4,367 research outputs found
Cellular-Automata model for dense-snow avalanches
This paper introduces a three-dimensional model for simulating dense-snow avalanches, based on the numerical method of cellular automata. This method allows one to study the complex behavior of the avalanche by dividing it into small elements, whose interaction is described by simple laws, obtaining a reduction of the computational power needed to perform a three-dimensional simulation. Similar models by several authors have been used to model rock avalanches, mud and lava flows, and debris avalanches. A peculiar aspect of avalanche dynamics, i.e., the mechanisms of erosion of the snowpack and deposition of material from the avalanche is taken into account in the model. The capability of the proposed approach has been illustrated by modeling three documented avalanches that occurred in Susa Valley (Western Italian Alps). Despite the qualitative observations used for calibration, the proposed method is able to reproduce the correct three-dimensional avalanche path, using a digital terrain model, and the order of magnitude of the avalanche deposit volume
The functional integral with unconditional Wiener measure for anharmonic oscillator
In this article we propose the calculation of the unconditional Wiener
measure functional integral with a term of the fourth order in the exponent by
an alternative method as in the conventional perturbative approach. In contrast
to the conventional perturbation theory, we expand into power series the term
linear in the integration variable in the exponent. In such a case we can
profit from the representation of the integral in question by the parabolic
cylinder functions. We show that in such a case the series expansions are
uniformly convergent and we find recurrence relations for the Wiener functional
integral in the - dimensional approximation. In continuum limit we find
that the generalized Gelfand - Yaglom differential equation with solution
yields the desired functional integral (similarly as the standard Gelfand -
Yaglom differential equation yields the functional integral for linear harmonic
oscillator).Comment: Source file which we sent to journa
Field theory of the inverse cascade in two-dimensional turbulence
A two-dimensional fluid, stirred at high wavenumbers and damped by both
viscosity and linear friction, is modeled by a statistical field theory. The
fluid's long-distance behavior is studied using renormalization-group (RG)
methods, as begun by Forster, Nelson, and Stephen [Phys. Rev. A 16, 732
(1977)]. With friction, which dissipates energy at low wavenumbers, one expects
a stationary inverse energy cascade for strong enough stirring. While such
developed turbulence is beyond the quantitative reach of perturbation theory, a
combination of exact and perturbative results suggests a coherent picture of
the inverse cascade. The zero-friction fluctuation-dissipation theorem (FDT) is
derived from a generalized time-reversal symmetry and implies zero anomalous
dimension for the velocity even when friction is present. Thus the Kolmogorov
scaling of the inverse cascade cannot be explained by any RG fixed point. The
beta function for the dimensionless coupling ghat is computed through two
loops; the ghat^3 term is positive, as already known, but the ghat^5 term is
negative. An ideal cascade requires a linear beta function for large ghat,
consistent with a Pad\'e approximant to the Borel transform. The conjecture
that the Kolmogorov spectrum arises from an RG flow through large ghat is
compatible with other results, but the accurate k^{-5/3} scaling is not
explained and the Kolmogorov constant is not estimated. The lack of scale
invariance should produce intermittency in high-order structure functions, as
observed in some but not all numerical simulations of the inverse cascade. When
analogous RG methods are applied to the one-dimensional Burgers equation using
an FDT-preserving dimensional continuation, equipartition is obtained instead
of a cascade--in agreement with simulations.Comment: 16 pages, 3 figures, REVTeX 4. Material added on energy flux,
intermittency, and comparison with Burgers equatio
Microscopic Features of Adhesive Bonds for Non-Destructive Measurements
Inelastic electron tunneling spectroscopy, or lETS, provides an extremely sensitive method for monitoring the chemical and physical state of a molecular substance adsorbed onto an oxide surface. Inelastic tunneling data directly reflect the molecular vibrational frequencies of the first monolayer of adsorbed molecules and changes in the vibrational spectrum can be correlated with changes in the chemical state of the molecule/oxide interface. We have carried out lETS experiments on the components of the commercial adhesive, Hercules 3501. This epoxy system consists ·of two molecular components; diamino diphenyl sulfone (DPS) and tetraglycidycl 4,4\u27 diamino diphenyl methane (DPM). lETS spectra of the individual components and of the epoxy mixture adsorbed on aluminum oxide have been obtained and the vibrational modes and frequencies assigned by comparison with computer calculations and existing infrared optical spectra. Some evidence for an aging effect has been observed for the adsorbed DPS. This effect appears as a dramatic change in the low frequency vibrational modes and may be associated with the formation of hydrogen bonds or the polymerization of the DPS. Further studies of this effect are in progress. The effects of water permeation may be studied using D2O as a tracer. The vibrational modes of D20 are easily distinguished from those of water which may be present as a contaminant. If the exchange reaciton D2O + HCR → DHO + DCR occurs, it would be easily detected in the lETS spectrum. Initial experiments performed by simply immersing the tunnel junction into liquid D2O for several hours were unsuccessful because severe corrosion of the tunnel junction resulted. Experiments employing aluminum/aluminum oxide/adhesive/gold thin film junction for the study of H2O permeation are in progress. Further studies are planned to monitor the effects of heat treatment on the adhesive components and mixture
Pseudo-random operators of the circular ensembles
We demonstrate quantum algorithms to implement pseudo-random operators that
closely reproduce statistical properties of random matrices from the three
universal classes: unitary, symmetric, and symplectic. Modified versions of the
algorithms are introduced for the less experimentally challenging quantum
cellular automata. For implementing pseudo-random symplectic operators we
provide gate sequences for the unitary part of the time-reversal operator.Comment: 5 pages, 4 figures, to be published PR
On the Efficient Calculation of a Linear Combination of Chi-Square Random Variables with an Application in Counting String Vacua
Linear combinations of chi square random variables occur in a wide range of
fields. Unfortunately, a closed, analytic expression for the pdf is not yet
known. As a first result of this work, an explicit analytic expression for the
density of the sum of two gamma random variables is derived. Then a
computationally efficient algorithm to numerically calculate the linear
combination of chi square random variables is developed. An explicit expression
for the error bound is obtained. The proposed technique is shown to be
computationally efficient, i.e. only polynomial in growth in the number of
terms compared to the exponential growth of most other methods. It provides a
vast improvement in accuracy and shows only logarithmic growth in the required
precision. In addition, it is applicable to a much greater number of terms and
currently the only way of computing the distribution for hundreds of terms. As
an application, the exponential dependence of the eigenvalue fluctuation
probability of a random matrix model for 4d supergravity with N scalar fields
is found to be of the asymptotic form exp(-0.35N).Comment: 21 pages, 19 figures. 3rd versio
A new neurosurgical tool incorporating differential geometry and cellular automata techniques
Using optical coherence imaging, it is possible to visualize seizure progression intraoperatively. However, it is difficult to pinpoint an exact epileptic focus. This is crucial in attempts to minimize the amount of resection necessary during surgical therapeutic interventions for epilepsy and is typically done approximately from visual inspection of optical coherence imaging stills. In this paper, we create an algorithm with the potential to pinpoint the source of a seizure from an optical coherence imaging still. To accomplish this, a grid is overlaid on optical coherence imaging stills. This then serves as a grid for a two-dimensional cellular automation. Each cell is associated with a Riemannian curvature tensor representing the curvature of the brain's surface in all directions for a cell. Cells which overlay portions of the image which show neurons that are firing are considered "depolarized"
Towards generalized measures grasping CA dynamics
In this paper we conceive Lyapunov exponents, measuring the rate of separation between two initially close configurations, and Jacobians, expressing the sensitivity of a CA's transition function to its inputs, for cellular automata (CA) based upon irregular tessellations of the n-dimensional Euclidean space. Further, we establish a relationship between both that enables us to derive a mean-field approximation of the upper bound of an irregular CA's maximum Lyapunov exponent. The soundness and usability of these measures is illustrated for a family of 2-state irregular totalistic CA
The Implications of Interactions for Science and Philosophy
Reductionism has dominated science and philosophy for centuries. Complexity
has recently shown that interactions---which reductionism neglects---are
relevant for understanding phenomena. When interactions are considered,
reductionism becomes limited in several aspects. In this paper, I argue that
interactions imply non-reductionism, non-materialism, non-predictability,
non-Platonism, and non-nihilism. As alternatives to each of these, holism,
informism, adaptation, contextuality, and meaningfulness are put forward,
respectively. A worldview that includes interactions not only describes better
our world, but can help to solve many open scientific, philosophical, and
social problems caused by implications of reductionism.Comment: 12 pages, 2 figure
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