1,823 research outputs found
The Sech(Xi)-type profiles: a Swiss-Army knife for exact analytical modelling of thermal diffusion and wave propagation in graded media
This work deals with exact analytical modelling of transfer phenomena in
heterogeneous materials exhibiting one-dimensional continuous variations of
their properties. Regarding heat transfer, it has recently been shown that by
applying a Liouville transformation and multiple Darboux transformations,
infinite sequences of solvable profiles of thermal effusivity can be
constructed together with the associated temperature (exact) solutions, all in
closed-form expressions (vs. the diffusion-time variable and with a growing
number of parameters). In addition, a particular class of profiles, so-called
sech(xi)-type profiles, exhibit high agility and in the same time parsimony. In
this paper we go further into the description of these solvable profiles and
their properties. Most importantly, their quadrupole formulation is provided
which allows building smooth synthetic profiles of effusivity of arbitrary
complexity and thereafter getting very easily the corresponding temperature
dynamic response. Examples are given with increasing variability of effusivity
and increasing number of elementary profiles. These highly flexible profiles
are equally relevant for providing an exact analytical solution to wave
propagation problems in 1D graded media (i.e. Maxwell's equations, acoustic
equation, telegraph equation...). From now on, let it be for diffusion-like or
wave-like problems, when the leading properties present (possibly piecewise-)
continuously heterogeneous profiles, the classical staircase model can be
advantageously replaced by a "high-level" quadrupole model consisting of one or
more sech(xi)-type profiles, which makes the latter a true Swiss-Army knife for
analytical modelling.Comment: 21 pages; 7 figure
Devil's staircase in kinetically limited growth of Ising model
The devil's staircase is a term used to describe surface or an equilibrium
phase diagram in which various ordered facets or phases are infinitely closely
packed as a function of some model parameter. A classic example is a 1-D Ising
model [bak] wherein long-range and short range forces compete, and the
periodicity of the gaps between minority species covers all rational values. In
many physical cases, crystal growth proceeds by adding surface layers which
have the lowest energy, but are then frozen in place. The emerging layered
structure is not the thermodynamic ground state, but is uniquely defined by the
growth kinetics. It is shown that for such a system, the grown structure tends
to the equilibrium ground state via a devil's staircase traversing an infinity
of intermediate phases. It would be extremely difficult to deduce the simple
growth law based on measurement made on such an grown structure.Comment: 4 pages, PRL submitte
Energy Harvesting Wireless Communications: A Review of Recent Advances
This article summarizes recent contributions in the broad area of energy
harvesting wireless communications. In particular, we provide the current state
of the art for wireless networks composed of energy harvesting nodes, starting
from the information-theoretic performance limits to transmission scheduling
policies and resource allocation, medium access and networking issues. The
emerging related area of energy transfer for self-sustaining energy harvesting
wireless networks is considered in detail covering both energy cooperation
aspects and simultaneous energy and information transfer. Various potential
models with energy harvesting nodes at different network scales are reviewed as
well as models for energy consumption at the nodes.Comment: To appear in the IEEE Journal of Selected Areas in Communications
(Special Issue: Wireless Communications Powered by Energy Harvesting and
Wireless Energy Transfer
Generalization on the Unseen, Logic Reasoning and Degree Curriculum
This paper considers the learning of logical (Boolean) functions with focus
on the generalization on the unseen (GOTU) setting, a strong case of
out-of-distribution generalization. This is motivated by the fact that the rich
combinatorial nature of data in certain reasoning tasks (e.g.,
arithmetic/logic) makes representative data sampling challenging, and learning
successfully under GOTU gives a first vignette of an 'extrapolating' or
'reasoning' learner. We then study how different network architectures trained
by (S)GD perform under GOTU and provide both theoretical and experimental
evidence that for a class of network models including instances of
Transformers, random features models, and diagonal linear networks, a
min-degree-interpolator is learned on the unseen. We also provide evidence that
other instances with larger learning rates or mean-field networks reach leaky
min-degree solutions. These findings lead to two implications: (1) we provide
an explanation to the length generalization problem (e.g., Anil et al. 2022);
(2) we introduce a curriculum learning algorithm called Degree-Curriculum that
learns monomials more efficiently by incrementing supports.Comment: To appear in ICML 202
Disorder and interference: localization phenomena
The specific problem we address in these lectures is the problem of transport
and localization in disordered systems, when interference is present, as
characteristic for waves, with a focus on realizations with ultracold atoms.Comment: Notes of a lecture delivered at the Les Houches School of Physics on
"Ultracold gases and quantum information" 2009 in Singapore. v3: corrected
mistakes, improved script for numerics, Chapter 9 in "Les Houches 2009 -
Session XCI: Ultracold Gases and Quantum Information" edited by C. Miniatura
et al. (Oxford University Press, 2011
On the Application of PSpice for Localised Cloud Security
The work reported in this thesis commenced with a review of methods for creating random binary sequences for encoding data locally by the client before storing in the Cloud. The first method reviewed investigated evolutionary computing software which generated noise-producing functions from natural noise, a highly-speculative novel idea since noise is stochastic. Nevertheless, a function was created which generated noise to seed chaos oscillators which produced random binary sequences and this research led to a circuit-based one-time pad key chaos encoder for encrypting data. Circuit-based delay chaos oscillators, initialised with sampled electronic noise, were simulated in a linear circuit simulator called PSpice. Many simulation problems were encountered because of the nonlinear nature of chaos but were solved by creating new simulation parts, tools and simulation paradigms. Simulation data from a range of chaos sources was exported and analysed using Lyapunov analysis and identified two sources which produced one-time pad sequences with maximum entropy. This led to an encoding system which generated unlimited, infinitely-long period, unique random one-time pad encryption keys for plaintext data length matching. The keys were studied for maximum entropy and passed a suite of stringent internationally-accepted statistical tests for randomness. A prototype containing two delay chaos sources initialised by electronic noise was produced on a double-sided printed circuit board and produced more than 200 Mbits of OTPs. According to Vladimir Kotelnikov in 1941 and Claude Shannon in 1945, one-time pad sequences are theoretically-perfect and unbreakable, provided specific rules are adhered to. Two other techniques for generating random binary sequences were researched; a new circuit element, memristance was incorporated in a Chua chaos oscillator, and a fractional-order Lorenz chaos system with order less than three. Quantum computing will present many problems to cryptographic system security when existing systems are upgraded in the near future. The only existing encoding system that will resist cryptanalysis by this system is the unconditionally-secure one-time pad encryption
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