2,371 research outputs found
Single and double linear and nonlinear flatband chains: spectra and modes
We report results of systematic analysis of various modes in the flatband
lattice, based on the diamond-chain model with the on-site cubic nonlinearity,
and its double version with the linear on-site mixing between the two lattice
fields. In the single-chain system, a full analysis is presented, first, for
the single nonlinear cell, making it possible to find all stationary states,
viz., antisymmetric, symmetric, and asymmetric ones, including an exactly
investigated symmetry-breaking bifurcation of the subcritical type. In the
nonlinear infinite single-component chain, compact localized states (CLSs) are
found in an exact form too, as an extension of known compact eigenstates of the
linear diamond chain. Their stability is studied by means of analytical and
numerical methods, revealing a nontrivial stability boundary. In addition to
the CLSs, various species of extended states and exponentially localized
lattice solitons of symmetric and asymmetric types are studied too, by means of
numerical calculations and variational approximation. As a result, existence
and stability areas are identified for these modes. Finally, the linear version
of the double diamond chain is solved in an exact form, producing two split
flatbands in the system's spectrum.Comment: Phys. Rev E, in pres
Diamondlike carbon protective coatings for IR materials
Diamondlike carbon (DLC) films have the potential to protect optical windows in applications where it is important to maintain the integrity of the specular transmittance of these films on ZnS and ZnSe infrared transmitting windows. The films must be adherent and durable such that they protect the windows from rain and particle erosion as well as chemical attack. In order to optimize the performance of these films, 0.1 micro m thick diamondlike carbon films were deposited on fused silica and silicon wafers, using three different methods of ion beam deposition. One method was sputter deposition from a carbon target using an 8 cm ion source. The merits of hydrogen addition were experimentally evaluated in conjunction with this method. The second method used a 30 cm hollow cathode ion source with hydrocarbon/Argon gases to deposit diamondlike carbon films from the primary beam at 90 to 250 eV. The third method used a dual beam system employing a hydrocarbon/Argon 30 cm ion source and an 8 cm ion source. Films were evaluated for adherence, intrinsic stress, infrared transmittance between 2.5 and 50 micro m, and protection from particle erosion. An erosion test using a sandblaster was used to give quantitative values of the protection afforded to the fused silica by the diamondlike carbon films. The fused silica surfaces protected by diamondlike carbon films were exposed to 100 micro m diameter SiO particles at 60 mi/hr (26.8/sec) in the sandblaster
Detecting New Physics from CP-violating phase measurements in B decays
The standard CKM model can be tested and New Physics detected using only
CP-violating phase measurements in B decays. This requires the measurement of a
phase factor which is small in the Standard Model, in addition to the usual
large phases and . We also point out that identifying
violations of the unitarity of the CKM matrix is rather difficult, and cannot
be done with phase measurements alone.Comment: 6 pages, Latex, no figure
Photonuclear sum rules and the tetrahedral configuration of He
Three well known photonuclear sum rules (SR), i.e. the Thomas-Reiche-Kuhn,
the bremsstrahlungs and the polarizability SR are calculated for 4He with the
realistic nucleon-nucleon potential Argonne V18 and the three-nucleon force
Urbana IX. The relation between these sum rules and the corresponding energy
weighted integrals of the cross section is discussed. Two additional
equivalences for the bremsstrahlungs SR are given, which connect it to the
proton-neutron and neutron-neutron distances. Using them, together with our
result for the bremsstrahlungs SR, we find a deviation from the tetrahedral
symmetry of the spatial configuration of 4He. The possibility to access this
deviation experimentally is discussed.Comment: 13 pages, 1 tabl
Slingshot: cell lineage and pseudotime inference for single-cell transcriptomics.
BackgroundSingle-cell transcriptomics allows researchers to investigate complex communities of heterogeneous cells. It can be applied to stem cells and their descendants in order to chart the progression from multipotent progenitors to fully differentiated cells. While a variety of statistical and computational methods have been proposed for inferring cell lineages, the problem of accurately characterizing multiple branching lineages remains difficult to solve.ResultsWe introduce Slingshot, a novel method for inferring cell lineages and pseudotimes from single-cell gene expression data. In previously published datasets, Slingshot correctly identifies the biological signal for one to three branching trajectories. Additionally, our simulation study shows that Slingshot infers more accurate pseudotimes than other leading methods.ConclusionsSlingshot is a uniquely robust and flexible tool which combines the highly stable techniques necessary for noisy single-cell data with the ability to identify multiple trajectories. Accurate lineage inference is a critical step in the identification of dynamic temporal gene expression
A Computationally Efficient FPTAS for Convex Stochastic Dynamic Programs
We propose a computationally efficient fully polynomial-time approximation scheme (FPTAS) to compute an approximation with arbitrary precision of the value function of convex stochastic dynamic programs, using the technique of K-approximation sets and functions introduced by Halman et al. [Math. Oper. Res., 34, (2009), pp. 674-685]. This paper deals with the convex case only, and it has the following contributions. First, we improve on the worst-case running time given by Halman et al. Second, we design and implement an FPTAS with excellent computational performance and show that it is faster than an exact algorithm even for small problem instances and small approximation factors, becoming orders of magnitude faster as the problem size increases. Third, we show that with careful algorithm design, the errors introduced by floating point computations can be bounded, so that we can provide a guarantee on the approximation factor over an exact infinite-precision solution. We provide an extensive computational evaluation based on randomly generated problem instances coming from applications in supply chain management and finance. The running time of the FPTAS is both theoretically and experimentally linear in the size of the uncertainty set
Solitons supported by localized nonlinearities in periodic media
Nonlinear periodic systems, such as photonic crystals and Bose-Einstein
condensates (BECs) loaded into optical lattices, are often described by the
nonlinear Schr\"odinger/Gross-Pitaevskii equation with a sinusoidal potential.
Here, we consider a model based on such a periodic potential, with the
nonlinearity (attractive or repulsive) concentrated either at a single point or
at a symmetric set of two points, which are represented, respectively, by a
single {\delta}-function or a combination of two {\delta}-functions. This model
gives rise to ordinary solitons or gap solitons (GSs), which reside,
respectively, in the semi-infinite or finite gaps of the system's linear
spectrum, being pinned to the {\delta}-functions. Physical realizations of
these systems are possible in optics and BEC, using diverse variants of the
nonlinearity management. First, we demonstrate that the single
{\delta}-function multiplying the nonlinear term supports families of stable
regular solitons in the self-attractive case, while a family of solitons
supported by the attractive {\delta}-function in the absence of the periodic
potential is completely unstable. We also show that the {\delta}-function can
support stable GSs in the first finite gap in both the self-attractive and
repulsive models. The stability analysis for the GSs in the second finite gap
is reported too, for both signs of the nonlinearity. Alongside the numerical
analysis, analytical approximations are developed for the solitons in the
semi-infinite and first two finite gaps, with the single {\delta}-function
positioned at a minimum or maximum of the periodic potential. In the model with
the symmetric set of two {\delta}-functions, we study the effect of the
spontaneous symmetry breaking of the pinned solitons. Two configurations are
considered, with the {\delta}-functions set symmetrically with respect to the
minimum or maximum of the potential
Short range correlations and the isospin dependence of nuclear correlation functions
Pair densities and associated correlation functions provide a critical tool
for introducing many-body correlations into a wide-range of effective theories.
Ab initio calculations show that two-nucleon pair-densities exhibit strong spin
and isospin dependence. However, such calculations are not available for all
nuclei of current interest. We therefore provide a simple model, which involves
combining the short and long separation distance behavior using a single
blending function, to accurately describe the two-nucleon correlations inherent
in existing ab initio calculations. We show that the salient features of the
correlation function arise from the features of the two-body short-range
nuclear interaction, and that the suppression of the pp and nn pair-densities
caused by the Pauli principle is important. Our procedure for obtaining
pair-density functions and correlation functions can be applied to heavy nuclei
which lack ab initio calculations.Comment: 5 pages, 4 figure
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