numerical codes for particle tr…
The energy minimization problem for two-level dissipative quantum systems
2010
In this article, we study the energy minimization problem of dissipative two-level quantum systems whose dynamics is governed by the Kossakowski–Lindblad equations. In the first part, we classify the extremal curve solutions of the Pontryagin maximum principle. The optimality properties are analyzed using the concept of conjugate points and the Hamilton–Jacobi–Bellman equation. This analysis completed by numerical simulations based on adapted algorithms allows a computation of the optimal control law whose robustness with respect to the initial conditions and dissipative parameters is also detailed. In the final section, an application in nuclear magnetic resonance is presented.
Quantum and classical integrability: new approaches in statistical mechanics
1991
Abstract The present status of the statistical mechanics (SM), quantum and classical, of integrable models is reviewed by reporting new results for their partition functions Z obtained for anyon type models in one space and one time (1 + 1) dimensions. The methods of functional integration developed already are extended further. Bose-Fermi equivalence and anyon descriptions are natural parts of the quantum theory and the anyon phase is quantised. The classical integrability is exploited throughout and both classical and quantum integrability theory are reviewed this way, and related to underlying algebraic structures - notably the Hopf algebras (“quantum groups”). A new “ q -boson” lattice …
Expansion cone for the 3-inch PMTs of the KM3NeT optical modules
2013
[EN] Detection of high-energy neutrinos from distant astrophysical sources will open a new window on the Universe. The detection principle exploits the measurement of Cherenkov light emitted by charged particles resulting from neutrino interactions in the matter containing the telescope. A novel multi-PMT digital optical module (DOM) was developed to contain 31 3-inch photomultiplier tubes (PMTs). In order to maximize the detector sensitivity, each PMT will be surrounded by an expansion cone which collects photons that would otherwise miss the photocathode. Results for various angles of incidence with respect to the PMT surface indicate an increase in collection efficiency by 30% on average…
A PCI Express optical link based on low-cost transceivers qualified for radiation hardness
2013
In this paper we want to demonstrate that an optical physical medium is compatible with the second generation of PCI Express. The benefit introduced by the optical decoupling of a PCI Express endpoint is twofold: it allows for a geographical detachment of the device and it remains compliant with the usual PCI accesses to the legacy I/O and memory spaces. We propose two boards that can bridge the PCI Express protocol over optical fiber. The first is a simple optical translator while the second is a more robust switch developed for connecting up to four devices to a single host. Such adapters are already working in the control and data acquisition system of a particle detector at CERN and hen…
Fixed domain approaches in shape optimization problems with Dirichlet boundary conditions
2009
Fixed domain methods have well-known advantages in the solution of variable domain problems including inverse interface problems. This paper examines two new control approaches to optimal design problems governed by general elliptic boundary value problems with Dirichlet boundary conditions. Numerical experiments are also included peerReviewed
Order of products of elements in finite groups
2018
If G is a finite group, p is a prime, and x∈G, it is an interesting problem to place x in a convenient small (normal) subgroup of G, assuming some knowledge of the order of the products xy, for certain p‐elements y of G.