arXiv subjects

G. M. Viswanathan

Publications and source records attributed to G. M. Viswanathan.

33 records · Page 2Linked to original sources

arXiv2014

How to efficiently destroy a network with limited information

We address the general problem of how best to attack and destroy a network by node removal, given limited or no prior information about the edges. We consider a family of strategies in which nodes are randomly chosen, but not removed. Instead, a random acquaintance (i.e., a first neighbour) of the chosen node is removed from the network. By assigning an informal cost to the information about the network structure, we show using cost-benefit analysis that acquaintance removal is the optimal strategy to destroy networks efficiently.

physics.soc-ph↗

arXiv2009

A Solvability criterion for Navier-Stokes equations in high dimensions

We define the Ladyzhenskaya-Lions exponent $α_{\rm {\tiny \sc l}} (n)=({2+n})/4$ for Navier-Stokes equations with dissipation $-(-Δ)^α$ in ${\Bbb R}^n$, for all $n\geq 2$. We review the proof of strong global solvability when $α\geq α_{\rm {\tiny \sc l}} (n)$, given smooth initial data. If the corresponding Euler equations for $n>2$ were to allow uncontrolled growth of the enstrophy ${1\over 2} \|\nabla u \|^2_{L^2}$, then no globally controlled coercive quantity is currently known to exist that can regularize solutions of the Navier-Stokes equations for $α<α_{\rm {\tiny \sc l}} (n)$. The energy is critical under scale transformations only for $α=α_{\rm {\tiny \sc l}} (n)$.

math.AP↗

arXiv2008

Spontaneous symmetry breaking and finite time singularities in $d$-dimensional incompressible flow with fractional dissipation

We investigate the formation of singularities in the incompressible Navier-Stokes equations in $d\geq 2$ dimensions with a fractional Laplacian $|\nabla |^α$. We derive analytically a sufficient but not necessary condition for solutions to remain always smooth and show that finite time singularities cannot form for $α\geq α_c= 1+d/2$. Moreover, initial singularities become unstable for $α>α_c$.

physics.flu-dyn↗

arXiv2008

Universal photocurrent-voltage characteristics of dye sensitized nanocrystalline TiO$_2$ photoelectrochemical cells

We propose a new linearizable model for the nonlinear photocurrent-voltage characteristics of nanocrystalline TiO$_2$ dye sensitized solar cells based on first principles and report predicted values for fill factors. Upon renormalization diverse experimental photocurrent-voltage data collapse onto a single universal function. These advances allow the estimation of the complete current-voltage curve and the fill factor from any three experimental data points, e.g., the open circuit voltage, the short circuit current and one intermediate measurement. The theoretical underpinning provides insight into the physical mechanisms responsible for the remarkably large fill factors as well as their known dependence on the open circuit voltage.

cond-mat.other↗

arXiv2007

Spontaneous symmetry breaking in amnestically induced persistence

We investigate a recently proposed non-Markovian random walk model characterized by loss of memories of the recent past and amnestically induced persistence. We report numerical and analytical results showing the complete phase diagram, consisting of 4 phases, for this system: (i) classical nonpersistence, (ii) classical persistence (iii) log-periodic nonpersistence and (iv) log-periodic persistence driven by negative feedback. The first two phases possess continuous scale invariance symmetry, however log-periodicity breaks this symmetry. Instead, log-periodic motion satisfies discrete scale invariance symmetry, with complex rather than real fractal dimensions. We find for log-periodic persistence evidence not only of statistical but also of geometric self-similarity.

cond-mat.stat-mech↗

arXiv2007

The origin of power-law distributions in deterministic walks: the influence of landscape geometry

We investigate the properties of a deterministic walk, whose locomotion rule is always to travel to the nearest site. Initially the sites are randomly distributed in a closed rectangular ($A/L \times L)$ landscape and, once reached, they become unavailable for future visits. As expected, the walker step lengths present characteristic scales in one ($L \to 0$) and two ($A/L \sim L$) dimensions. However, we find scale invariance for an intermediate geometry, when the landscape is a thin strip-like region. This result is induced geometrically by a dynamical trapping mechanism, leading to a power law distribution for the step lengths. The relevance of our findings in broader contexts -- of both deterministic and random walks -- is also briefly discussed.

cond-mat.dis-nn↗

arXiv2007

Amnestically induced persistence in random walks

We study how the Hurst exponent $α$ depends on the fraction $f$ of the total time $t$ remembered by non-Markovian random walkers that recall only the distant past. We find that otherwise nonpersistent random walkers switch to persistent behavior when inflicted with significant memory loss. Such memory losses induce the probability density function of the walker's position to undergo a transition from Gaussian to non-Gaussian. We interpret these findings of persistence in terms of a breakdown of self-regulation mechanisms and discuss their possible relevance to some of the burdensome behavioral and psychological symptoms of Alzheimer's disease and other dementias.

cond-mat.stat-mech↗

arXiv2006

Forecasting extreme events in collective dynamics: an analytic signal approach to detecting discrete scale invariance

A challenging problem in physics concerns the possibility of forecasting rare but extreme phenomena such as large earthquakes, financial market crashes, and material rupture. A promising line of research involves the early detection of precursory log-periodic oscillations to help forecast extreme events in collective phenomena where discrete scale invariance plays an important role. Here I investigate two distinct approaches towards the general problem of how to detect log-periodic oscillations in arbitrary time series without prior knowledge of the location of the moveable singularity. I first show that the problem has a definite solution in Fourier space, however the technique involved requires an unrealistically large signal to noise ratio. I then show that the quadrature signal obtained via analytic continuation onto the imaginary axis, using the Hilbert transform, necessarily retains the log-periodicities found in the original signal. This finding allows the development of a new method of detecting log-periodic oscillations that relies on calculation of the instantaneous phase of the analytic signal. I illustrate the method by applying it to the well documented stock market crash of 1987. Finally, I discuss the relevance of these findings for parametric rather than nonparametric estimation of critical times.

physics.data-an↗

arXiv2003

Variance fluctuations in nonstationary time series: a comparative study of music genres

An important problem in physics concerns the analysis of audio time series generated by transduced acoustic phenomena. Here, we develop a new method to quantify the scaling properties of the local variance of nonstationary time series. We apply this technique to analyze audio signals obtained from selected genres of music. We find quantitative differences in the correlation properties of high art music, popular music, and dance music. We discuss the relevance of these objective findings in relation to the subjective experience of music.

cond-mat.dis-nn↗

arXiv2003

Critical behavior of an epidemic model of drug resistant diseases

In this work, we study the critical behavior of an epidemic propagation model that considers individuals that can develop drug resistance. In our lattice model, each site can be found in one of four states: empty, healthy, normally infected (not drug resistant) and strain infected (drug resistant) states. The most relevant parameters in our model are related to the mortality, cure and mutation rates. This model presents two distinct stationary active phases: a phase with co-existing normal and drug resistant infected individuals and an intermediate active phase with only drug resistant individuals. We employ a finite-size scaling analysis to compute the critical points the critical exponents ratio $β/ν$ governing the phase-transitions between these active states and the absorbing inactive state. Our results are consistent with the hypothesis that these transitions belong to the directed percolation universality class.

cond-mat.dis-nn↗

arXiv2002

The origin of fat tailed distributions in financial time series

A classic problem in physics is the origin of fat tailed distributions generated by complex systems. We study the distributions of stock returns measured over different time lags $τ.$ We find that destroying all correlations without changing the $τ= 1$ d distribution, by shuffling the order of the daily returns, causes the fat tails almost to vanish for $τ>1$ d. We argue that the fat tails are caused by known long-range volatility correlations. Indeed, destroying only sign correlations, by shuffling the order of only the signs (but not the absolute values) of the daily returns, allows the fat tails to persist for $τ>1$ d.

cond-mat.dis-nn↗

arXiv2002

Kinematics of stock prices

We investigate the general problem of how to model the kinematics of stock prices without considering the dynamical causes of motion. We propose a stochastic process with long-range correlated absolute returns. We find that the model is able to reproduce the experimentally observed clustering, power law memory, fat tails and multifractality of real financial time series. We find that the distribution of stock returns is approximated by a Gaussian with log-normally distributed local variance and shows excellent agreement with the behavior of the NYSE index for a range of time scales.

cond-mat.dis-nn↗

arXiv2001

Average Time Spent by Levy Flights and Walks on an Interval with Absorbing Boundaries

We consider a Levy flyer of order alpha that starts from a point x0 on an interval [O,L] with absorbing boundaries. We find a closed-form expression for the average number of flights the flyer takes and the total length of the flights it travels before it is absorbed. These two quantities are equivalent to the mean first passage times for Levy flights and Levy walks, respectively. Using fractional differential equations with a Riesz kernel, we find exact analytical expressions for both quantities in the continuous limit. We show that numerical solutions for the discrete Levy processes converge to the continuous approximations in all cases except the case of alpha approaching 2 and the cases of x0 near absorbing boundaries. For alpha larger than 2 when the second moment of the flight length distribution exists, our result is replaced by known results of classical diffusion. We show that if x0 is placed in the vicinity of absorbing boundaries, the average total length has a minimum at alpha=1, corresponding to the Cauchy distribution. We discuss the relevance of this result to the problem of foraging, which has received recent attention in the statistical physics literature.

cond-mat.soft↗

arXiv2000

The Strange Behavior of Critical Branched Polymers

We find that 2-dimensional (2-D) critical branched polymers with no impurities conclusively belong to the same universality class as 2-D random percolation clusters, although pure critical 3-D branched polymers do not belong to the 3-D percolation universality class. We find, moreover, that the fractal dimension of critical branched polymers in 2-D is independent of the presence of a random environment, and explore possible explanations for these strange results. We also report that when there are no impurities the critical branching probability in 3-D is bc=3.34e-4 +- 0.16e-4.

cond-mat.stat-mech↗

arXiv2000

Quantifying Nonstationary Radioactivity Concentration Fluctuations Near Chernobyl: A Complete Statistical Description

We analyze nonstationary $^{137}$Cs atmospheric activity concentration fluctuations measured near Chernobyl after the 1986 disaster and find three new results: (i) the histogram of fluctuations is well described by a log-normal distribution, (ii) there is a pronounced spectral component with period T=1 y, and (iii) the fluctuations are long-range correlated. These findings allow us to quantify two fundamental statistical properties of the data - the probability distribution and the correlation properties of the time series. We interpret our findings as evidence that the atmospheric radionuclide resuspension processes are tightly coupled to the surrounding ecosystems and to large time scale weather patterns.

cond-mat.stat-mech↗