2,017 research outputs found
SUSY transformation of the Green function and a trace formula
An integral relation is established between the Green functions corresponding
to two Hamiltonians which are supersymmetric (SUSY) partners and in general may
possess both discrete and continuous spectra. It is shown that when the
continuous spectrum is present the trace of the difference of the Green
functions for SUSY partners is a finite quantity which may or may not be equal
to zero despite the divergence of the traces of each Green function. Our
findings are illustrated by using the free particle example considered both on
the whole real line and on a half line
Recovery of a quarkonium system from experimental data
For confining potentials of the form q(r)=r+p(r), where p(r) decays rapidly
and is smooth for r>0, it is proved that q(r) can be uniquely recovered from
the data {E_j,s_j}, where E_j are the bound states energies and s_j are the
values of u'_j(0), and u_j(r) are the normalized eigenfunctions of the problem
-u_j" +q(r)u_j=E_ju_j, r>0, u_j(0)=0, ||u_j||=1, where the norm is L^2(0,
\infty) norm. An algorithm is given for recovery of p(r) from few experimental
data
Topological model of soap froth evolution with deterministic T2-processes
We introduce a topological model for the evolution of 2d soap froth. The
topological rearrangements (T2 processes) are deterministic (unlike the
standard stochastic model): the final topology depends on the areas of the
neighboring cells. The new model gives agreement with experiments in the
transient regime, where the previous models failed qualitatively, and also
improves agreement in the scaling state.Comment: latex, 12 pages, 2 figure
Diffusion of a granular pulse in a rotating drum
The diffusion of a pulse of small grains in an horizontal rotating drum is
studied through discrete elements methods simulations. We present a theoretical
analysis of the diffusion process in a one-dimensional confined space in order
to elucidate the effect of the confining end-plate of the drum. We then show
that the diffusion is neither subdiffusive nor superdiffusive but normal. This
is demonstrated by rescaling the concentration profiles obtained at various
stages and by studying the time evolution of the mean squared deviation.
Finally we study the self-diffusion of both large and small grains and we show
that it is normal and that the diffusion coefficient is independent of the
grain size
Signatures of the order parameter of a superconducting adatom layer in quasiparticle interference patterns
Experiments have observed superconductivity in atomically-thin metallic
layers deposited on semiconducting substrates. As in any superconductor, it is
important to determine the structure of the superconducting pairing function in
order to reveal the mechanism responsible for superconductivity. To that end,
we study the possible superconducting states of two-dimensional triangular
lattices. We calculate the quasiparticle interference (QPI) patterns which
would result from various nearest-neighbor pairing order parameters, and show
how the QPI can be used to distinguish between those order parameters. The QPI
patterns are the momentum-space representations of real-space local
density-of-states fluctuations: the QPI signal at momentum reveals the
strength of scattering processes at that momentum transfer. We show how
characteristic differences between scattering from charge disorder (i.e.
impurities) and from order-parameter disorder (i.e. vortices) can be used to
identify the angular momentum of the superconducting pairs.Comment: 12 pages, 8 figure
Example of two different potentials which have practically the same fixed-energy phase shifts
It is shown that the Newton-Sabatier procedure for inverting the fixed-energy
phase shifts for a potential is not an inversion method but a parameter-fitting
procedure. Theoretically there is no guarantee that this procedure is
applicable to the given set of the phase shifts, if it is applicable, there is
no guaran- tee that the potential it produces generates the phase shifts from
which it was reconstructed. Moreover, no generic potential, specifically, no
potential which is not analytic in a neighborhood of the positive real semiaxis
can be reconstructed by the Newton-Sabatier procedure.
A numerical method is given for finding spherically symmetric compactly
supported potentials which produce practically the same set of fixed-energy
phase shifts for all values of angular momentum. Concrete example of such
potentials is given
Effects of Noise in a Cortical Neural Model
Recently Segev et al. (Phys. Rev. E 64,2001, Phys.Rev.Let. 88, 2002) made
long-term observations of spontaneous activity of in-vitro cortical networks,
which differ from predictions of current models in many features. In this paper
we generalize the EI cortical model introduced in a previous paper (S.Scarpetta
et al. Neural Comput. 14, 2002), including intrinsic white noise and analyzing
effects of noise on the spontaneous activity of the nonlinear system, in order
to account for the experimental results of Segev et al.. Analytically we can
distinguish different regimes of activity, depending from the model parameters.
Using analytical results as a guide line, we perform simulations of the
nonlinear stochastic model in two different regimes, B and C. The Power
Spectrum Density (PSD) of the activity and the Inter-Event-Interval (IEI)
distributions are computed, and compared with experimental results. In regime B
the network shows stochastic resonance phenomena and noise induces aperiodic
collective synchronous oscillations that mimic experimental observations at 0.5
mM Ca concentration. In regime C the model shows spontaneous synchronous
periodic activity that mimic activity observed at 1 mM Ca concentration and the
PSD shows two peaks at the 1st and 2nd harmonics in agreement with experiments
at 1 mM Ca. Moreover (due to intrinsic noise and nonlinear activation function
effects) the PSD shows a broad band peak at low frequency. This feature,
observed experimentally, does not find explanation in the previous models.
Besides we identify parametric changes (namely increase of noise or decreasing
of excitatory connections) that reproduces the fading of periodicity found
experimentally at long times, and we identify a way to discriminate between
those two possible effects measuring experimentally the low frequency PSD.Comment: 25 pages, 10 figures, to appear in Phys. Rev.
SLOB, a SLOWPOKE Channel Binding Protein, Regulates Insulin Pathway Signaling and Metabolism in Drosophila
There is ample evidence that ion channel modulation by accessory proteins within a macromolecular complex can regulate channel activity and thereby impact neuronal excitability. However, the downstream consequences of ion channel modulation remain largely undetermined. The Drosophila melanogaster large conductance calcium-activated potassium channel SLOWPOKE (SLO) undergoes modulation via its binding partner SLO-binding protein (SLOB). Regulation of SLO by SLOB influences the voltage dependence of SLO activation and modulates synaptic transmission. SLO and SLOB are expressed especially prominently in median neurosecretory cells (mNSCs) in the pars intercerebralis (PI) region of the brain; these cells also express and secrete Drosophila insulin like peptides (dILPs). Previously, we found that flies lacking SLOB exhibit increased resistance to starvation, and we reasoned that SLOB may regulate aspects of insulin signaling and metabolism. Here we investigate the role of SLOB in metabolism and find that slob null flies exhibit changes in energy storage and insulin pathway signaling. In addition, slob null flies have decreased levels of dilp3 and increased levels of takeout, a gene known to be involved in feeding and metabolism. Targeted expression of SLOB to mNSCs rescues these alterations in gene expression, as well as the metabolic phenotypes. Analysis of fly lines mutant for both slob and slo indicate that the effect of SLOB on metabolism and gene expression is via SLO. We propose that modulation of SLO by SLOB regulates neurotransmission in mNSCs, influencing downstream insulin pathway signaling and metabolism
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