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2004-12-30 | The Construction of a Partially Regular Solution to the Landau-Lifshitz-Gilbert Equation in $\mathbb{R}^2$ | We establish a framework to construct a global solution in the space of
finite energy to a general form of the Landau-Lifshitz-Gilbert equation in
$\mathbb{R}^2$. Our characterization yields a partially regular solution,
smooth away from a 2-dimensional locally finite Hausdorff measure set. This
construction relies on approximation by discretization, using the special
geometry to express an equivalent system whose highest order terms are linear
and the translation of the machinery of linear estimates on the fundamental
solution from the continuous setting into the discrete setting. This method is
quite general and accommodates more general geometries involving targets that
are compact smooth hypersurfaces. | 0412534v1 |
2002-01-13 | Inverse Cascade Regime in Shell Models of 2-Dimensional Turbulence | We consider shell models that display an inverse energy cascade similar to
2-dimensional turbulence (together with a direct cascade of an enstrophy-like
invariant). Previous attempts to construct such models ended negatively,
stating that shell models give rise to a "quasi-equilibrium" situation with
equipartition of the energy among the shells. We show analytically that the
quasi-equilibrium state predicts its own disappearance upon changing the model
parameters in favor of the establishment of an inverse cascade regime with K41
scaling. The latter regime is found where predicted, offering a useful model to
study inverse cascades. | 0201020v1 |
2002-04-23 | Algebraic decay in hierarchical graphs | We study the algebraic decay of the survival probability in open hierarchical
graphs. We present a model of a persistent random walk on a hierarchical graph
and study the spectral properties of the Frobenius-Perron operator. Using a
perturbative scheme, we derive the exponent of the classical algebraic decay in
terms of two parameters of the model. One parameter defines the geometrical
relation between the length scales on the graph, and the other relates to the
probabilities for the random walker to go from one level of the hierarchy to
another. The scattering resonances of the corresponding hierarchical quantum
graphs are also studied. The width distribution shows the scaling behavior
$P(\Gamma) \sim 1/\Gamma$. | 0204056v1 |
2004-03-11 | Statistics of active vs. passive advections in magnetohydrodynamic turbulence | Active turbulent advection is considered in the context of
magneto-hydrodynamics. In this case, an auxiliary passive field bears no
apparent connection to the active field. The scaling properties of the two
fields are different. In the framework of a shell model, we show that the
two-point structure function of the passive field has a unique zero mode,
characterizing the scaling of this field only. In other words, the existence of
statistical invariants for the decaying passive field carries no information on
the scaling properties of the active field. | 0403017v1 |
2006-01-19 | Drift of particles in self-similar systems and its Liouvillian interpretation | We study the dynamics of classical particles in different classes of
spatially extended self-similar systems, consisting of (i) a self-similar
Lorentz billiard channel, (ii) a self-similar graph, and (iii) a master
equation. In all three systems the particles typically drift at constant
velocity and spread ballistically. These transport properties are analyzed in
terms of the spectral properties of the operator evolving the probability
densities. For systems (i) and (ii), we explain the drift from the properties
of the Pollicott-Ruelle resonance spectrum and corresponding eigenvectors | 0601042v1 |
1997-11-20 | Quantum self-dual codes and symmetric matrices | This paper has been withdrawn since a Gilbert-Varshamov bound for general
quantum codes has already appeared in Ekert and Macchiavello, Prys. Rev. Lett.
77, p. 2585, and a Gilbert-Varshamov bound for stabilizer codes connected with
orthogonal geometry, or equivalently, with symmetric matrices as in this paper,
has been proved by Calredbank, Rains, Shor and Sloane, Phys. Rev. Lett. 78, p.
405. I would like to thank Robert Calderbank for pointing out these references
to me. | 9711047v2 |
2001-06-06 | Constraints on Eavesdropping on the BB84 Protocol | An undetected eavesdropping attack must produce count rate statistics that
are indistinguishable from those that would arise in the absence of such an
attack. In principle this constraint should force a reduction in the amount of
information available to the eavesdropper. In this paper we illustrate, by
considering a particular class of eavesdropping attacks, how the general
analysis of this problem may proceed. | 0106034v2 |
2007-09-14 | A complete proof of The Graceful Tree Conjecture using the concept of Edge Degree | We show the Graceful Tree Conjecture holds. | 0709.2201v9 |
2007-09-24 | An extension of a result concerning convex geometric graphs | We show a general result known as the Erdos_Sos Conjecture: if
$E(G)>{1/2}(k-1)n$ where $G$ has order $n$ then $G$ contains every tree of
order $k+1$ as a subgraph. | 0709.3590v5 |
2008-06-13 | Heat conduction and Fourier's law by consecutive local mixing and thermalization | We present a first-principles study of heat conduction in a class of models
which exhibit a new multi-step local thermalization mechanism which gives rise
to Fourier's law. Local thermalization in our models occurs as the result of
binary collisions among locally confined gas particles. We explore the
conditions under which relaxation to local equilibrium, which involves no
energy exchange, takes place on time scales shorter than that of the binary
collisions which induce local thermalization. The role of this mechanism in
multi-phase material systems such as aerogels is discussed. | 0806.2193v1 |
2010-04-09 | Strict inequalities of critical probabilities on Gilbert's continuum percolation graph | Any infinite graph has site and bond percolation critical probabilities
satisfying $p_c^{site}\geq p_c^{bond}$. The strict version of this inequality
holds for many, but not all, infinite graphs.
In this paper, the class of graphs for which the strict inequality holds is
extended to a continuum percolation model. In Gilbert's graph with
supercritical density on the Euclidean plane, there is almost surely a unique
infinite connected component. We show that on this component $p_c^{site} >
p_c^{bond}$. This also holds in higher dimensions. | 1004.1596v2 |
2010-04-15 | Rank of mapping tori and companion matrices | Given $f$ in $GL(d,Z)$, it is decidable whether its mapping torus (the
semi-direct product of $Z^d$ with $Z$) may be generated by two elements or not;
if so, one can classify generating pairs up to Nielsen equivalence. If $f$ has
infinite order, the mapping torus of $f^n$ cannot be generated by two elements
for $n$ large enough; equivalently, $f^n$ is not conjugate to a companion
matrix in $GL(d,Z)$ if $n$ is large. | 1004.2649v1 |
2010-04-30 | Limit theory for planar Gilbert tessellations | A Gilbert tessellation arises by letting linear segments (cracks) in the
plane unfold in time with constant speed, starting from a homogeneous Poisson
point process of germs in randomly chosen directions. Whenever a growing edge
hits an already existing one, it stops growing in this direction. The resulting
process tessellates the plane. The purpose of the present paper is to establish
law of large numbers, variance asymptotics and a central limit theorem for
geometric functionals of such tessellations. The main tool applied is the
stabilization theory for geometric functionals. | 1005.0023v1 |
2010-06-24 | Periodic solutions for the Landau-Lifshitz-Gilbert equation | Ferromagnetic materials tend to develop very complex magnetization patterns
whose time evolution is modeled by the so-called Landau-Lifshitz-Gilbert
equation (LLG). In this paper, we construct time-periodic solutions for LLG in
the regime of soft and small ferromagnetic particles which satisfy a certain
shape condition. Roughly speaking, it is assumed that the length of the
particle is greater than its hight and its width. The approach is based on a
perturbation argument and the spectral analysis of the corresponding linearized
problem as well as the theory of sectorial operators. | 1006.4765v1 |
2010-12-19 | A counterexample to a Penrose inequality conjectured by Gibbons | We show that the Brill-Lindquist initial data provides a counterexample to a
Riemannian Penrose inequality with charge conjectured by G. Gibbons. The
observation illustrates a sub-additive characteristic of the area radii for the
individual connected components of an outermost horizon as a lower bound of the
ADM mass. | 1012.4190v2 |
2012-01-12 | Coil-helix transition in poly(L-glutamic acid) : Evidence for a 3-state non-cooperative process | A careful analysis of measurements of circular dichroism of poly(L-glutamic
acid) (PGA) shows that the data can be very accurately described by introducing
a third state for the PGA configuration, in addition to the helix and coil
ones, and considering a simple equilibrium between these three states, without
cooperativity. The third state is more conspicuous when high molecular weight
polyethyleneglycol (PEG) is added. Excluded volume effects shown by differences
in presence of short and long PEG chains indicate a direct interaction of PEG
and PGA rather than an osmotic effect. | 1201.2566v1 |
2012-03-20 | Vortex dynamics in the presence of excess energy for the Landau-Lifschitz-Gilbert equation | We study the Landau-Lifshitz-Gilbert equation for the dynamics of a magnetic
vortex system. We present a PDE-based method for proving vortex dynamics that
does not rely on strong well-preparedness of the initial data and allows for
instantaneous changes in the strength of the gyrovector force due to bubbling
events. The main tools are estimates of the Hodge decomposition of the
supercurrent and an analysis of the defect measure of weak convergence of the
stress energy tensor. Ginzburg-Landau equations with mixed dynamics in the
presence of excess energy are also discussed. | 1203.4426v1 |
2012-12-22 | Cumulative Distance Enumerators of Random Codes and their Thresholds | Cumulative weight enumerators of random linear codes are introduced, their
asymptotic properties are studied, and very sharp thresholds are exhibited; as
a consequence, it is shown that the asymptotic Gilbert-Varshamov bound is a
very sharp threshold point for the density of the linear codes whose relative
distance is greater than a given positive number. For arbitrary random codes,
similar settings and results are exhibited; in particular, the very sharp
threshold point for the density of the codes whose relative distance is greater
than a given positive number is located at half the asymptotic
Gilbert-Varshamov bound. | 1212.5679v1 |
2013-01-23 | The Importance of Continuous Value Based Project Management in the Context of Requirements Engineering | Despite several scientific achievements in the last years, there are still a
lot of IT projects that fail. Researchers found that one out of five
IT-projects run out of time, budget or value. Major reasons for this failure
are unexpected economic risk factors that emerge during the runtime of
projects. In order to be able to identify emerging risks early and to
counteract reasonably, financial methods for a continuous IT-project-steering
are necessary, which as of today to the best of our knowledge are missing
within scientific literature. | 1301.5438v1 |
2013-04-08 | On Automorphisms and Subtowers of an asymptotically optimal Tower of Function Fields | In this article we investigate the automorphism group of an asymptotically
optimal tower of function fields introduced by Garcia and Stichtenoth. In
particular we provide a detailed description of the decomposition group of some
rational places. This group acts on the algebraic-geometric standard codes
obtained by the Garcia-Stichtenoth tower exceeding the Gilbert-Varshamov bound.
The fields fixed by the decomposition groups form an asymptotically optimal
non-Galois subtower, which has been first found by Bezerra and Garcia and
yields an improvement for computing codes above the Gilbert-Varshamov bound. In
this article we also describe its proportionality to the Garcia-Stichtenoth
tower and obtain new precise results on its rational places and their
Weierstra{\ss} semigroups. | 1304.2145v1 |
2013-05-06 | The Moment Generating function for ray lengths in the Half Gilbert Model with Rectangular Cells | In the full rectangular version of Gilbert's tessellation lines extend either
horizontally (with east- and west--growing rays) or vertically (north- and
south--growing rays) from seed points which form a Poisson point process, each
ray stopping when another ray is met. In the half rectangular version, east and
south growing rays do not interact with west and north rays. Using techniques
developed in our previous paper, we derive an exact expression for the moment
generating function for the ray length distribution in the half rectangular
model. | 1305.1289v1 |
2013-07-15 | Degenerate transition pathways for screw dislocations: implications for migration | In body-centred-cubic (bcc) metals migrating 1/2<111> screw dislocations
experience a periodic energy landscape with a triangular symmetry. Atomistic
simulations, such as those performed using the nudged-elastic-band (NEB)
method, generally predict a transition-pathway energy-barrier with a
double-hump; contradicting Ab Initio findings. Examining the trajectories
predicted by NEB for a particle in a Peierls energy landscape representative of
that obtained for a screw dislocation, reveals an unphysical anomaly caused by
the occurrence of monkey saddles in the landscape. The implications for motion
of screws with and without stress are discussed. | 1307.3848v2 |
2013-08-17 | The Riemannian Penrose Inequality with Charge for Multiple Black Holes | We present a proof of the Riemannian Penrose inequality with charge $r\leq m
+ \sqrt{m^2-q^2}$, where $A=4\pi r^2$ is the area of the outermost apparent
horizon with possibly multiple connected components, $m$ is the total ADM mass,
and $q$ the total charge of a strongly asymptotically flat initial data set for
the Einstein-Maxwell equations, satisfying the charged dominant energy
condition, with no charged matter outside the horizon. | 1308.3771v3 |
2013-08-23 | Quotients and subgroups of Baumslag-Solitar groups | We determine all generalized Baumslag-Solitar groups (finitely generated
groups acting on a tree with all stabilizers infinite cyclic) which are
quotients of a given Baumslag-Solitar group BS(m,n), and (when BS(m,n) is not
Hopfian) which of them also admit BS(m,n) as a quotient. We determine for which
values of r,s one may embed BS(r,s) into a given BS(m,n), and we characterize
finitely generated groups which embed into some BS(n,n). | 1308.5122v2 |
2013-12-17 | Limit theory for the Gilbert graph | For a given homogeneous Poisson point process in $\mathbb{R}^d$ two points
are connected by an edge if their distance is bounded by a prescribed distance
parameter. The behaviour of the resulting random graph, the Gilbert graph or
random geometric graph, is investigated as the intensity of the Poisson point
process is increased and the distance parameter goes to zero. The asymptotic
expectation and covariance structure of a class of length-power functionals are
computed. Distributional limit theorems are derived that have a Gaussian, a
stable or a compound Poisson limiting distribution. Finally, concentration
inequalities are provided using a concentration inequality for the convex
distance. | 1312.4861v2 |
2014-03-13 | Fibrations of ordered groupoids and the factorization of ordered functors | We investigate canonical factorizations of ordered functors of ordered
groupoids through star-surjective functors. Our main construction is a quotient
ordered groupoid, depending on an ordered version of the notion of normal
subgroupoid, that results is the factorization of an ordered functor as a
star-surjective functor followed by a star-injective functor. Any
star-injective functor possesses a universal factorization through a covering,
by Ehresmann's Maximum Enlargement Theorem. We also show that any ordered
functor has a canonical factorization through a functor with the ordered
homotopy lifting property. | 1403.3254v2 |
2014-06-10 | A thin-film limit in the Landau-Lifshitz-Gilbert equation relevant for the formation of Néel walls | We consider an asymptotic regime for two-dimensional ferromagnetic films that
is consistent with the formation of transition layers (N\'eel walls). We first
establish compactness of S2-valued magnetizations in the energetic regime of
N\'eel walls and characterize the set of accumulation points. We then prove
that N\'eel walls are asymptotically the unique energy minimizing
configurations. We finally study the corresponding dynamical issues, namely the
compactness properties of the magnetizations under the flow of the
Landau-Lifshitz-Gilbert equation. | 1406.2709v1 |
2014-12-11 | Gamma factors of pairs and a local converse theorem in families | We prove a GL(n)xGL(n-1) local converse theorem for l-adic families of smooth
representations of GL(n,F) where F is a finite extension of Q_p and l is
different from p. To do so, we also extend the theory of Rankin-Selberg
integrals, first introduced by Jacquet, Piatetski-Shapiro, and Shalika, to the
setting of families, continuing previous work of the author. | 1412.3500v2 |
2015-05-28 | A Geometric Interpretation of the Boolean Gilbert-Johnson-Keerthi Algorithm | The Gilbert-Johnson-Keerthi (GJK) algorithm is an iterative improvement
technique for finding the minimum distance between two convex objects. It can
easily be extended to work with concave objects and return the pair of closest
points. [4] The key operation of GJK is testing whether a Voronoi region of a
simplex contains the origin or not. In this paper we show that, in the context
where one is interested only in the Boolean value of whether two convex objects
intersect, and not in the actual distance between them, the number of test
cases in GJK can be significantly reduced. This results in a simpler and more
efficient algorithm that can be used in many computational geometry
applications. | 1505.07873v1 |
2016-01-29 | Ordered groupoid quotients and congruences on inverse semigroups | We introduce a preorder on an inverse semigroup $S$ associated to any normal
inverse subsemigroup $N$, that lies between the natural partial order and
Green's ${\mathscr J}$-relation. The corresponding equivalence relation
$\simeq_N$ is not necessarily a congruence on $S$, but the quotient set does
inherit a natural ordered groupoid structure. We show that this construction
permits the factorisation of any inverse semigroup homomorphism into a
composition of a quotient map and a star-injective functor, and that this
decomposition implies a classification of congruences on $S$. We give an
application to the congruence and certain normal inverse subsemigroups
associate to an inverse monoid presentation. | 1601.08194v1 |
2016-08-16 | Closed inverse subsemigroups of graph inverse semigroups | As part of his study of representations of the polycylic monoids, M.V. Lawson
described all the closed inverse submonoids of a polycyclic monoid $P_n$ and
classified them up to conjugacy. We show that Lawson's description can be
extended to closed inverse subsemigroups of graph inverse semigroups. We then
apply B. Schein's theory of cosets in inverse semigroups to the closed inverse
subsemigroups of graph inverse semigroups: we give necessary and sufficient
conditions for a closed inverse subsemigroup of a graph inverse semigroup to
have finite index, and determine the value of the index when it is finite. | 1608.04538v1 |
2016-10-11 | Converse theorems and the local Langlands correspondence in families | We prove a descent criterion for certain families of smooth representations
of GL_n(F) (F a p-adic field) in terms of the gamma factors of pairs
constructed in previous work of the second author. We then use this descent
criterion, together with a theory of gamma factors for families of
representations of the Weil group W_F (developed previously by both authors),
to prove a series of conjectures, due to the first author, that give a complete
description of the integral Bernstein center in terms of Galois theory and the
local Langlands correspondence. An immediate consequence is the conjectural
"local Langlands correspondence in families" of Emerton and Helm. | 1610.03277v1 |
2016-10-14 | An alternative view on dissipation in turbulent flows | An original experimental setup has been elaborated in order to get a better
view of turbulent flows in a von Karman geometry. The availability of a very
fast camera allowed to follow in time the evolution of the flows. A surprising
finding is that the development of smaller whorls ceases earlier than expected
and the aspect of the flows remains the same above Reynolds number of a few
thousand. This fact provides an explanation of the constancy of the reduced
dissipation in the same range without the need of singularity. Its cause could
be in relation with the same type of behavior observed in a rotating frame. | 1610.05356v2 |
2017-03-02 | Small Superposition Dimension and Active Set Construction for Multivariate Integration Under Modest Error Demand | Constructing active sets is a key part of the Multivariate Decomposition
Method. An algorithm for constructing optimal or quasi-optimal active sets is
proposed in the paper. By numerical experiments, it is shown that the new
method can provide sets that are significantly smaller than the sets
constructed by the already existing method. The experiments also show that the
superposition dimension could surprisingly be very small, at most 3, when the
error demand is not smaller than $10^{-3}$ and the weights decay sufficiently
fast. | 1703.00985v1 |
2017-03-03 | Heat conduction and the nonequilibrium stationary states of stochastic energy exchange processes | I revisit the exactly solvable Kipnis--Marchioro--Presutti model of heat
conduction [J. Stat. Phys. 27 65 (1982)] and describe, for one-dimensional
systems of arbitrary sizes whose ends are in contact with thermal baths at
different temperatures, a systematic characterization of their non-equilibrium
stationary states. These arguments avoid resorting to the analysis of a dual
process and yield a straightforward derivation of Fourier's law, as well as
higher-order static correlations, such as the covariant matrix. The
transposition of these results to families of gradient models generalizing the
KMP model is established and specific cases are examined. | 1703.01240v1 |
2017-03-04 | Algebraic geometry codes with complementary duals exceed the asymptotic Gilbert-Varshamov bound | It was shown by Massey that linear complementary dual (LCD for short) codes
are asymptotically good. In 2004, Sendrier proved that LCD codes meet the
asymptotic Gilbert-Varshamov (GV for short) bound. Until now, the GV bound
still remains to be the best asymptotical lower bound for LCD codes. In this
paper, we show that an algebraic geometry code over a finite field of even
characteristic is equivalent to an LCD code and consequently there exists a
family of LCD codes that are equivalent to algebraic geometry codes and exceed
the asymptotical GV bound. | 1703.01441v1 |
2017-03-17 | A finite element approximation for the stochastic Landau--Lifshitz--Gilbert equation with multi-dimensional noise | We propose an unconditionally convergent linear finite element scheme for the
stochastic Landau--Lifshitz--Gilbert (LLG) equation with multi-dimensional
noise. By using the Doss-Sussmann technique, we first transform the stochastic
LLG equation into a partial differential equation that depends on the solution
of the auxiliary equation for the diffusion part. The resulting equation has
solutions absolutely continuous with respect to time. We then propose a
convergent $\theta$-linear scheme for the numerical solution of the
reformulated equation. As a consequence, we are able to show the existence of
weak martingale solutions to the stochastic LLG equation. | 1703.05901v1 |
2017-04-12 | The homology of principally directed ordered groupoids | We present some homological properties of a relation $\beta$ on ordered
groupoids that generalises the minimum group congruence for inverse semigroups.
When $\beta$ is a transitive relation on an ordered groupoid $G$, the quotient
$G / \beta$ is again an ordered groupoid, and construct a pair of adjoint
functors between the module categories of $G$ and of $G / \beta$. As a
consequence, we show that the homology of $G$ is completely determined by that
of $G / \beta$, generalising a result of Loganathan for inverse semigroups. | 1704.03689v1 |
2017-06-15 | Absence of correlations in the energy exchanges of an exactly solvable model of heat transport with many degrees of freedom | A process based on the exactly solvable Kipnis--Marchioro--Presutti model of
heat conduction [J. Stat. Phys. 27 65 (1982)] is described whereby lattice
cells share their energies among many identical degrees of freedom while, in
each cell, only two of them are associated with energy exchanges connecting
neighbouring cells. It is shown that, up to dimensional constants, the heat
conductivity is half the interaction rate, regardless of the degrees of
freedom. Moreover, as this number becomes large, correlations between the
energy variables involved in the exchanges vanish. In this regime, the process
thus boils down to the time-evolution of the local temperatures which is
prescribed by the discrete heat equation. | 1706.04849v1 |
2017-11-29 | On the local converse theorem and the descent theorem in families | We prove an analogue of Jacquet's conjecture on the local converse theorem
for \ell-adic families of co-Whittaker representations of GL_n(F), where F is a
finite extension of Q_p and \ell does not equal p. We also prove an analogue of
Jacquet's conjecture for a descent theorem, which asks for the smallest
collection of gamma factors determining the subring of definition of an
\ell-adic family. These two theorems are closely related to the local Langlands
correspondence in \ell-adic families. | 1711.11159v1 |
2018-06-23 | List Decodability of Symbol-Pair Codes | We investigate the list decodability of symbol-pair codes in the present
paper. Firstly, we show that list decodability of every symbol-pair code does
not exceed the Gilbert-Varshamov bound. On the other hand, we are able to prove
that with high probability, a random symbol-pair code can be list decoded up to
the Gilbert-Varshamov bound. Our second result of this paper is to derive the
Johnson-type bound, i.e., a lower bound on list decoding radius in terms of
minimum distance. Finally, we present a list decoding algorithm of Reed-Solomon
codes beyond the Johnson-type bound. | 1806.08992v1 |
2018-07-05 | Volumetric performance capture from minimal camera viewpoints | We present a convolutional autoencoder that enables high fidelity volumetric
reconstructions of human performance to be captured from multi-view video
comprising only a small set of camera views. Our method yields similar
end-to-end reconstruction error to that of a probabilistic visual hull computed
using significantly more (double or more) viewpoints. We use a deep prior
implicitly learned by the autoencoder trained over a dataset of view-ablated
multi-view video footage of a wide range of subjects and actions. This opens up
the possibility of high-end volumetric performance capture in on-set and
prosumer scenarios where time or cost prohibit a high witness camera count. | 1807.01950v2 |
2018-10-26 | Immobilization of convex bodies in $R^n$ | We extend to arbitrary finite $n$ the notion of immobilization of a convex
body $O$ in $R^n$ by a finite set of points $P$ in the boundary of $O$. Because
of its importance for this problem, necessary and sufficient conditions are
found for the immobilization of an $n$-simplex. A fairly complete geometric
description of these conditions is given: as $n$ increases from $n = 2$, some
qualitative difference in the nature of the sets $P$ emerges. | 1810.11381v1 |
2019-01-14 | Groupoids and the algebra of rewriting in group presentations | Presentations of groups by rewriting systems (that is, by monoid
presentations), have been fruitfully studied by encoding the rewriting system
in a $2$--complex -- the Squier complex -- whose fundamental groupoid then
describes the derivation of consequences of the rewrite rules. We describe a
reduced form of the Squier complex, investigate the structure of its
fundamental groupoid, and show that key properties of the presentation are
still encoded in the reduced form. | 1901.04348v1 |
2019-05-27 | Tuning Free Rank-Sparse Bayesian Matrix and Tensor Completion with Global-Local Priors | Matrix and tensor completion are frameworks for a wide range of problems,
including collaborative filtering, missing data, and image reconstruction.
Missing entries are estimated by leveraging an assumption that the matrix or
tensor is low-rank. Most existing Bayesian techniques encourage rank-sparsity
by modelling factorized matrices and tensors with Normal-Gamma priors. However,
the Horseshoe prior and other "global-local" formulations provide
tuning-parameter-free solutions which may better achieve simultaneous
rank-sparsity and missing-value recovery. We find these global-local priors
outperform commonly used alternatives in simulations and in a collaborative
filtering task predicting board game ratings. | 1905.11496v1 |
2019-06-26 | Fairness criteria through the lens of directed acyclic graphical models | A substantial portion of the literature on fairness in algorithms proposes,
analyzes, and operationalizes simple formulaic criteria for assessing fairness.
Two of these criteria, Equalized Odds and Calibration by Group, have gained
significant attention for their simplicity and intuitive appeal, but also for
their incompatibility. This chapter provides a perspective on the meaning and
consequences of these and other fairness criteria using graphical models which
reveals Equalized Odds and related criteria to be ultimately misleading. An
assessment of various graphical models suggests that fairness criteria should
ultimately be case-specific and sensitive to the nature of the information the
algorithm processes. | 1906.11333v1 |
2020-01-14 | Neural Architecture Search for Deep Image Prior | We present a neural architecture search (NAS) technique to enhance the
performance of unsupervised image de-noising, in-painting and super-resolution
under the recently proposed Deep Image Prior (DIP). We show that evolutionary
search can automatically optimize the encoder-decoder (E-D) structure and
meta-parameters of the DIP network, which serves as a content-specific prior to
regularize these single image restoration tasks. Our binary representation
encodes the design space for an asymmetric E-D network that typically converges
to yield a content-specific DIP within 10-20 generations using a population
size of 500. The optimized architectures consistently improve upon the visual
quality of classical DIP for a diverse range of photographic and artistic
content. | 2001.04776v1 |
2020-07-18 | Finslerian convolution metrics and their special classes | Here, it is introduced a concept of convolution metric in Finslerian
Geometry. This convolution metric is a kind of function obtained by a given
mathematical operation between two Finslerian metrics. Some basic properties of
the Finslerian convolution metrics are studied. Then it is characterized
Finslerian convolution metrics which are of type Riemannian, Minkowskian as
well as Randers. Furthermore, some examples of the Finslerian convolutions are
given. | 2007.14803v3 |
2020-09-14 | What mathematical billiards teach us about statistical physics? | We survey applications of the theory of hyperbolic (and to a lesser extent
non hyperbolic) billiards to some fundamental problems of statistical physics
and their mathematically rigorous derivations in the framework of classical
Hamiltonian systems. | 2009.06284v2 |
2020-11-29 | Applications of the Backus-Gilbert method to linear and some non linear equations | We investigate the use of a functional analytical version of the
Backus-Gilbert Method as a reconstruction strategy to get specific information
about the solution of linear and slightly non-linear systems with Frech\'et
derivable operators. Some a priori error estimates are shown and tested for two
classes of problems: a nonlinear moment problem and a linear elliptic Cauchy
problem. For this second class of problems a special version of the
Green-formula is developed in order to analyze the involved adjoint equations. | 2011.14407v1 |
2021-11-30 | Global weak solutions for the Landau-Lifshitz-Gilbert-Vlasov-Maxwell system coupled via emergent electromagnetic fields | Motivated by recent models of current driven magnetization dynamics, we
examine the coupling of the Landau-Lifshitz-Gilbert equation and classical
electron transport governed by the Vlasov-Maxwell system. The interaction is
based on space-time gyro-coupling in the form of emergent electromagnetic
fields of quantized helicity that add up to the conventional Maxwell fields. We
construct global weak solutions of the coupled system in the framework of
frustrated magnets with competing first and second order gradient interactions
known to host topological solitons such as magnetic skyrmions and hopfions. | 2111.15482v1 |
2022-04-02 | Introduction to the Artificial Intelligence that can be applied to the Network Automation Journey | The computer network world is changing and the NetDevOps approach has brought
the dynamics of applications and systems into the field of communication
infrastructure. Businesses are changing and businesses are faced with
difficulties related to the diversity of hardware and software that make up
those infrastructures. The "Intent-Based Networking - Concepts and Definitions"
document describes the different parts of the ecosystem that could be involved
in NetDevOps. The recognize, generate intent, translate and refine features
need a new way to implement algorithms. This is where artificial intelligence
comes in. | 2204.00800v1 |
2022-05-24 | Theory of the Energy Variance in a Quantum Bit | We define a new quantum Hermitian operator (namely, the energy variance
operator) which is simply duplicated from the statistical definition of energy
variance in classical physics. Its expectation value yields the standard
deviation of the energy about the mean value of this latter. We show by use of
an exact Hamiltonian description that this standard deviation is due to the
high-frequeny energy oscillations which are usually discarded in the rotating
wave aproximation. We check the present theory by recovering the duration of an
abrupt quantum jump that has been described in a recent experiment. | 2205.12763v1 |
2022-07-11 | Quasilinear rough evolution equations | We investigate the abstract Cauchy problem for a quasilinear parabolic
equation in a Banach space of the form \( du_t -L_t(u_t)u_t dt = N_t(u_t)dt +
F(u_t)\cdot d\mathbf X_t \), where \( \mathbf X\) is a \( \gamma\)-H\"older
rough path for \( \gamma\in(1/3,1/2)\). We explore the mild formulation that
combines functional analysis techniques and controlled rough paths theory which
entail the local well-posedness of such equations. We apply our results to the
stochastic Landau-Lifshitz-Gilbert and Shigesada-Kawasaki-Teramoto equation. In
this framework we obtain a random dynamical system associated to the
Landau-Lifshitz-Gilbert equation. | 2207.04787v1 |
2022-08-01 | A Pansiot-type subword complexity theorem for automorphisms of free groups | Inspired by Pansiot's work on substitutions, we prove a similar theorem for
automorphisms of a free group F of finite rank: if a right-infinite word
represents an attracting fixed point of an automorphism of F, the subword
complexity of X is equivalent to n, n log log n, n log n, or n^2. The proof
uses combinatorial arguments analogue to Pansiot's as well as train tracks. We
also define the recurrence complexity of X, and we apply it to laminations. In
particular, we show that attracting laminations have complexity equivalent to
n, n log log n, n log n, or n^2 (to n if the automorphism is fully
irreducible). | 2208.00676v1 |
2022-08-13 | May the force be with you | Modern methods in dimensionality reduction are dominated by nonlinear
attraction-repulsion force-based methods (this includes t-SNE, UMAP,
ForceAtlas2, LargeVis, and many more). The purpose of this paper is to
demonstrate that all such methods, by design, come with an additional feature
that is being automatically computed along the way, namely the vector field
associated with these forces. We show how this vector field gives additional
high-quality information and propose a general refinement strategy based on
ideas from Morse theory. The efficiency of these ideas is illustrated
specifically using t-SNE on synthetic and real-life data sets. | 2208.06676v1 |
2022-10-26 | Linearized frequency domain Landau-Lifshitz-Gilbert equation formulation | We present a general finite element linearized Landau-Lifshitz-Gilbert
equation (LLGE) solver for magnetic systems under weak time-harmonic excitation
field. The linearized LLGE is obtained by assuming a small deviation around the
equilibrium state of the magnetic system. Inserting such expansion into LLGE
and keeping only first order terms gives the linearized LLGE, which gives a
frequency domain solution for the complex magnetization amplitudes under an
external time-harmonic applied field of a given frequency. We solve the linear
system with an iterative solver using generalized minimal residual method. We
construct a preconditioner matrix to effectively solve the linear system. The
validity, effectiveness, speed, and scalability of the linear solver are
demonstrated via numerical examples. | 2210.14525v1 |
2022-11-10 | Secure Aggregation Is Not All You Need: Mitigating Privacy Attacks with Noise Tolerance in Federated Learning | Federated learning is a collaborative method that aims to preserve data
privacy while creating AI models. Current approaches to federated learning tend
to rely heavily on secure aggregation protocols to preserve data privacy.
However, to some degree, such protocols assume that the entity orchestrating
the federated learning process (i.e., the server) is not fully malicious or
dishonest. We investigate vulnerabilities to secure aggregation that could
arise if the server is fully malicious and attempts to obtain access to
private, potentially sensitive data. Furthermore, we provide a method to
further defend against such a malicious server, and demonstrate effectiveness
against known attacks that reconstruct data in a federated learning setting. | 2211.06324v1 |
2022-12-22 | Theory and construction of Quasi-Monte Carlo rules for option pricing and density estimation | In this paper we propose and analyse a method for estimating three quantities
related to an Asian option: the fair price, the cumulative distribution
function, and the probability density. The method involves preintegration with
respect to one well chosen integration variable to obtain a smooth function of
the remaining variables, followed by the application of a tailored lattice
Quasi-Monte Carlo rule to integrate over the remaining variables. | 2212.11493v2 |
2022-12-30 | Asymptotic stability of 2-domain walls for the Landau-Lifshitz-Gilbert equation in a nanowire with Dzyaloshinskii-Moriya interaction | We consider a ferromagnetic nanowire, with an energy functional $E$ with
easy-axis in the direction $e_1$, and which takes into account the
Dzyaloshinskii-Moriya interaction. We consider configurations of the
magnetization which are perturbations of two well separated domain wall, and
study their evolution under the Landau-Lifshitz-Gilbert flow associated to E.
Our main result is that, if the two walls have opposite speed, these
configurations are asymptotically stable, up to gauges intrinsic to the
invariances of the energy $E$. Our analysis builds on the framework developed
in [4], taking advantage that it is amenable to space localisation. | 2212.14589v1 |
2023-01-12 | Time Domain Verification of Differential Transmission Line Modeling Methods | The advantages and limitations of time-domain pseudo-random binary sequence
(PRBS) excitation methods for system identification of individual modes within
a multi-conductor transmission system are discussed. We develop the
modifications necessary to standard frequency-domain transmission-line models
to match time-domain experimental data from several types of transmission
systems. We show a variety of experimental results showing very good to
excellent agreement with our model's predictions, up to approximately 10 GHz. | 2301.05281v1 |
2023-01-17 | Power Supply Compensation for Capacitive Loads | As ASIC supply voltages approach one volt, the source-impedance goals for
power distribution networks are driven ever lower as well. One approach to
achieving these goals is to add decoupling capacitors of various values until
the desired impedance profile is obtained. An unintended consequence of this
approach can be reduced power supply stability and even oscillation. In this
paper, we present a case study of a system design which encountered these
problems and we describe how these problems were resolved. Time-domain and
frequency-domain analysis techniques are discussed and measured data is
presented. | 2301.09580v1 |
2023-01-17 | Applications of Optimization Routines in Signal Integrity Analysis | Signal integrity analysis often involves the development of design guidelines
through manual manipulation of circuit parameters and judicious interpretation
of results. Such an approach can result in significant effort and sub-optimal
conclusions. Optimization routines have been well proven to aid analysis across
a variety of common tasks. In addition, there are several non-traditional
applications where optimization can be useful. This paper begins by describing
the basics of optimization followed by two specific case studies where
non-traditional optimization provides significant improvements in both analysis
efficiency and channel performance. | 2301.10157v1 |
2023-01-17 | High Speed Parallel Signal Crosstalk Cancellation Concept | High performance computing (HPC) systems make extensive use of high speed
electrical interconnects, in routing signals among processing elements, or
between processing elements and memory. Increasing bandwidth demands result in
high density, parallel I/O exposed to crosstalk due to tightly coupled
transmission lines. The crosstalk cancellation signaling concept discussed in
this paper utilizes the known, predictable theory of coupled transmission lines
to cancel crosstalk from neighboring traces with carefully chosen resistive
cross-terminations between them. Through simulation and analysis of practical
bus architectures, we explore the merits of crosstalk cancellation which could
be used in dense interconnect HPC (or other) applications. | 2301.10170v1 |
2023-04-05 | Elimination and Factorization | If a matrix $A$ has rank $r$, then its row echelon form (from elimination)
contains the identity matrix in its first $r$ independent columns. How do we
\emph{interpret the matrix} $F$ that appears in the remaining columns of that
echelon form\,? $F$ multiplies those first $r$ independent columns of $A$ to
give its $n-r$ dependent columns. Then $F$ reveals bases for the row space and
the nullspace of the original matrix $A$. And $F$ is the key to the column-row
factorization $\boldsymbol{A}=\boldsymbol{CR}$. | 2304.02659v1 |
2023-04-25 | Jet: Multilevel Graph Partitioning on Graphics Processing Units | The multilevel heuristic is the dominant strategy for high-quality sequential
and parallel graph partitioning. Partition refinement is a key step of
multilevel graph partitioning. In this work, we present Jet, a new parallel
algorithm for partition refinement specifically designed for Graphics
Processing Units (GPUs). We combine Jet with GPU-aware coarsening to develop a
$k$-way graph partitioner, the Jet partitioner. The new partitioner achieves
superior quality compared to state-of-the-art shared memory partitioners on a
large collection of test graphs. | 2304.13194v2 |
2023-05-16 | QHDL: a Low-Level Circuit Description Language for Quantum Computing | This paper proposes a descriptive language called QHDL, akin to VHDL, to
program gate-based quantum computing systems. Unlike other popular quantum
programming languages, QHDL targets low-level quantum computing programming and
aims to provide a common framework for programming FPGAs and gate-based quantum
computing systems. The paper presents an initial implementation and design
principles of the QHDL framework, including a compiler and quantum computer
simulator. We discuss the challenges of low-level integration of streaming
models and quantum computing for programming FPGAs and gate-based quantum
computing systems. | 2305.09419v1 |
2023-05-21 | An Alternative Derivation of the Landau-Lifshitz-Gilbert Equation for Saturated Ferromagnets | The Landau-Lifshitz-Gilbert equation for rigid and saturated ferromagnets is
derived using a two-continuum model constructed by H.F. Tiersten for elastic
and saturated ferromagnets. The relevant basic laws of physics are applied
systematically to the two continua or their combination. The exchange
interaction is introduced into the model through surface distributed magnetic
couples. This leads to a continuum theory with magnetization gradients in the
stored energy density. The saturation condition of the magnetization functions
as constraints on the energy density and has implications in the constitutive
relations. | 2305.18232v1 |
2023-06-25 | Gilbert's conjecture and A new way to octonionic analytic functions from the clifford analysis | In this article we will give a affirmative answer to Gilbert's conjecture on
Hardy spaces of Clifford analytic functions in upper half-space of
$\mathbb{R}^8$. It depends on a explicit construction of Spinor space
$\mathcal{R}_8$ and Clifford algebra $Cl_8$ by octonion algbra. What's more ,
it gives us an associative way to octonionic analytic function theory. And the
similar question has been discussed in Octonionic Hardy space in upper-half
space, some classical results about octonionic analytic functions have been
reformulated, too. | 2306.14164v1 |
2023-06-28 | Stochastic Landau-Lifshitz-Gilbert equations for frustrated magnets under fluctuating currents | We examine a stochastic Landau-Lifshitz-Gilbert equation for a frustrated
ferromagnet with competing first and second order exchange interactions exposed
to deterministic and random spin transfer torques in form of transport noise.
We prove the existence and pathwise uniqueness of weak martingale solutions in
the energy space. The result ensures the persistence of topological patterns,
occurring in such magnetic systems, under the influence of a fluctuating spin
current. | 2306.15843v1 |
2023-07-28 | MDS, Hermitian Almost MDS, and Gilbert-Varshamov Quantum Codes from Generalized Monomial-Cartesian Codes | We construct new stabilizer quantum error-correcting codes from generalized
monomial-Cartesian codes. Our construction uses an explicitly defined twist
vector, and we present formulas for the minimum distance and dimension.
Generalized monomial-Cartesian codes arise from polynomials in $m$ variables.
When $m=1$ our codes are MDS, and when $m=2$ and our lower bound for the
minimum distance is $3$ the codes are at least Hermitian Almost MDS. For an
infinite family of parameters when $m=2$ we prove that our codes beat the
Gilbert-Varshamov bound. We also present many examples of our codes that are
better than any known code in the literature. | 2307.15488v1 |
2023-09-06 | Optimal Control of the 2D Landau-Lifshitz-Gilbert Equation with Control Energy in Effective Magnetic Field | The optimal control of magnetization dynamics in a ferromagnetic sample at a
microscopic scale is studied. The dynamics of this model is governed by the
Landau-Lifshitz-Gilbert equation on a two-dimensional bounded domain with the
external magnetic field (the control) applied through the effective field. We
prove the global existence and uniqueness of a regular solution in $\mathbb
S^2$ under a smallness condition on control and initial data. We establish the
existence of optimal control and derive a first-order necessary optimality
condition using the Fr\'echet derivative of the control-to-state operator and
adjoint problem approach. | 2309.02786v1 |
2023-09-22 | Relaxed optimal control for the stochastic Landau-Lifshitz-Gilbert equation | We consider the stochastic Landau-Lifshitz-Gilbert equation, perturbed by a
real-valued Wiener process. We add an external control to the effective field
as an attempt to drive the magnetization to a desired state and also to control
thermal fluctuations. We use the theory of Young measures to relax the given
control problem along with the associated cost. We consider a control operator
that can depend (possibly non-linearly) on both the control and the associated
solution. Moreover, we consider a fairly general associated cost functional
without any special convexity assumption. We use certain compactness arguments,
along with the Jakubowski version of the Skorohod Theorem to show that the
relaxed problem admits an optimal control. | 2309.12556v1 |
2024-01-14 | Multilevel Metamodels: A Novel Approach to Enhance Efficiency and Generalizability in Monte Carlo Simulation Studies | Metamodels, or the regression analysis of Monte Carlo simulation (MCS)
results, provide a powerful tool to summarize MCS findings. However, an as of
yet unexplored approach is the use of multilevel metamodels (MLMM) that better
account for the dependent data structure of MCS results that arises from
fitting multiple models to the same simulated data set. In this study, we
articulate the theoretical rationale for the MLMM and illustrate how it can
dramatically improve efficiency over the traditional regression approach,
better account for complex MCS designs, and provide new insights into the
generalizability of MCS findings. | 2401.07294v2 |
2024-02-29 | Evaluating the Gilbert-Varshamov Bound for Constrained Systems | We revisit the well-known Gilbert-Varshamov (GV) bound for constrained
systems. In 1991, Kolesnik and Krachkovsky showed that GV bound can be
determined via the solution of some optimization problem. Later, Marcus and
Roth (1992) modified the optimization problem and improved the GV bound in many
instances. In this work, we provide explicit numerical procedures to solve
these two optimization problems and hence, compute the bounds. We then show the
procedures can be further simplified when we plot the respective curves. In the
case where the graph presentation comprise a single state, we provide explicit
formulas for both bounds. | 2402.18869v1 |
2003-08-25 | Detection of molecular hydrogen at z=1.15 toward HE 0515-4414 | A new molecular hydrogen cloud is found in the sub-damped Ly-alpha absorber
[log N(HI)=19.88+/-0.05] at the redshift z=1.15 toward the bright quasar
HE0515-4414 (zem = 1.71). More than 30 absorption features in the Lyman band
system of H2 are identified in the UV spectrum of this quasar obtained with the
Space Telescope Imaging Spectrograph (STIS) aboard the Hubble Space Telescope.
The H2-bearing cloud shows a total H2 column density N(H2)=(8.7^{+8.7}_-{4.0})
10^16 cm^-2, and a fractional molecular abundance f(H2)=(2.3^{+2.3}_{-1.1})
10^-3 derived from the H2 lines arising from the J=0-5 rotational levels of the
ground electronic vibrational state. The estimated rate of photodissociation at
the cloud edge I_0<=1.8 10^{-8} s^-1 is much higher than the mean Galactic disk
value, I_MW~=5.5 10^{-11} s^-1. This may indicate an enhanced star-formation
activity in the z=1.15 system as compared with molecular clouds at z~=3 where
I~=I_MW. We also find a tentative evidence that the formation rate coefficient
of H2 upon grain surfaces at z=1.15 is a factor of 10 larger than a canonical
Milky Way value, R_MW~=3 10^-17 cm^3 s^-1. The relative dust-to-gas ratio
estimated from the [Cr/Zn] ratio is equal to k=0.89+/-0.19 (in units of the
mean Galactic disk value), which is in good agreement with a high molecular
fraction in this system. The estimated line-of-sight size of L~=0.25 pc may
imply that the H2 is confined within small and dense filaments embedded in a
more rarefied gas giving rise to the z=1.15 sub-damped Ly-alpha absorber. | 0308432v1 |
2004-10-04 | Dissipative dynamics of topological defects in frustrated Heisenberg spin systems | We study the dynamics of topological defects of a frustrated spin system
displaying spiral order. As a starting point we consider the SO(3) nonlinear
sigma model to describe long-wavelength fluctuations around the noncollinear
spiral state. Besides the usual spin-wave magnetic excitations, the model
allows for topologically non-trivial static solutions of the equations of
motion, associated with the change of chirality (clockwise or counterclockwise)
of the spiral. We consider two types of these topological defects, single
vortices and vortex-antivortex pairs, and quantize the corresponding solutions
by generalizing the semiclassical approach to a non-Abelian field theory. The
use of the collective coordinates allows us to represent the defect as a
particle coupled to a bath of harmonic oscillators, which can be integrated out
employing the Feynman-Vernon path-integral formalism. The resulting effective
action for the defect indicates that its motion is damped due to the scattering
by the magnons. We derive a general expression for the damping coefficient of
the defect, and evaluate its temperature dependence in both cases, for a single
vortex and for a vortex-antivortex pair. Finally, we consider an application of
the model for cuprates, where a spiral state has been argued to be realized in
the spin-glass regime. By assuming that the defect motion contributes to the
dissipative dynamics of the charges, we can compare our results with the
measured inverse mobility in a wide range of temperature. The relatively good
agreement between our calculations and the experiments confirms the possible
relevance of an incommensurate spiral order for lightly doped cuprates. | 0410082v3 |
2010-09-14 | Modeling laser wakefield accelerators in a Lorentz boosted frame | Modeling of laser-plasma wakefield accelerators in an optimal frame of
reference \cite{VayPRL07} is shown to produce orders of magnitude speed-up of
calculations from first principles. Obtaining these speedups requires
mitigation of a high-frequency instability that otherwise limits effectiveness
in addition to solutions for handling data input and output in a
relativistically boosted frame of reference. The observed high-frequency
instability is mitigated using methods including an electromagnetic solver with
tunable coefficients, its extension to accomodate Perfectly Matched Layers and
Friedman's damping algorithms, as well as an efficient large bandwidth digital
filter. It is shown that choosing the frame of the wake as the frame of
reference allows for higher levels of filtering and damping than is possible in
other frames for the same accuracy. Detailed testing also revealed
serendipitously the existence of a singular time step at which the instability
level is minimized, independently of numerical dispersion, thus indicating that
the observed instability may not be due primarily to Numerical Cerenkov as has
been conjectured. The techniques developed for Cerenkov mitigation prove
nonetheless to be very efficient at controlling the instability. Using these
techniques, agreement at the percentage level is demonstrated between
simulations using different frames of reference, with speedups reaching two
orders of magnitude for a 0.1 GeV class stages. The method then allows direct
and efficient full-scale modeling of deeply depleted laser-plasma stages of 10
GeV-1 TeV for the first time, verifying the scaling of plasma accelerators to
very high energies. Over 4, 5 and 6 orders of magnitude speedup is achieved for
the modeling of 10 GeV, 100 GeV and 1 TeV class stages, respectively. | 1009.2727v2 |
2013-03-07 | The coupling between internal waves and shear-induced turbulence in stellar radiation zones: the critical layer | Internal gravity waves (hereafter IGWs) are known as one of the candidates
for explaining the angular velocity profile in the Sun and in solar-type
main-sequence and evolved stars, due to their role in the transport of angular
momentum. Our bringing concerns critical layers, a process poorly explored in
stellar physics, defined as the location where the local relative frequency of
a given wave to the rotational frequency of the fluid tends to zero (i.e that
corresponds to co-rotation resonances). IGW propagate through stably-stratified
radiative regions, where they extract or deposit angular momentum through two
processes: radiative and viscous dampings and critical layers. Our goal is to
obtain a complete picture of the effects of this latters. First, we expose a
mathematical resolution of the equation of propagation for IGWs in adiabatic
and non-adiabatic cases near critical layers. Then, the use of a dynamical
stellar evolution code, which treats the secular transport of angular momentum,
allows us to apply these results to the case of a solar-like star.The analysis
reveals two cases depending on the value of the Richardson number at critical
layers: a stable one, where IGWs are attenuated as they pass through a critical
level, and an unstable turbulent case where they can be reflected/transmitted
by the critical level with a coefficient larger than one. Such
over-reflection/transmission can have strong implications on our vision of
angular momentum transport in stellar interiors. This paper highlights the
existence of two regimes defining the interaction between an IGW and a critical
layer. An application exposes the effect of the first regime, showing a
strengthening of the damping of the wave. Moreover, this work opens new ways
concerning the coupling between IGWs and shear instabilities in stellar
interiors. | 1303.1715v1 |
2014-05-01 | Energy Loss of Solar $p$ Modes due to the excitation of Magnetic Sausage Tube Waves: Importance of Coupling the Upper Atmosphere | We consider damping and absorption of solar $p$ modes due to their energy
loss to magnetic tube waves that can freely carry energy out of the acoustic
cavity. The coupling of $p$ modes and sausage tube waves is studied in a model
atmosphere composed of a polytropic interior above which lies an isothermal
upper atmosphere. The sausage tube waves, excited by $p$ modes, propagate along
a magnetic fibril which is assumed to be a vertically aligned, stratified, thin
magnetic flux-tube. The deficit of $p$-mode energy is quantified through the
damping rate, $\Gamma$ and absorption coefficient, $\alpha$. The variation of
$\Gamma$ and $\alpha$ as a function of frequency and the tube's plasma
properties is studied in detail. Previous similar studies have considered only
a subphotospheric layer, modelled as a polytrope that has been truncated at the
photosphere (Bogdan et al. (1996), Hindman & Jain 2008, Gascoyne et al.
(2011)). Such studies have found that the resulting energy loss by the $p$
modes is very sensitive to the upper boundary condition, which because of the
lack of a upper atmosphere have been imposed in a somewhat ad hoc manner. The
model presented here avoids such problems by using an isothermal layer to model
the overlying atmosphere (chromosphere), and consequently, allows us to analyse
the propagation of $p$-mode driven sausage waves above the photosphere. In this
paper we restrict our attention to frequencies below the acoustic cut-off
frequency. We demonstrate the importance of coupling all waves (acoustic,
magnetic) in the subsurface solar atmosphere with the overlying atmosphere in
order to accurately model the interaction of solar $f$ and $p$ modes with
sausage tube waves. | 1405.0130v2 |
2015-09-01 | Excitation of surface and volume plasmons in metal nanocluster by fast electrons | Surface and volume plasmons excited in a metal cluster by moving electron and
corresponding inelastic scattering spectra are studied based on the
hydrodynamic approach. Along with the bulk losses traditionally taken into
account, the surface and radiative ones are also considered as the physical
mechanisms responsible for the plasmon damping. The second and third mechanisms
are found to be essential for the surface plasmons and depend very differently
on the multipole mode order. The differential equations are obtained which
describe the temporal evolution of every particular mode as that one of a
linear oscillator excited by the given external force, and the electron energy
loss spectra are calculated. The changes in spectrum shape with the impact
parameter and with the electron passage time are analyzed and found to be in
good enough agreement with the data of scanning transmission electron
microscopy (STEM) experiments. It is shown that, in the general case, a
pronounced contribution to the formation of the loss spectrum is given by the
both surface and volume plasmons with low and high multipole indices. In
particular, at long electron passage time, the integral loss spectrum which is
calculated for the free-electron cluster model contains two main peaks: a broad
peak from merging of many high-order multipole resonances of the surface
plasmons and a narrower peak of nearly the same height from merged volume
plasmons excited by the electrons that travel through the central region of the
cluster. Comparatively complex dependences of the calculated excitation
coefficients and damping constants of various plasmons on the order of the
excited multipole result in wide diversity of possible types of the loss
spectrum even for the same cluster material and should be taken into account in
interpretation of corresponding electron energy loss spectroscopy (EELS)
experiments. | 1509.00405v2 |
2016-01-29 | New class of quantum error-correcting codes for a bosonic mode | We construct a new class of quantum error-correcting codes for a bosonic mode
which are advantageous for applications in quantum memories, communication, and
scalable computation. These 'binomial quantum codes' are formed from a finite
superposition of Fock states weighted with binomial coefficients. The binomial
codes can exactly correct errors that are polynomial up to a specific degree in
bosonic creation and annihilation operators, including amplitude damping and
displacement noise as well as boson addition and dephasing errors. For
realistic continuous-time dissipative evolution, the codes can perform
approximate quantum error correction to any given order in the timestep between
error detection measurements. We present an explicit approximate quantum error
recovery operation based on projective measurements and unitary operations. The
binomial codes are tailored for detecting boson loss and gain errors by means
of measurements of the generalized number parity. We discuss optimization of
the binomial codes and demonstrate that by relaxing the parity structure, codes
with even lower unrecoverable error rates can be achieved. The binomial codes
are related to existing two-mode bosonic codes but offer the advantage of
requiring only a single bosonic mode to correct amplitude damping as well as
the ability to correct other errors. Our codes are similar in spirit to 'cat
codes' based on superpositions of the coherent states, but offer several
advantages such as smaller mean number, exact rather than approximate
orthonormality of the code words, and an explicit unitary operation for
repumping energy into the bosonic mode. The binomial quantum codes are
realizable with current superconducting circuit technology and they should
prove useful in other quantum technologies, including bosonic quantum memories,
photonic quantum communication, and optical-to-microwave up- and
down-conversion. | 1602.00008v3 |
2016-05-31 | Constraint on a cosmological variation in the proton-to-electron mass ratio from electronic CO absorption | Carbon monoxide (CO) absorption in the sub-damped Lyman-$\alpha$ absorber at
redshift $z_{abs} \simeq 2.69$, toward the background quasar SDSS
J123714.60+064759.5 (J1237+0647), was investigated for the first time in order
to search for a possible variation of the proton-to-electron mass ratio, $\mu$,
over a cosmological time-scale. The observations were performed with the Very
Large Telescope/Ultraviolet and Visual Echelle Spectrograph with a
signal-to-noise ratio of 40 per 2.5 kms$^{-1}$ per pixel at $\sim 5000$ \AA.
Thirteen CO vibrational bands in this absorber are detected: the A$^{1}\Pi$ -
X$^{1}\Sigma^{+}$ ($\nu'$,0) for $\nu' = 0 - 8$, B$^{1}\Sigma^{+}$ -
X$^{1}\Sigma^{+}$ (0,0), C$^{1}\Sigma^{+}$ - X$^{1}\Sigma^{+}$ (0,0), and
E$^{1}\Pi$ - X$^{1}\Sigma^{+}$ (0,0) singlet-singlet bands and the
d$^{3}\Delta$ - X$^{1}\Sigma^{+}$ (5,0) singlet-triplet band. An updated
database including the most precise molecular inputs needed for a
$\mu$-variation analysis is presented for rotational levels $J = 0 - 5$,
consisting of transition wavelengths, oscillator strengths, natural lifetime
damping parameters, and sensitivity coefficients to a variation of the
proton-to-electron mass ratio. A comprehensive fitting method was used to fit
all the CO bands at once and an independent constraint of $\Delta\mu/\mu = (0.7
\pm 1.6_{stat} \pm 0.5_{syst}) \times 10^{-5}$ was derived from CO only. A
combined analysis using both molecular hydrogen and CO in the same J1237+0647
absorber returned a final constraint on the relative variation of
$\Delta\mu/\mu = (-5.6 \pm 5.6_{stat} \pm 3.1_{syst}) \times 10^{-6}$, which is
consistent with no variation over a look-back time of $\sim 11.4$ Gyrs. | 1605.09742v1 |
2017-11-01 | Entanglement entropy of a three-spin interacting spin chain with a time-reversal breaking impurity at one boundary | We investigate the effect of a time-reversal breaking impurity term on both
the equilibrium and non-equilibrium critical properties of entanglement entropy
(EE) in a three-spin interacting transverse Ising model which can be mapped to
a one-dimensional p-wave superconductor with next-nearest-neighbor hopping. Due
to the presence of next-nearest-neighbor hopping, a new topological phase with
two zero-energy Majorana modes at each end of an open chain appears in the
phase diagram. We show that the derivative of EE with respect to one of the
parameters of the Hamiltonian can detect the quantum phase transitions by
exhibiting cusp like structure at those points; impurity strength ($\la_d$) can
substantially modify the peak/dip height associated with the cusp. Importantly,
we find that the logarithmic scaling of the EE with block size remains
unaffected by the application of the impurity term, although, the coefficient
(i.e., central charge) varies logarithmically with the impurity strength for a
lower range of $\la_d$ and eventually saturates with an exponential damping
factor ($\sim \exp(-\la_d)$) for the phase boundaries shared with the phase
containing two Majorana edge modes. On the other hand, it receives a linear
correction in term of $\la_d$ for an another phase boundary. Finally, we focus
to study the effect of the impurity in the time evolution of the EE for the
critical quenching case where impurity term is applied only to the final
Hamiltonian. Interestingly, it has been shown that for all the phase boundaries
in contrary to the equilibrium case, the saturation value of the EE increases
logarithmically with the strength of impurity in a certain region of $\la_d$
and finally, for higher values of $\la_d$, it increases very slowly which is
dictated by an exponential damping factor. | 1711.01164v2 |
2018-01-23 | Predicting Quasar Continua Near Lyman-$α$ with Principal Component Analysis | Measuring the proximity effect and the damping wing of intergalactic neutral
hydrogen in quasar spectra during the epoch of reionization requires an
estimate of the intrinsic continuum at rest-frame wavelengths $\lambda_{\rm
rest}\sim1200$-$1260$ {\AA}. In contrast to previous works which used composite
spectra with matched spectral properties or explored correlations between
parameters of broad emission lines, we opted for a non-parametric predictive
approach based on principal component analysis (PCA) to predict the intrinsic
spectrum from the spectral properties at redder (i.e. unabsorbed) wavelengths.
We decomposed a sample of $12764$ spectra of $z\sim2$-$2.5$ quasars from
SDSS/BOSS into 10 red-side ($1280$ {\AA} $<\lambda_{\rm rest}<2900$ {\AA}) and
6 blue-side ($1180$ {\AA} $<\lambda_{\rm rest}<1280$ {\AA}) PCA basis spectra,
and constructed a projection matrix to predict the blue-side coefficients from
a fit to the red-side spectrum. We found that our method predicts the blue-side
continuum with $\sim6$-$12\%$ precision and $\lesssim1\%$ bias by testing on
the full training set sample. We then computed predictions for the blue-side
continua of the two quasars currently known at $z>7$: ULAS J1120+0641
($z=7.09$) and ULAS J1342+0928 ($z=7.54$). Both of these quasars are known to
exhibit extreme emission line properties, so we individually calibrated the
precision of the continuum predictions from similar quasars in the training
set. We find that both $z>7$ quasars, and in particular ULAS J1342+0928, show
signs of damping wing-like absorption at wavelengths redward of Ly$\alpha$. | 1801.07679v1 |
2018-05-23 | Quantifying the validity and breakdown of the overdamped approximation in stochastic thermodynamics: Theory and experiment | Stochastic thermodynamics provides an important framework to explore small
physical systems where thermal fluctuations are inevitable. In the studies of
stochastic thermodynamics, some thermodynamic quantities, such as the
trajectory work, associated with the complete Langevin equation (the Kramers
equation) are often assumed to converge to those associated with the overdamped
Langevin equation (the Smoluchowski equation) in the overdamped limit under the
overdamped approximation. Nevertheless, a rigorous mathematical proof of the
convergence of the work distributions to our knowledge has not been reported so
far. Here we study the convergence of the work distributions explicitly. In the
overdamped limit, we rigorously prove the convergence of the extended
Fokker-Planck equations including work using a multiple timescale expansion
approach. By taking the linearly dragged harmonic oscillator as an exactly
solvable example, we analytically calculate the work distribution associated
with the Kramers equation, and verify its convergence to that associated with
the Smoluchowski equation in the overdamped limit. We quantify the accuracy of
the overdamped approximation as a function of the damping coefficient. In
addition, we experimentally demonstrate that the data of the work distribution
of a levitated silica nanosphere agrees with the overdamped approximation in
the overdamped limit, but deviates from the overdamped approximation in the
low-damping case. Our work fills a gap between the stochastic thermodynamics
based on the complete Langevin equation (the Kramers equation) and the
overdamped Langevin equation (the Smoluchowski equation), and deepens our
understanding of the overdamped approximation in stochastic thermodynamics. | 1805.09080v3 |
2018-09-05 | Experiments on wave propagation in grease ice: combined wave gauges and PIV measurements | Water wave attenuation by grease ice is a key mechanism for the polar
regions, as waves in ice influence many phenomena such as ice drift, ice
breaking, and ice formation. However, the models presented so far in the
literature are limited in a number of regards, and more insights are required
from either laboratory experiments or fieldwork for these models to be
validated and improved. Unfortunately, performing detailed measurements of wave
propagation in grease ice, either on the field or in the laboratory, is
challenging. As a consequence, laboratory data are relatively scarce, and often
consist of only a couple of wave elevation measurements along the length of the
wave tank. We present combined measurements of wave elevation using an array of
ultrasonic probes, and water kinematics using Particle Image Velocimetry (PIV),
in a small-scale wave tank experiment. Experiments are performed over a wider
frequency range than what has been previously investigated. The wave elevation
measurements are used to compute the wave number and exponential damping
coefficient. By contrast with a previous study in grease ice, we find that the
wave number is consistent with the mass loading model, i.e. it increases
compared with the open water case. Wave attenuation is compared with a series
of one-layer models, and we show that they satisfactorily describe the viscous
damping that is taking place. PIV data are also consistent with exponential
wave amplitude attenuation, and a POD analysis reveals the existence of mean
flows under the ice that are a consequence of the displacement and packing of
the ice induced by the gradient in the wave-induced stress. Finally, we show
that the dynamics of grease ice can generate eddy structures that inject eddy
viscosity in the water under the grease ice, which would lead to enhanced
mixing and participating in energy dissipation. | 1809.01476v2 |
2022-02-08 | Evolution of energy, momentum, and spin parameter in dark matter flow and integral constants of motion | N-body equations of motion in comoving system and expanding background are
reformulated in a transformed system with static background and fixed damping.
The energy and momentum evolution in dark matter flow are rigorously formulated
for both systems. The energy evolution in transformed system has a simple form
that is identical to the damped harmonic oscillator. The cosmic energy equation
can be easily derived in both systems. For entire N-body system, 1) combined
with the two-body collapse model (TBCM), kinetic and potential energy increase
linearly with time $t$ such that $K_p=\varepsilon_ut$ and
$P_y=-7\varepsilon_ut/5$, where $\varepsilon_u$ is a constant rate of energy
cascade; 2) an effective gravitational potential exponent $n_e=-10/7\ne-1$
($n_e=-1.38$ from simulation) can be identified due to surface energy of fast
growing halos; 3) the radial momentum $G\propto a^{3/2}$ and angular momentum
$H\propto a^{5/2}$, where $a$ is the scale factor. On halo scale, 1) halo
kinetic and potential energy can be modelled by two dimensionless constants
$\alpha_s^*$ and $\beta_s^*$. Both constants are independent of time and halo
mass; 2) both halo radial and angular momentum $\propto a^{3/2}$ and can be
modeled by two mass-dependent coefficients $\tau_s^*$ and $\eta_s^*$; 3) halo
spin parameter is determined by $\alpha_s^*$ and $\eta_s^*$ and decreases with
halo mass with derived values of 0.09 and 0.031 for small and large halos.
Finally, the radial and angular momentum are closely related to the integral
constants of motion $I_m$, i.e. the integral of velocity correlation or the
$m$th derivative of energy spectrum at long wavelength limit. On large scale,
angular momentum is negligible, $I_2$=0 reflects the conservation of linear
momentum, while $I_4$ reflects the fluctuation of radial momentum $G$. On halo
scale, $I_4$ is determined by both momentum that are comparable with each
other. | 2202.04054v2 |
2022-09-10 | Self-Consistent Computation of Spin Torques and Magneto-Resistance in Tunnel Junctions and Magnetic Read-Heads with Metallic Pinhole Defects | A three-dimensional self-consistent spin transport model is developed, which
includes both tunnelling transport, as well as metallic transport. Using the
spin accumulation computed either side of a tunnel barrier, spin torques are
obtained, and it is shown the model reproduces both damping-like and field-like
spin-transfer torques, with the expected sinusoidal angular dependence, and
inverse ferromagnetic layer thickness dependence. An explicit solution to the
drift-diffusion model is derived, which allows analysing the effect of both the
reference and free layer thickness on the spin-transfer torque polarization and
field-like coefficient. In particular, when the layers are thin, additional
spin-dependent scattering contributions due to incomplete absorption of
transverse spin components reduce both the damping-like and field-like spin
torques. It is shown the model developed here can be used to compute the
signal-to-noise ratio in realistic magnetic read-heads, where spin
torque-induced fluctuations and instabilities limit the maximum operating
voltage. The effect of metallic pinhole defects in the insulator layer is also
analysed, which results in a mixture of metallic and tunnelling transport, and
highly non-uniform charge and spin currents, requiring the full spin transport
model to compute the resulting magneto-resistance and spin torques. Increasing
the area covered by pinholes results in a rapid degradation of the
magneto-resistance, following an inverse dependence. Moreover, the spin torque
angular dependence becomes skewed, and the spin-transfer torque polarization
decreases. The same results are obtained when considering tunnel junctions with
a single pinhole defect, but decreasing cross-sectional area, showing that even
a single pinhole defect can significantly degrade the performance of tunnel
junctions and magnetic read-heads below the 40 nm node. | 2209.04613v1 |
2023-06-23 | Nonlinear asymptotic stability and transition threshold for 2D Taylor-Couette flows in Sobolev spaces | In this paper, we investigate the stability of the 2-dimensional (2D)
Taylor-Couette (TC) flow for the incompressible Navier-Stokes equations. The
explicit form of velocity for 2D TC flow is given by $u=(Ar+\frac{B}{r})(-\sin
\theta, \cos \theta)^T$ with $(r, \theta)\in [1, R]\times \mathbb{S}^1$ being
an annulus and $A, B$ being constants. Here, $A, B$ encode the rotational
effect and $R$ is the ratio of the outer and inner radii of the annular region.
Our focus is the long-term behavior of solutions around the steady 2D TC flow.
While the laminar solution is known to be a global attractor for 2D channel
flows and plane flows, it is unclear whether this is still true for rotating
flows with curved geometries. In this article, we prove that the 2D
Taylor-Couette flow is asymptotically stable, even at high Reynolds number
($Re\sim \nu^{-1}$), with a sharp exponential decay rate of
$\exp(-\nu^{\frac13}|B|^{\frac23}R^{-2}t)$ as long as the initial perturbation
is less than or equal to $\nu^\frac12 |B|^{\frac12}R^{-2}$ in Sobolev space.
The powers of $\nu$ and $B$ in this decay estimate are optimal. It is derived
using the method of resolvent estimates and is commonly recognized as the
enhanced dissipative effect. Compared to the Couette flow, the enhanced
dissipation of the rotating Taylor-Couette flow not only depends on the
Reynolds number but also reflects the rotational aspect via the rotational
coefficient $B$. The larger the $|B|$, the faster the long-time dissipation
takes effect. We also conduct space-time estimates describing inviscid-damping
mechanism in our proof. To obtain these inviscid-damping estimates, we find and
construct a new set of explicit orthonormal basis of the weighted
eigenfunctions for the Laplace operators corresponding to the circular flows.
These provide new insights into the mathematical understanding of the 2D
Taylor-Couette flows. | 2306.13562v1 |
2023-12-18 | Size dependent optical response in coupled systems of plasmons and electron-hole pairs in metallic nanostructures | In bulk materials, the collective modes and individual modes are orthogonal
each other, and no connection occurs if there is no damping processes. In the
presence of damping, the collective modes, i.e., plasmons decay into the hot
carriers. In finite systems, the collective and individual modes are coupled by
the Coulomb interaction. Such couplings by longitudinal (L) field have been
intensively investigated, whereas a coupling via transverse (T) field has been
poorly studied although the plasmon is excited by an irradiated light on
surface and in finite nanostructures. Then, the T field would play a
significant role in the coupling between the collective and individual
excitations. In this study, we investigate how the T field mediates the
coherent coupling. This study is based on the recently developed microscopic
nonlocal theory of electronic systems in metals and the results of eigenmode
analyses by this theory. To tune the coupling strength in a single nanorod, we
examine three parameters: Rod length $L_z$, background refractive index $n_{\rm
b}$, and Fermi energy $\varepsilon_{\rm F}$. We discuss the modulation ratio of
the spectrum of optical response coefficients to evaluate the coupling by the T
field. The T field shifts the collective excitation energy, which causes a
finite modulation at both collective excitation and individual excitations. The
three parameters can change the energy distance between the collective and
individual excitations. Thus, the coherent coupling by the T field is enhanced
for a proper tuning of the parameters. The results of the investigation of
system parameter dependence would give insight into the guiding principle of
designing the materials for highly efficient hot carrier generation. | 2312.10867v2 |
2024-03-04 | Cosmic-ray diffusion in two local filamentary clouds | A fairly uniform cosmic-ray (CR) distribution is observed near the Sun,
except in the nearby Eridu cloud, which shows an unexplained 30-50% deficit in
GeV to TeV CR flux. To explore the origin of this deficit, we studied the
Reticulum cloud, which shares notable traits with Eridu: a comparable distance
in the low-density region of the Local Valley and a filamentary structure of
atomic hydrogen extending along ordered magnetic-field lines that are steeply
inclined to the Galactic plane. Using 14 years of Fermi-LAT data in the 0.16 to
63 GeV energy band, we found that the gamma-ray emissivity in the Reticulum
cloud is fully consistent with the average spectrum measured in the solar
neighbourhood, but this emissivity, and therefore the CR flux, is 1.57 $\pm$
0.09 times larger than in Eridu across the whole energy band. The difference
cannot be attributed to uncertainties in gas mass. Nevertheless, we find that
the two clouds are similar in many respects at a parsec scale: both have
magnetic-field strengths of a few micro-Gauss in the plane of the sky; both are
in approximate equilibrium between magnetic and thermal pressures; they have
similar turbulent velocities and sonic Mach numbers; and both show
magnetic-field regularity with a dispersion in orientation lower than 10-15
degrees over large zones. The gas in Reticulum is colder and denser than in
Eridu, but we find similar parallel diffusion coefficients around a few times
1e28 cm2/s in both clouds if CRs above 1 GV in rigidity diffuse on resonant,
self-excited Alfv\'en waves that are damped by ion-neutral interactions. The
loss of CRs in Eridu remains unexplained, but these two clouds provide
important test cases to further study how magnetic turbulence, line tangling,
and ion-neutral damping regulate CR diffusion in the dominant gas phase of the
interstellar medium. | 2403.02466v1 |
1999-04-20 | Experimentally Derived Dielectronic Recombination Rate Coefficients for Heliumlike C V and Hydrogenic O VIII | Using published measurements of dielectronic recombination (DR) resonance
strengths and energies for C V to C IV and O VIII to O VII, we have calculated
the DR rate coefficient for these ions. Our derived rates are in good agreement
with multiconfiguration, intermediate-coupling and multiconfiguration,
fully-relativistic calculations as well as with most LS coupling calculations.
Our results are not in agreement with the recommended DR rates commonly used
for modeling cosmic plasmas. We have used theoretical radiative recombination
(RR) rates in conjunction with our derived DR rates to produce a total
recombination rate for comparison with unified RR+DR calculations in LS
coupling. Our results are not in agreement with undamped, unified calculations
for C V but are in reasonable agreement with damped, unified calculations for O
VIII. For C V, the Burgess general formula (GF) yields a rate which is in very
poor agreement with our derived rate. The Burgess & Tworkowski modification of
the GF yields a rate which is also in poor agreement. The Merts et al.
modification of the GF yields a rate which is in fair agreement. For O VIII the
GF yields a rate which is in fair agreement with our derived rate. The Burgess
& Tworkowski modification of the GF yields a rate which is in good agreement.
And the Merts et al. modification yields a rate which is in very poor
agreement. These results suggest that for DN=1 DR it is not possible to know a
priori which formula will yield a rate closer to the true DR rate. We describe
the technique used to obtain DR rate coefficients from laboratory measurements
of DR resonance strengths and energies. For use in plasma modeling, we also
present easy-to-use fitting formulae for the experimentally derived DR rates. | 9904258v1 |
2016-10-12 | Optical Properties Of Nanometer-Scale Structures | Two approaches (micro- and macro- investigations) are used to determine the
dimension dependences of the optical parameters of the nanometer-scale layers
of materials. It is shown that both an index of refraction and coefficient of
absorption depend strongly on the thickness of the layer. In this region of
thicknesses, the dimension resonance occurs, where an index of refraction has a
maximum and a coefficient of absorption has a minimum. The numerical
calculation of the optical parameters of some materials (Ag, Al, Fe, Ge, Si,
Se, Te) have been carried out with the use of the experimental data of
reflection and transparency of thin layers, obtained in a series of works, and
with our formulas for the wave amplitudes and the laws of refractions. The
analogues of the Fresnel formulas and the Snell law have been derived from the
Maxwell boundary conditions where the absorption and conductivity of media were
taken into account. The use of our formulas for the wave amplitudes leads to
the fulfillment of the conservation law of energy both for the TE- and TM-
polarizations of light. The reemission of light is possible for the
thicknesses, which is equal to the wavelength of light in a medium, divisible
by integer:
$\frac{2{\pi}d_{res}}{2}={\lambda}_m{\cdot}m=\frac{{\lambda}_0}{n}{\cdot}m$,
where m=1,2,3... The visible luminescence of the porous silicon, silicon
whiskers and other nanometer-scale structures can be explained by their
emission in the case of dimension resonance because in this region of
thicknesses, layers have a big negative coefficient of absorption and little -
of a damping. It is also shown that in the case of the TM-polarization, in a
material with a high conductivity, light refracts in a "wrong" direction (at
all positive optical parameters) due to a surface current. In the case of the
TE-polarization, light refracts only in a "right" direction. | 1610.03775v1 |
1992-06-18 | Wormholes and Supersymmetry | Revisions: reference added to: G. Gilbert, {\sl Nucl.Phys.} {\bf B328}, 159
(1989) | 9206072v2 |
1993-05-26 | Musings on Magnus | The object of this paper is to describe a simple method for proving that
certain groups are residually torsion-free nilpotent, to describe some new
parafree groups and to raise some new problems in honour of the memory of
Wilhelm Magnus. | 9305201v1 |
2001-10-17 | Expected number of distinct part sizes in a random integer composition | The asymptotics, as $n\to\infty$, for the expected number of distinct part
sizes in a random composition of an integer n is obtained. | 0110189v1 |
2003-12-29 | Non-hopfian relatively free groups | To solve problems of Gilbert Baumslag and Hanna Neumann, posed in the 1960's,
we construct a nontrivial variety of groups all of whose noncyclic free groups
are non-hopfian. | 0312491v1 |
2005-10-26 | Winning rate in the full-information best choice problem | Following a long-standing suggestion by Gilbert and Mosteller, we derive an
explicit formula for the asymptotic winning rate in the full-information
problem of the best choice. | 0510568v3 |
2007-12-20 | The dark matter as a light gravitino (II) | We address the question of gravitino dark matter in the context of gauge
mediated supersymmetry breaking models. | 0712.3465v1 |
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