266 research outputs found
Composition-tuned smeared phase transitions
Phase transitions in random systems are smeared if individual spatial regions
can order independently of the bulk system. In this paper, we study such
smeared phase transitions (both classical and quantum) in substitutional alloys
AB that can be tuned from an ordered phase at composition to
a disordered phase at . We show that the ordered phase develops a
pronounced tail that extends over all compositions . Using optimal
fluctuation theory, we derive the composition dependence of the order parameter
and other quantities in the tail of the smeared phase transition. We also
compare our results to computer simulations of a toy model, and we discuss
experiments.Comment: 6 pages, 4 eps figures included, final version as publishe
Stream instabilities in relativistically hot plasma
The instabilities of relativistic ion beams in a relativistically hot
electron background are derived for general propagation angles. It is shown
that the Weibel instability in the direction perpendicular to the streaming
direction is the fastest growing mode, and probably the first to appear,
consistent with the aligned filaments that are seen in PIC simulations.
Oblique, quasiperpendicular modes grow almost as fast, as the growth rate
varies only moderately with angle, and they may distort or corrugate the
filaments after the perpendicular mode saturates.Comment: 10 pages, 6 figure
Estimating the amount of vorticity generated by cosmological perturbations in the early universe
We estimate the amount of vorticity generated at second order in cosmological
perturbation theory from the coupling between first order energy density and
non-adiabatic pressure, or entropy, perturbations. Assuming power law input
spectra for the source terms, and working in a radiation background, we
calculate the wave number dependence of the vorticity power spectrum and its
amplitude. We show that the vorticity generated by this mechanism is
non-negligible on small scales, and hence should be taken into consideration in
current and future CMB experiments.Comment: 9 pages, revtex4, 1 figure; v2: typos and minor error corrected,
result unchange
Effective Hamiltonian study of excitations in a boson- fermion mixture with attraction between components
An effective Hamiltonian for the Bose subsystem in the mixture of ultracold
atomic clouds of bosons and fermions with mutual attractive interaction is used
for investigating collective excitation spectrum. The ground state and mode
frequencies of the Rb and K mixture are analyzed quantitatively
at zero temperature. We find analytically solutions of the hydrodynamics
equations in the Thomas- Fermi approximation. We discuss the relation between
the onset of collapse and collective modes softening and the dependence of
collective oscillations on scattering length and number of boson atoms.Comment: 9 pages, 5 figure
Comments on gauge-invariance in cosmology
We revisit the gauge issue in cosmological perturbation theory, and highlight
its relation to the notion of covariance in general relativity. We also discuss
the similarities and differences of the covariant approach in perturbation
theory to the Bardeen or metric approach in a non-technical fashion.Comment: 7 pages, 1 figure, revtex4; v3: minor changes, typos corrected,
discussion extended; v4: typos corrected, corresponding to published versio
Inferring the time-dependent complex Ginzburg-Landau equation from modulus data
We present a formalism for inferring the equation of evolution of a complex
wave field that is known to obey an otherwise unspecified (2+1)-dimensional
time-dependent complex Ginzburg-Landau equation, given field moduli over three
closely-spaced planes. The phase of the complex wave field is retrieved via a
non-interferometric method, and all terms in the equation of evolution are
determined using only the magnitude of the complex wave field. The formalism is
tested using simulated data for a generalized nonlinear system with a
single-component complex wave field. The method can be generalized to
multi-component complex fields.Comment: 9 pages, 9 figure
Interpreting the results of chemical stone analysis in the era of modern stone analysis techniques
INTRODUCTION AND OBJECTIVE:
Stone analysis should be performed in all first-time stone formers. The preferred analytical procedures are Fourier-transform infrared spectroscopy (FT-IR) or X-ray diffraction (XRD). However, due to limited resources, chemical analysis (CA) is still in use throughout the world. The aim of the study was to compare FT-IR and CA in well matched stone specimens and characterize the pros and cons of CA.
METHODS:
In a prospective bi-center study, urinary stones were retrieved from 60 consecutive endoscopic procedures. In order to assure that identical stone samples were sent for analyses, the samples were analyzed initially by micro-computed tomography to assess uniformity of each specimen before submitted for FTIR and CA.
RESULTS:
Overall, the results of CA did not match with the FTIR results in 56 % of the cases. In 16 % of the cases CA missed the major stone component and in 40 % the minor stone component. 37 of the 60 specimens contained CaOx as major component by FTIR, and CA reported major CaOx in 47/60, resulting in high sensitivity, but very poor specificity. CA was relatively accurate for UA and cystine. CA missed struvite and calcium phosphate as a major component in all cases. In mixed stones the sensitivity of CA for the minor component was poor, generally less than 50 %.
CONCLUSIONS:
Urinary stone analysis using CA provides only limited data that should be interpreted carefully. Urinary stone analysis using CA is likely to result in clinically significant errors in its assessment of stone composition. Although the monetary costs of CA are relatively modest, this method does not provide the level of analytical specificity required for proper management of patients with metabolic stones
On the structure of subsets of the discrete cube with small edge boundary
On the structure of subsets of the discrete cube with small edge boundary, Discrete Analysis 2018:9, 29 pp.
An isoperimetric inequality is a statement that tells us how small the boundary of a set can be given the size of the set, for suitable notions of "size" and "boundary". For example, one formulation of the classical isoperimetric inequality in is as follows. Given a subset of , define the -_expansion_ of to be the open set . If in addition is measurable, define the size of its boundary to be . (If is a set with a suitably smooth topological boundary , then this turns out to equal the surface measure of .) Then amongst all sets of a given measure, the one with the smallest boundary is an -dimensional ball.
Isoperimetric inequalities have been the focus of a great deal of research, partly for their intrinisic interest, but also because they have numerous applications. One particularly useful one is the _edge-isoperimetric inequality in the discrete cube_. This concerns subsets of the -dimensional cube , which we turn into a graph by joining two points and if they differ in exactly one coordinate. The size of a set is simply its cardinality, the _edge-boundary_ of is defined to be the set of edges between and its complement, and the size of the edge-boundary is the number of such edges. If , then it is known that the edge-boundary is minimized when is a -dimensional subspace of generated by standard basis vectors. More generally, if , then the edge-boundary is minimized when is an initial segment in the lexicographical ordering, which is the ordering where we set if for the first coordinate where and differ. (This coincides with the ordering we obtain if we think of the sequences as binary representations of integers.)
For the two isoperimetric inequalities just mentioned, as well as many others, it is known that the extremal examples provided are essentially the only ones: a subset of with a boundary that is as small as possible has to be an -dimensional ball, and a subset of the discrete cube with edge-boundary that is as small as possible has to be an initial segment of the lexicographical ordering, up to the symmetries of the graph. Furthermore, there are _stablity_ results: a set with a boundary that is _almost_ as small as possible must be close to an extremal example. Such a result tells us that the isoperimetric inequalities are "robust", in the sense that if you slightly perturb the condition on the set, then you only slightly perturb what the set has to look like.
This paper is about an extremely precise stability result for the edge isoperimetric inequality in the discrete cube. There have been a number of papers on such results (see the introduction to the paper for details), but they have been mainly for sets of size for some , where the goal is to prove that they must be close to -dimensional subcubes -- that is, subspaces (or their translates) generated by standard basis vectors. This paper considers sets of arbitrary size and proves the following result. Suppose that is a subset of of size . Suppose that the size of the edge-boundary of is at most , where is the size of the edge-boundary of the initial segment of size in the lexicographical order. Then there is an automorphism of (meaning a bijection that takes neighbouring points to neighbouring points) such that , where is an absolute constant. They give an example to show that must be at least 2, and thus that their result is best possible up to the value of the constant .
Previous proofs of stability versions of the edge-isoperimetric inequality in the cube have used Fourier analysis. The proof in this paper uses purely combinatorial methods, such as induction on the dimension, and compressions. To get these methods to work, several interesting ideas are needed, including some new results about the influence of variables
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