1,034 research outputs found
Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model
We investigate non-stationary heat transfer in the Kipnis-Marchioro-Presutti
(KMP) lattice gas model at long times in one dimension when starting from a
localized heat distribution. At large scales this initial condition can be
described as a delta-function, . We characterize the
process by the heat, transferred to the right of a specified point by
time , and study the full probability
distribution . The particular case of has been
recently solved [Bettelheim \textit{et al}. Phys. Rev. Lett. \textbf{128},
130602 (2022)]. At fixed , the distribution as a function of
and has the same long-time dynamical scaling properties as the position
of a tracer in a single-file diffusion. Here we evaluate
by exploiting the recently uncovered complete integrability of the equations of
the macroscopic fluctuation theory (MFT) for the KMP model and using the
Zakharov-Shabat inverse scattering method. We also discuss asymptotics of
which we extract from the exact solution, and also obtain
by applying two different perturbation methods directly to the MFT equations.Comment: 23 pages, 6 figure
Clustering, advection and patterns in a model of population dynamics with neighborhood-dependent rates
We introduce a simple model of population dynamics which considers birth and
death rates for every individual that depend on the number of particles in its
neighborhood. The model shows an inhomogeneous quasistationary pattern with
many different clusters of particles.
We derive the equation for the macroscopic density of particles, perform a
linear stability analysis on it, and show that there is a finite-wavelength
instability leading to pattern formation. This is the responsible for the
approximate periodicity with which the clusters of particles arrange in the
microscopic model.
In addition, we consider the population when immersed in a fluid medium and
analyze the influence of advection on global properties of the model.Comment: Some typos and some problems with the figures correcte
Transition Phenomena Induced by Internal Noise and Quasi-absorbing State
We study a simple chemical reaction system and effects of the internal noise.
The chemical reaction system causes the same transition phenomenon discussed by
Togashi and Kaneko [Phys. Rev. Lett. 86 (2001) 2459; J. Phys. Soc. Jpn. 72
(2003) 62]. By using the simpler model than Togashi-Kaneko's one, we discuss
the transition phenomenon by means of a random walk model and an effective
model. The discussion makes it clear that quasi-absorbing states, which are
produced by the change of the strength of the internal noise, play an important
role in the transition phenomenon. Stabilizing the quasi-absorbing states
causes bifurcation of the peaks in the stationary probability distribution
discontinuously.Comment: 6 pages, 5 figure
Effects of endocrine therapy on steroid-receptor content of breast cancer.
In order to determine the mechanisms of relapse following response to endocrine therapy, we have measured the oestrogen receptor (RE) content of biopsies of breast cancer in patients receiving various types of endocrine treatment. RE content fell in responding (means of 260.2 to 12 fmol/mg protein) and in nonresponding (means of 155.1 to 31.8 fmol/mg protein) patients who had measurable receptor at the start of treatment. Some of these patients, and a further group of responders to endocrine therapy, were monitored until relapse. Tumour biopsies at the time of relapse showed that 10/14 tumour samples contained significant RE (mean of 86.7 fmol/mg protein; range less than 10-271 fmol/mg protein) after successful endocrine therapy. No relationship could be found between RE content and plasma gonadotrophin or steroid-hormone concentration, but the fall in RE content correlated with reduced numbers of tumour cells in the biopsy. These results indicate that relapse following successful endocrine therapy in breast cancer does not appear to be due to the emergence of RE-negative tumour cells. The fall in RE content during response to endocrine therapy may be due to reduced tumour-cell content of the biopsy
The experience of enchantment in human-computer interaction
Improving user experience is becoming something of a rallying call in human–computer interaction but experience is not a unitary thing. There are varieties of experiences, good and bad, and we need to characterise these varieties if we are to improve user experience. In this paper we argue that enchantment is a useful concept to facilitate closer relationships between people and technology. But enchantment is a complex concept in need of some clarification. So we explore how enchantment has been used in the discussions of technology and examine experiences of film and cell phones to see how enchantment with technology is possible. Based on these cases, we identify the sensibilities that help designers design for enchantment, including the specific sensuousness of a thing, senses of play, paradox and openness, and the potential for transformation. We use these to analyse digital jewellery in order to suggest how it can be made more enchanting. We conclude by relating enchantment to varieties of experience.</p
Quantum Hall transitions: An exact theory based on conformal restriction
We revisit the problem of the plateau transition in the integer quantum Hall
effect. Here we develop an analytical approach for this transition, based on
the theory of conformal restriction. This is a mathematical theory that was
recently developed within the context of the Schramm-Loewner evolution which
describes the stochastic geometry of fractal curves and other stochastic
geometrical fractal objects in 2D space. Observables elucidating the connection
with the plateau transition include the so-called point-contact conductances
(PCCs) between points on the boundary of the sample, described within the
language of the Chalker-Coddington network model. We show that the
disorder-averaged PCCs are characterized by classical probabilities for certain
geometric objects in the plane (pictures), occurring with positive statistical
weights, that satisfy the crucial restriction property with respect to changes
in the shape of the sample with absorbing boundaries. Upon combining this
restriction property with the expected conformal invariance at the transition
point, we employ the mathematical theory of conformal restriction measures to
relate the disorder-averaged PCCs to correlation functions of primary operators
in a conformal field theory (of central charge ). We show how this can be
used to calculate these functions in a number of geometries with various
boundary conditions. Since our results employ only the conformal restriction
property, they are equally applicable to a number of other critical disordered
electronic systems in 2D. For most of these systems, we also predict exact
values of critical exponents related to the spatial behavior of various
disorder-averaged PCCs.Comment: Published versio
Semiclassical evolution of the spectral curve in the normal random matrix ensemble as Whitham hierarchy
We continue the analysis of the spectral curve of the normal random matrix
ensemble, introduced in an earlier paper. Evolution of the full quantum curve
is given in terms of compatibility equations of independent flows. The
semiclassical limit of these flows is expressed through canonical differential
forms of the spectral curve. We also prove that the semiclassical limit of the
evolution equations is equivalent to Whitham hierarchy.Comment: 14 page
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