18,267 research outputs found
Stochastic Block Models are a Discrete Surface Tension
Networks, which represent agents and interactions between them, arise in
myriad applications throughout the sciences, engineering, and even the
humanities. To understand large-scale structure in a network, a common task is
to cluster a network's nodes into sets called "communities", such that there
are dense connections within communities but sparse connections between them. A
popular and statistically principled method to perform such clustering is to
use a family of generative models known as stochastic block models (SBMs). In
this paper, we show that maximum likelihood estimation in an SBM is a network
analog of a well-known continuum surface-tension problem that arises from an
application in metallurgy. To illustrate the utility of this relationship, we
implement network analogs of three surface-tension algorithms, with which we
successfully recover planted community structure in synthetic networks and
which yield fascinating insights on empirical networks that we construct from
hyperspectral videos.Comment: to appear in Journal of Nonlinear Scienc
Simulating causal collapse models
We present simulations of causal dynamical collapse models of field theories
on a 1+1 null lattice. We use our simulations to compare and contrast two
possible interpretations of the models, one in which the field values are real
and the other in which the state vector is real. We suggest that a procedure of
coarse graining and renormalising the fundamental field can overcome its
noisiness and argue that this coarse grained renormalised field will show
interesting structure if the state vector does on the coarse grained scale.Comment: 18 pages, 8 fugures, LaTeX, Reference added, discussion of
probability distribution of labellings correcte
Four-dimensional understanding of quantum mechanics and Bell violation
While our natural intuition suggests us that we live in 3D space evolving in
time, modern physics presents fundamentally different picture: 4D spacetime,
Einstein's block universe, in which we travel in thermodynamically emphasized
direction: arrow of time. Suggestions for such nonintuitive and nonlocal living
in kind of "4D jello" come among others from: Lagrangian mechanics we use from
QFT to GR saying that history between fixed past and future situation is the
one optimizing action, special relativity saying that different velocity
observers have different present 3D hypersurface and time direction, general
relativity deforming shape of the entire spacetime up to switching time and
space below the black hole event horizon, or the CPT theorem concluding
fundamental symmetry between past and future.
Accepting this nonintuitive living in 4D spacetime: with present moment being
in equilibrium between past and future - minimizing tension as action of
Lagrangian, leads to crucial surprising differences from intuitive "evolving
3D" picture, in which we for example conclude satisfaction of Bell inequalities
- violated by the real physics. Specifically, particle in spacetime becomes own
trajectory: 1D submanifold of 4D, making that statistical physics should
consider ensembles like Boltzmann distribution among entire paths, what leads
to quantum behavior as we know from Feynman's Euclidean path integrals or
similar Maximal Entropy Random Walk (MERW). It results for example in Anderson
localization, or the Born rule with squares - allowing for violation of Bell
inequalities. Specifically, quantum amplitude turns out to describe probability
at the end of half-spacetime from a given moment toward past or future, to
randomly get some value of measurement we need to "draw it" from both time
directions, getting the squares of Born rules.Comment: 13 pages, 18 figure
Metastability in the dilute Ising model
Consider Glauber dynamics for the Ising model on the hypercubic lattice with
a positive magnetic field. Starting from the minus configuration, the system
initially settles into a metastable state with negative magnetization. Slowly
the system relaxes to a stable state with positive magnetization. Schonmann and
Shlosman showed that in the two dimensional case the relaxation time is a
simple function of the energy required to create a critical Wulff droplet.
The dilute Ising model is obtained from the regular Ising model by deleting a
fraction of the edges of the underlying graph. In this paper we show that even
an arbitrarily small dilution can dramatically reduce the relaxation time. This
is because of a catalyst effect---rare regions of high dilution speed up the
transition from minus phase to plus phase.Comment: 49 page
Nonlinear physics of electrical wave propagation in the heart: a review
The beating of the heart is a synchronized contraction of muscle cells
(myocytes) that are triggered by a periodic sequence of electrical waves (action
potentials) originating in the sino-atrial node and propagating over the atria and
the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF)
or ventricular tachycardia (VT) are caused by disruptions and instabilities of these
electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent
wave patterns (AF,VF). Numerous simulation and experimental studies during the
last 20 years have addressed these topics. In this review we focus on the nonlinear
dynamics of wave propagation in the heart with an emphasis on the theory of pulses,
spirals and scroll waves and their instabilities in excitable media and their application
to cardiac modeling. After an introduction into electrophysiological models for action
potential propagation, the modeling and analysis of spatiotemporal alternans, spiral
and scroll meandering, spiral breakup and scroll wave instabilities like negative line
tension and sproing are reviewed in depth and discussed with emphasis on their impact
in cardiac arrhythmias.Peer ReviewedPreprin
Stochastic Resonance Can Drive Adaptive Physiological Processes
Stochastic resonance (SR) is a concept from the physics and engineering communities that has applicability to both systems physiology and other living systems. In this paper, it will be argued that stochastic resonance plays a role in driving behavior in neuromechanical systems. The theory of stochastic resonance will be discussed, followed by a series of expected outcomes, and two tests of stochastic resonance in an experimental setting. These tests are exploratory in nature, and provide a means to parameterize systems that couple biological and mechanical components. Finally, the potential role of stochastic resonance in adaptive physiological systems will be discussed
A computational toy model for shallow landslides: Molecular Dynamics approach
The aim of this paper is to propose a 2D computational algorithm for modeling
of the trigger and the propagation of shallow landslides caused by rainfall. We
used a Molecular Dynamics (MD) inspired model, similar to discrete element
method (DEM), that is suitable to model granular material and to observe the
trajectory of single particle, so to identify its dynamical properties. We
consider that the triggering of shallow landslides is caused by the decrease of
the static friction along the sliding surface due to water infiltration by
rainfall. Thence the triggering is caused by two following conditions: (a) a
threshold speed of the particles and (b) a condition on the static friction,
between particles and slope surface, based on the Mohr-Coulomb failure
criterion. The latter static condition is used in the geotechnical model to
estimate the possibility of landslide triggering. Finally the interaction force
between particles is defined trough a potential that, in the absence of
experimental data, we have modeled as the Lennard-Jones 2-1 potential. In the
model the viscosity is also introduced and for a large range of values of the
model's parameters, we observe a characteristic velocity pattern, with
acceleration increments, typical of real landslides. The results of simulations
are quite promising: the energy and the time triggering distributions of local
avalanches shows a power law distribution, analogous to the observed
Gutenberg-Richter and Omori power law distributions for earthquakes. Finally it
is possible to apply the method of the inverse surface displacement velocity
[Fukuzono 1985] for predicting the failure time
Pores in Bilayer Membranes of Amphiphilic Molecules: Coarse-Grained Molecular Dynamics Simulations Compared with Simple Mesoscopic Models
We investigate pores in fluid membranes by molecular dynamics simulations of
an amphiphile-solvent mixture, using a molecular coarse-grained model. The
amphiphilic membranes self-assemble into a lamellar stack of amphiphilic
bilayers separated by solvent layers. We focus on the particular case of
tension less membranes, in which pores spontaneously appear because of thermal
fluctuations. Their spatial distribution is similar to that of a random set of
repulsive hard discs. The size and shape distribution of individual pores can
be described satisfactorily by a simple mesoscopic model, which accounts only
for a pore independent core energy and a line tension penalty at the pore
edges. In particular, the pores are not circular: their shapes are fractal and
have the same characteristics as those of two dimensional ring polymers.
Finally, we study the size-fluctuation dynamics of the pores, and compare the
time evolution of their contour length to a random walk in a linear potential
Recent advances in the simulation of particle-laden flows
A substantial number of algorithms exists for the simulation of moving
particles suspended in fluids. However, finding the best method to address a
particular physical problem is often highly non-trivial and depends on the
properties of the particles and the involved fluid(s) together. In this report
we provide a short overview on a number of existing simulation methods and
provide two state of the art examples in more detail. In both cases, the
particles are described using a Discrete Element Method (DEM). The DEM solver
is usually coupled to a fluid-solver, which can be classified as grid-based or
mesh-free (one example for each is given). Fluid solvers feature different
resolutions relative to the particle size and separation. First, a
multicomponent lattice Boltzmann algorithm (mesh-based and with rather fine
resolution) is presented to study the behavior of particle stabilized fluid
interfaces and second, a Smoothed Particle Hydrodynamics implementation
(mesh-free, meso-scale resolution, similar to the particle size) is introduced
to highlight a new player in the field, which is expected to be particularly
suited for flows including free surfaces.Comment: 16 pages, 4 figure
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