the global well posedness and global attractor for the solutions to the 2d boussinesq system with variable viscosity and thermal diffusivity abstract global well posedness of strong solutions and existence of the global attractor to the initial and boundary value problem of 2d boussinesq system in a periodic channel with non homogeneous boundary conditions for the temperature and viscosity and thermal diffusivity depending on the temperature are proved

experimental evidence of stochastic resonance without tuning due to non gaussian noises in order to test theoretical predictions we have studied the phenomenon of stochastic resonance in an electronic experimental system driven by white non gaussian noise in agreement with the theoretical predictions our main findings are an enhancement of the sensibility of the system together with a remarkable widening of the response robustness this implies that even a single resonant unit can reach a marked reduction in the need for noise tuning

spatio temporal patterns in population dynamics abstract the transient dynamics of interacting biological species extracted from two ecosystems is investigated we model the environment interaction by a multiplicative noise and the temperature oscillations by a periodic forcing we find noise induced effects such as enhanced temporal oscillations spatial patterns and noise delayed extinction for the model of two competing species we extend our analysis to an ecosystem of three interacting species namely one predator and two preys we find spatial patterns induced by the noise

mechanism of stochastic resonance enhancement in neuronal models driven by 1 f noise noise can assist neurons in the detection of weak signals via a mechanism known as stochastic resonance sr in a previous study phys lett a 243 281 1998 we showed that when colored noise with 1 f ensuremath beta spectrum is added to the fitzhugh nagumo fhn neuronal model the optimal noise variance for sr could be minimized with ensuremath beta ensuremath approx 1 in this study we investigate analytically how the noise color ensuremath beta affects the sr profile in a linearized version of the fhn model we demonstrate that the aforementioned effect of 1 f noise is related to the dynamical characteristics of the model neuron i e the refractory period the low pass filtering effect of the membrane capacitance and the high pass filtering effect of the recovery variable

theoretical study of a benard marangoni problem abstract in this paper we prove the existence of strong solutions for the stationary benard marangoni problem in a finite domain flat on the top bifurcating from the basic heat conductive state the benard marangoni problem is a physical phenomenon of thermal convection in which the effects of buoyancy and surface tension are taken into account this problem is modelled with a system of partial differential equations of the type navier stokes and heat equation the boundary conditions include crossed boundary conditions involving tangential derivatives of the temperature and normal derivatives of the velocity field to define tangential derivatives at the boundary intended in the trace sense it is necessary order two derivatives in the interior of the domain and thus the boundary term contains as high derivatives as the interior term we overcome this difficulty by considering the weak formulation and transforming the boundary integral into an equivalent integral defined in the whole domain this allows us to reformulate the weak problem with a temperature having only order one weak derivatives concerning regularity results we obtain strong solutions for the stationary benard marangoni problem

analog study of the first passage time problem driven by power law distributed noise abstract in this work we develop an analog circuit to generate a stochastic signal with stationary distribution exhibiting a tunable power law tail the proposed circuit design is a variant of a recently introduced one based on a differential equation with both multiplicative and additive noises here the circuit is carefully designed in order to ensure that all components operate within their specific regimes we provide a detailed characterization of the output signal including the power law exponent dependence on the tunable component we apply the present circuit to study the first passage time problem in a simple integrate fire model of neural dynamics driven by a non gaussian noise

indication of multiscaling in the volatility return intervals of stock markets a certain trend with the mean interval we generate surrogate records using the schreiber method and find that their cumulative distributions almost collapse to a single curve and moments are almost constant for most ranges of those substantial differences suggest that nonlinear correlations in the original volatility sequence account for the deviations from a single scaling law we also find that the original and surrogate records exhibit slight tendencies for short and long due to the discreteness and finite size effects of the records respectively to avoid as possible those effects for testing the multiscaling behavior we investigate the moments in the range 10100 and find that the exponent from the power law fitting m has a narrow distribution around 0 which depends on m for the 500 stocks the distribution of for the surrogate records are very narrow and centered around 0 this suggests that the return interval distribution exhibits multiscaling behavior due to the nonlinear correlations in the original volatility

the behavior of the life span for solutions tout δu a x upinrd abstract let t denote the life span of the positive bounded solution u x t to the equation u t u a u u p in r d and u x 0 x where 0 a x c r d 0 x c b r d p 1 and 0 is a parameter depending on a p and d it is possible that t for 0 sufficiently small or that t 0 in which case lim 0 t it is always true that lim t 0 in this paper we investigate the asymptotic behavior of t as 0 in the case that t 0 and as in all cases the asymptotic order depends heavily on a p and d in the case that 0 whereas in the case that it depends only on whether there exists an x 0 with a x 0 x 0 0 or whether the supports of a and are separated by a positive distance

statistical analysis of 5 s index data of the budapest stock exchange abstract a statistical analysis of the budapest stock index bux is presented the high time resolution 5 s sampling makes it possible to extract information on market functioning which does not emerge from daily data the main results are as follows from a statistical point of view the large drop in october 1997 was a normal event strong autocorrelation has been detected in the volatility and market activity data detrended fluctuation analysis reveals superdiffusive scaling without persistence finally we report on a simple method for mapping local trends to represent sequences in order to obtain pattern statistics

time periodic solutions for a generalized boussinesq model with neumann boundary conditions for temperature the aim of this work is to prove the existence of regular time periodic solutions for a generalized boussinesq model with nonlinear diffusion for the equations of velocity and temperature the ma

error estimates of finite element methods for nonstationary thermal convection problems with temperature dependent coefficients general error estimates are proved for a class of finite element schemes for nonstationary thermal convection problems with temperature dependent coefficients these variable coefficients turn the diffusion and the buoyancy terms to be nonlinear which increases the nonlinearity of the problems an argument based on the energy method leads to optimal error estimates for the velocity and the temperature without any stability conditions error estimates are also provided for schemes modified by approximate coefficients which are used conveniently in practical computations

life span of solutions for a semilinear parabolic problem with small diffusion abstract this paper is concerned with the initial boundary value problem formula where p 1 e 0 is a bounded domain in rn and is a continuous function on it is shown that the blowup time t e of the solution of this problem satisfies t e 1 p 1 1 p as e 0 moreover when the maximum of x is attained at one point we determine the higher order term of t e which reflects the pointedness of the peak of the proof is based on a careful construction of super and subsolutions

statistical properties of deterministic threshold elements the case of market price abstract we analyze statistical properties of a set of deterministic threshold elements which is introduced as a model for the stock market the macroscopic variable of the stock market price shows seemingly stochastic fluctuation with a f 2 power spectrum consistent with real economic fluctuations the maximum lyapunov exponent is estimated to be zero indicating that the system is at the edge of chaos

life span of solutions with large initial data for a semilinear parabolic system we investigate the initial boundary value problem ut u vpin 0 t vt v uqin 0 t u x t v x t 0on 0 t u x 0 x v x 0 x in where p q 1 and pq 1 is a bounded domain in rn with a smooth boundary 0 is a parameter x and x are nonnegative continuous functions on we show that the life span or blow up time of the solution of this problem approaches the life span of the solution of the ode system obtained when dropping the diffusion terms as the proof is based on the comparison principle and kaplan s method

life span of solutions with large initial data for a superlinear heat equation abstract we investigate the initial boundary problem u t u f u in 0 u 0 on 0 u x 0 x in where is a bounded domain in r n with a smooth boundary 0 x is a nonnegative continuous function on f u is a nonnegative superlinear continuous function on 0 we show that the life span or blow up time of the solution of this problem denoted by t satisfies t d u f u h o t as moreover when the maximum of is attained at a finite number of points in we can determine the higher order term of t which depends on the minimal value of at the maximal points of the proof is based on a careful construction of a supersolution and a subsolution

stochastic resonance in neuron models periodically stimulated sensory neurons typically exhibit a kind of statistical phase locking to the stimulus they tend to fire at a preferred phase of the stimulus cycle but not at every cycle hence the histogram of interspike intervals isih i e of times between successive firings is multimodal for these neurons with peaks centered at integer multiples of the driving period a particular kind of residence time histogram for a large class of noisy bistable systems has recently been shown to exhibit the major features of the neural data in the present paper we show that an excitable cell model the fitzhugh nagumo equations also reproduces these features when driven by additive periodic and stochastic forces this model exhibits its own brand of stochastic resonance as the peaks of the isih successively go through a maximum when the noise intensity is increased further the presence of a noise induced limit cycle introduces a third time scale in the problem this limit cycle is found to modify qualitatively the phase locking picture e g by suppressing certain peaks in the isih finally the role of noise and possibly of stochastic resonance sr in the neural encoding of sensory information is discussed

econophysics scaling and its breakdown in finance we discuss recent empirical results obtained by analyzing high frequency data of a stock market index the standard and poor s 500 we focus on the scaling properties and on its breakdown of the index dynamics a simple stochastic model the truncated levy flight is illustrated successes and limitations of this model are presented a discussion about similarities and differences between the scaling properties observed in financial markets and in fully developed turbulence is also provided

local well posedness for boussinesq approximation with shear dependent viscosities in 3d in this paper we prove the existence and uniqueness of regular weak solutions for a nonlinear boussinesq system in a small time interval the viscosity is assumed to be with a p structure depending on the shear rate we mainly work on 3d case with periodic boundary and initial value conditions the w 2 p type regularity for velocity and h 2 type regularity for temperature were obtained for 7 5 p 2

long time behavior of the two dimensional boussinesq equations without buoyancy diffusion abstract we study the global well posedness and stability instability of perturbations near a special type of hydrostatic equilibrium associated with the 2d boussinesq equations without buoyancy a k a thermal diffusion on a bounded domain subject to stress free boundary conditions the boundary of the domain is not necessarily smooth and may have corners such as in the case of rectangles we achieve three goals first we establish the global in time existence and uniqueness of large amplitude classical solutions efforts are made to reduce the regularity assumptions on the initial data second we obtain the large time asymptotics of the full nonlinear perturbation in particular we show that the kinetic energy and the first order derivatives of the velocity field converge to zero as time goes to infinity regardless of the magnitude of the initial data and the flow stratifies in the vertical direction in a weak topology third we prove the linear stability of the hydrostatic equilibrium t y satisfying t y 0 and the linear instability of periodic perturbations when t y 0 numerical simulations are supplemented to corroborate the analytical results and predict some phenomena that are not proved the authors are pleased to dedicate this paper to professor edriss saleh titi on the occasion of his 60th birthday professor titi s myriad research contributions including contributions to the problem constituting the focus of this work and leadership in the mathematical fluid dynamics community serve as an inspiration to his students collaborators and colleagues

on coupled navier stokes and energy equations in exterior like domains we investigate a class of nonlinear evolution systems modeling time dependent flows of incompressible viscous and heat conducting fluids with temperature dependent transport coefficients in three dimensional exterior like domains we prove a local existence theorem for the fully coupled parabolic system with a source term involving the square of the velocity gradient and a combination of dirichlet and artificial boundary conditions

self modulation processes and resulting generic 1 f fluctuations we analyze high precision data of transaction intervals in a foreign exchange market and show that it is nicely approximated by a non stationary poisson process whose expectation value is given by a moving average of its own trace generalizing this result we introduce novel stochastic processes called the self modulation processes by the self modulation effect clustering occurs automatically resulting in fat tailed interval distributions including the zipf s law in an extreme case we prove rigorously that the corresponding power spectrum follows the 1 f spectrum

life span of positive solutions for a semilinear heat equation with general non decaying initial data abstract we prove upper bounds on the life span of positive solutions for a semilinear heat equation for non decaying initial data it is well known that the solutions blow up in finite time we give two types estimates of the life span in terms of the limiting values of the initial data in space

dynamic numerical models of stock market price from microscopic determinism to macroscopic randomness abstract a variant of threshold dynamics is introduced to model the behaviors of a large assembly of dealers in a stock market although the microscopic evolution dynamics is deterministic the collective behaviors such as market prices show seemingly stochastic fluctuations the statistical properties of market price change can be well approximated by a simple discrete langevin type equation with random amplification the macroscopic stochastic equation is solved both numerically and analytically showing that the market price change generally follow power law distributions in the steady state the reason for the appearance of rapid decay in the distribution tails are discussed

stochastic bifurcation for a tumor immune system with symmetric levy noise abstract in this paper we investigate stochastic bifurcation for a tumor immune system in the presence of a symmetric non gaussian levy noise stationary probability density functions will be numerically obtained to define stochastic bifurcation via the criteria of its qualitative change and bifurcation diagram at parameter plane is presented to illustrate the bifurcation analysis versus noise intensity and stability index the effects of both noise intensity and stability index on the average tumor population are also analyzed by simulation calculation we find that stochastic dynamics induced by gaussian and non gaussian levy noises are quite different

stock market dynamics and turbulence parallel analysis of fluctuation phenomena abstract we report analogies and differences between the fluctuations in an economic index and the fluctuations in velocity of a fluid in a fully turbulent state specifically we systematically compare i the statistical properties of the s p 500 cash index recorded during the period january 84 december 89 with ii the statistical properties of the velocity of turbulent air measured in the atmospheric surface layer about 6 m above a wheat canopy in the connecticut agricultural research station we find non gaussian statistics and intermittency for both processes i and ii but the deviation from a gaussian probability density function are different for stock market dynamics and turbulence

life span and a new critical exponent for a degenerate parabolic equation abstract in this paper we consider the positive solution of the cauchy problem for the equation u t u p u u q p 1 q 1 and give a secondary critical exponent of the behavior of initial value at infinity for the existence of global and nonglobal solutions of the cauchy problem furthermore the life span of solutions are also studied

a hierarchical model of financial crashes abstract we follow up our previous conjecture that large stock market crashes are analogous to critical points in statistical physics the term critical refers to regimes of cooperative behavior such as magnetism at the curie temperature and liquid gas transitions and is characterized by the singular mathematical behavior of relevant observables to illustrate the concept of criticality we present a simple hierarchical model of traders exhibiting crowd behavior and show that it has a well defined critical point whose mathematical signature is a power law dependence of the price modulated by log periodic structures as recently found in market data by several independent groups

self similar subsolutions and blow up for nonlinear parabolic equations abstract for a wide class of nonlinear parabolic equations of the form u t u f u u we give finite time blow up results for large initial data blow up time estimates are also provided these results rely on a new method of comparison with suitable blowing up self similar subsolutions as a consequence we improve several known results on reaction diffusion equations on generalized burgers equations and on the equation of chipot and weissler this method can also apply to degenerate equations of porous medium type and provides a unified treatment for a large class of problems both semilinear and quasilinear

scaling behavior in economics the problem of quantifying company growth inspired by work of both widom and mandelbrot we analyze the computstat database comprising all publicly traded united states manufacturing companies in the years 1974 1993 we find that the distribution of company size remains stable for the 20 years we study i e the mean value and standard deviation remain approximately constant we study the distribution of sizes of the new companies in each year and find it to be well approximated by a log normal we find i the distribution of the logarithm of the growth rates for a fixed growth period of t years and for companies with approximately the same size s displays an exponential tent shaped form rather than the bell shaped gaussian one would expect for a log normal distribution and ii the fluctuations in the growth rates measured by the width of this distribution t decrease with company size and increase with time t we find that for annual growth rates t 1 t s and that the exponent takes the same value within the error bars for several measures of the size of a company in particular we obtain 0 20 0 03 for sales 0 18 0 03 for number of employees 0 18 0 03 for assets 0 18 0 03 for cost of goods sold and 0 20 0 03 for propert plant and equipment we propose models that may lead to some insight into these phenomena first we study a model in which the growth rate of a company is affected by a tendency to retain an optimal size that model leads to an exponential distribution of the logarithm of growth rate in agreement with the empirical results then we study a hierarchical tree like model of a company that enables us to relate to parameters of a company structure we find that 1n 1nz where z defines the mean branching ratio of the hierarchical tree and is the probability that the lower levels follow the policy of higher levels in the hierarchy we also study the output distribution of growth rates of this hierarchical model we find that the distribution is consistent with the exponential form found empirically we also discuss the time dependence of the shape of the distribution of the growth rates

enhancement of stochastic resonance the role of non gaussian noises abstract we have analyzed the phenomenon of stochastic resonance in a double well potential driven by a colored non gaussian noise using a path integral approach we have obtained a consistent markovian approximation that enables us to get through the two state theory analytical expressions for the signal to noise ratio finding an enhancement of this quantity when the system departs from gaussian behavior this finding is supported by extensive numerical simulations we discuss the relation of these results to some experiments in sensory systems

statistical analysis of the overnight and daytime return we investigate the two components of the total daily return close to close the overnight return close to open and the daytime return open to close as well as the corresponding volatilities of the 2215 new york stock exchange stocks for the 20 year period from 1988 to 2007 the tail distribution of the volatility the long term memory in the sequence and the cross correlation between different returns are analyzed our results suggest that i the two component returns and volatilities have features similar to that of the total return and volatility the tail distribution follows a power law for all volatilities and long term correlations exist in the volatility sequences but not in the return sequences ii the daytime return contributes more to the total return both the tail distribution and the long term memory of the daytime volatility are more similar to that of the total volatility compared to the overnight records in addition the cross correlation between the daytime return and the total return is also stronger iii the two component returns tend to be anticorrelated moreover we find that the cross correlations between the three different returns total overnight and daytime are quite stable over the entire 20 year period

thermal convection in a cylindrical annulus heated laterally in this paper we study thermoconvective instabilities appearing in a fluid within a cylindrical annulus heated laterally as soon as a horizontal temperature gradient is applied a convective state appears as the temperature gradient reaches a critical value a stationary or oscillatory bifurcation takes place the problem is modelled with a novel method which extends the one described in herrero and mancho herrero h and mancho a m 2001 int j numer methods fluids preprint math ap 0109200 the navier stokes equation is solved in the primitive variable formulation with appropriate boundary conditions for pressure this is a low order formulation which in cylindrical coordinates introduces lower order singularities the problem is discretized with a chebyshev collocation method easily implemented and its convergence has been checked the results obtained are not only in very good agreement with those obtained in experiments but also provide a deeper insight into important physical parameters developing the instability which has not been reported before

life span of solutions for a semilinear heat equation with initial data having positive limit inferior at infinity abstract we present a new upper bound of the life span of positive solutions of a semilinear heat equation for initial data having positive limit inferior at space infinity the upper bound is expressed by the data in limit inferior not in every direction but around a specific direction it is also shown that the minimal time blow up occurs when initial data attains its maximum at space infinity

global regularity for the initial value problem of a 2 d kazhikhov smagulov type model abstract we prove global in time existence of regular solution to the initial value problem of a 2 d kazhikhov smagulov type model for incompressible nonhomogeneous fluids with mass diffusion

multiplicative processes and power laws takayasu sato and takayasu phys rev lett 79 966 1997 revisited the question of stochastic processes with multiplicative noise which have been studied in several different contexts over the past decades we focus on the regime found for a generic set of control parameters in which stochastic processes with multiplicative noise produce intermittency of a special kind characterized by a power law probability density distribution we briefly explain the physical mechanism leading to a power law probability distribution function and provide a list of references for these results dating back from a quarter of century we explain how the formulation in terms of the characteristic function developed by takayasu sato and takayasu can be extended to exponents ensuremath mu g2 which explains the reason for the lucky coincidence the multidimensional generalization of the results of takayasu sato and takayasu and the present status of the problem are briefly summarized the discovery of stretched exponential tails in the presence of the cutoff introduced by takayasu sato and takayasu is explained theoretically we end by briefly listing applications

stationary solutions for generalized boussinesq models abstract we study the existence regularity and conditions for uniqueness of solutions of a generalized boussinesq model for thermally driven convection the model allows temperature dependent viscosity and thermal conductivity

non gaussian noise weakened stability in a foraging colony system with time delay abstract in this paper the dynamical properties in a foraging colony system with time delay and non gaussian noise were investigated using delay fokker planck approach the stationary probability distribution spd the associated relaxation time art and normalization correlation function ncf are obtained respectively the results show that i the time delay and non gaussian noise can induce transition from a single peak to double peaks in the spd i e a type of bistability occurring in a foraging colony system where time delay and non gaussian noise not only cause transitions between stable states but also construct the states themselves numerical simulations are presented and are in good agreement with the approximate theoretical results ii there exists a maximum in the art as a function of the noise intensity this maximum for art is identified as the characteristic of the non gaussian noise weakened stability of the foraging colonies in the steady state iii the art as a function of the noise correlation time exhibits a maximum and a minimum where the minimum for art is identified as the signature of the non gaussian noise enhanced stability of the foraging colonies and iv the time delay can enhance the stability of the foraging colonies in the steady state while the departure from gaussian noise can weaken it namely the time delay and departure from gaussian noise play opposite roles in art or ncf

a semilinear pseudo parabolic equation with initial data non rarefied at abstract in this paper we study the cauchy problem for a semilinear pseudo parabolic equation with initial data non rarefied at our interest lies in the discussion of the effect of the non rarefied factors on the bow up phenomenon and the life span of the solution

life span and a new critical exponent for a doubly degenerate parabolic equation with slow decay initial values abstract in this paper we investigate the behavior of the positive solution of the following cauchy problem u t div u m p 2 u m u q with initial value decaying at infinity and give a new secondary critical exponent for the existence of global and nonglobal solutions furthermore the large time behavior and the life span of solutions are also studied

global regularity for the initial boundary value problem of the 2 d boussinesq system with variable viscosity and thermal diffusivity abstract we prove the global existence of strong solution to the initial boundary value problem of the 2 d boussinesq system and 3 d infinite prandtl number model with viscosity and thermal conductivity depending on the temperature

levy walks and enhanced diffusion in milan stock exchange abstract we perform statistical analyses of the general and sectorial historical m i b indices of the milan stock exchange our analyses show that the price indices have statistical properties which are compatible with a levy random walk the time evolution of the daily variations of indices is intermittent on a time scale of years and the variance of almost all indices displays a superdiffusive behavior by using the theory of enhanced diffusion in levy walks as theoretical framework we ascribe the superdiffusive behavior to a nonlocal memory coupling price and time

scaling and correlation in financial time series we discuss the results of three recent phenomenological studies focussed on understanding the distinctive statistical properties of nancial time series i the probability distribution of stock price uctuations stock price uctuations occur in all magnitudes in analogy to earthquakes from tiny uctuations to very drastic events such as the crash of 19 october 1987 sometimes referred to as black monday the distribution of price uctuations decays with a power law tail well outside the levy stable regime and describes uctuations that dier by as much as 8 orders of magnitude in addition this distribution preserves its functional form for uctuations on time scales that dier by 3 orders of magnitude from 1 min up to approximately 10 days ii correlations in nancial time series while price uctuations themselves have rapidly decaying correlations the magnitude of uctuations measured by either the absolute value or the square of the price uctuations has correlations that decay as a power law persisting for several months iii volatility and trading activity we quantify the relation between trading activity measured by the number of transactions nt and the price change gt for a given stock over a time interval t t t we nd that nt displays long range power law correlations in time which leads to the interpretation that the long range correlations previously found for jgtj are connected to those of nt c 2000 elsevier science b v all rights reserved

effective markovian approximation for non gaussian noises a path integral approach abstract we have analyzed diffusion in a double well potential driven by a colored non gaussian noise using a path integral approach we have obtained a consistent markovian approximation to the initially non markovian problem such an approximation allows us to get analytical expressions for the mean first passage time that has been tested against extensive numerical simulations

self similar subsolutions and blowup for nonlinear parabolic equations abstract for a wide class of nonlinear parabolic equations of the formut u f u u we prove the nonexistence of global solutions for large initial data we also estimate the maximal existence time to do so we use a method of comparison with suitable blowing up self similar subsolutions as a consequence we improve several known results onut u up on generalized burgers equations and on other semilinear equations this method can also apply to degenerate equations of porous medium type and provides a unified treatment for a large class of problems both semilinear and quasilinear

coherence enhancement in nonlinear systems subject to multiplicative ornstein uhlenbeck noise we show that for two biologically relevant models with self sustained oscillations under the action of a multiplicative ornstein uhlenbeck process their coherence response behaves nonmonotonically with the process correlation time there is a correlation time for which the quality factor is optimized this phenomenon is a consequence of the interplay between the correlation time and the system s periodicity this relation is evidenced through a power law relation with an exponent close to 1 2

the vanishing diffusivity limit for the 2 d boussinesq equations with boundary effect abstract in this paper we tackle the issue of the vanishing diffusivity limit of the 2 d incompressible boussinesq equations in the half plane our main purpose is to study the boundary layer effect and the convergence rates as the thermal diffusion parameter goes to zero under the homogeneous dirichlet boundary condition of velocity and the nonhomogeneous dirichlet boundary condition in the x direction for temperature we show that the boundary layer thickness is of the order o with 0 2 3 in contrast with jiang et al 2011 the bl thickness we got is thinner than that in jiang et al 2011 moreover we prove that as diffusivity tends to zero the solutions of the fully viscous equations converge strongly to those of zero diffusion equations we also obtain the convergence rates of the vanishing diffusivity limit

on the existence and uniqueness of the stationary solution to equations of natural convection with boundary data in l2 this paper deals with the existence and uniqueness of a stationary solution to the boussinesq system with no regular data on the boundary we introduce very weak solutions and we prove their existence using more hypotheses on the problem data we prove the continuous dependence and uniqueness for this class of solutions

on the blowup criteria and global regularity for the non diffusive boussinesq equations with temperature dependent viscosity coefficient abstract in this paper we consider the boussinesq equations with temperature dependent viscosity and zero thermal diffusivity a blowup criterion of classical solution depending only on l q 0 t l p with p 2 and 1 p 1 q 1 2 is obtained for the two dimensional equations this is in particular consistent with the results in chae 2006 hou and li 2005 lai et al 2011 where the global regularity of the 2d non diffusive boussinesq equations with constant viscosity coefficient i e const was proved a serrin s type blowup criterion depending on u l s 0 t l r l q 0 t l p with r p 3 3 r 2 s 1 and 3 p 2 q 1 is obtained for the three dimensional case we also study the global regularity with large data for the two dimensional equations in a non divergence form

global well posedness for the 2d boussinesq equations with zero viscosity we prove the global well posedness of the two dimensional boussinesq equations with zero viscosity and positive diffusivity in bounded domains for rough initial data u0 l2 curlu0 l and 0 bq p2 2 p with p 1 q 2 our method is based on the maximal regularity for heat equation

blow up set for a semilinear heat equation with small diffusion abstract we consider the blow up problem for a semilinear heat equation t u u u p in 0 t u x t 0 on 0 t if u x 0 x 0 in where is a domain in r n n 1 0 p 1 and t 0 in this paper under suitable assumptions on we prove that if the family of the solutions u satisfies a uniform type i blow up estimate with respect to then the solution u blows up only near the maximum points of the initial datum for any sufficiently small 0 this is proved without any conditions on the exponent p and the domain such as n 2 p n 2 and the convexity of the domain

econophysics financial time series from a statistical physics point of view in recent years physicists have started applying concepts and methods of statistical physics to study economic problems the word econophysics is sometimes used to refer to this work much recent work is focused on understanding the statistical properties of nancial time series one reason for this interest is that nancial markets are examples of complex interacting systems for which a huge amount of data exist and it is possible that nancial time series viewed from a dierent perspective might yield new results this article reviews the results of three recent phenomenological studies i the probability distribution of stock price uctuations stock price uctuations occur in all magnitudes in analogy to earthquakes from tiny uctuations to drastic events such as market crashes the distribution of price uctuations decays with a power law tail well outside the levy stable regime and describes uctuations that dier by as much as eight orders of magnitude in addition this distribution preserves its functional form for uctuations on time scales that dier by three orders of magnitude from 1 min up to approximately 10 d ii correlations in nancial time series while price uctuations themselves have rapidly decaying correlations the magnitude of uctuations measured by either the absolute value or the square of the price uctuations has correlations that decay as a power law and persist for several months iii correlations among dierent companies the third result bears on the application of random matrix theory to understand the correlations among price uctuations of any two dierent stocks from a study of the eigenvalue statistics of the cross correlation matrix constructed from price uctuations of the leading 1000 stocks we nd that the largest 1 of the eigenvalues and the corresponding eigenvectors show systematic deviations from the predictions for a random matrix whereas the rest of the eigenvalues conform to random matrix behavior suggesting that these 1 of the eigenvalues contain system specic information about correlated time evolution of dierent companies c 2000 published by elsevier science b v all rights reserved

uniform regularity for the 2d boussinesq system with a slip boundary condition abstract we prove a global in time regularity which is uniform in the vanishing viscosity limit for the 2d boussinesq system in a domain 0 1 with a slip boundary condition

simple stochastic order book model of swarm behavior in continuous double auction abstract in this study we present a simple stochastic order book model for investors swarm behaviors seen in the continuous double auction mechanism which is employed by major global exchanges our study shows a characteristic called fat tail seen in the data obtained from our model that incorporates the investors swarm behaviors our model captures two swarm behaviors one is investors behavior to follow a trend in the historical price movement and another is investors behavior to send orders that contradict a trend in the historical price movement in order to capture the features of influence by the swarm behaviors from price data derived from our simulations using these models we analyzed the price movement range that is how much the price is moved when it is continuously moved in a single direction depending on the type of swarm behavior we saw a difference in the cumulative frequency distribution of this price movement range in particular for the model of investors who followed a trend in the historical price movement we saw the power law in the tail of the cumulative frequency distribution of this price movement range in addition we analyzed the shape of the tail of the cumulative frequency distribution the result demonstrated that one of the reasons the trend following of price occurs is that orders temporarily swarm on the order book in accordance with past price trends

stochastic resonance reverse resonance and resonant activation induced by a multi state noise abstract in this paper we investigate the periodic response for a linear system driven by a multiplicative multi state noise which is composed of the multiplication of two dichotomous noises to an input temporal oscillatory signal and the escape of brownian particles over the fluctuating potential barrier for a system with a piece wise linear potential and driven by an additive multi state noise which is also composed of the multiplication of two dichotomous noises for the first system we get the stochastic resonance phenomenon for the amplitude of the periodic response vs the two dichotomous noise strengths and the phenomenon of reverse resonance for the amplitude of the periodic response vs k which represents the asymmetry degree of the dichotomous noises for the second system we obtain the resonant activation phenomenon for which the mean first passage time of the brownian particles over the fluctuating potential barrier shows a minimum as the function of the transition rates of the multi state noise

blowup stability of solutions of the nonlinear heat equation with a large life span abstract we study the cauchy problem for the nonlinear heat equation u t u u p 1 u in r n the initial data is of the form u 0 where c 0 r n is fixed and 0 we first take 1 p p f where p f is the fujita critical exponent and c 0 r n l 1 r n with nonzero mean we show that u t blows up for small extending the h fujita blowup result for sign changing solutions next we consider 1 p p s where p s is the sobolev critical exponent and x decaying as x at infinity where p 1 2 we also prove that u t blows up when is small extending a result of t lee and w ni for both cases the solution enjoys some stable blowup properties for example there is single point blowup even if is not radial

second critical exponent and life span for pseudo parabolic equation this paper studies the second critical exponent and life span of solutions for the pseudo parabolic equation ut k ut u up in rn 0 t with p 1 k 0 it is proved that the second critical exponent i e the decay order of the initial data required by global solutions in the coexistence region of global and non global solutions is independent of the pseudo parabolic parameter k nevertheless it is revealed that the viscous term k ut relaxes restrictions on the amplitude of the initial data required by the global solutions moreover it is observed that the life span of the non global solutions will be delayed by the third order viscous term finally some numerical examples are given to illustrate all these results

global well posedness for the 2 d boussinesq system with the temperature dependent viscosity and thermal diffusivity abstract we prove the global well posedness for the 2 d boussinesq system with the temperature dependent viscosity and thermal diffusivity

kinetic theory for financial brownian motion from microscopic dynamics recent technological development has enabled researchers to study social phenomena scientifically in detail and financial markets has particularly attracted physicists since the brownian motion has played the key role as in physics in our previous report arxiv 1703 06739 to appear in phys rev lett we have presented a microscopic model of trend following high frequency traders hfts and its theoretical relation to the dynamics of financial brownian motion directly supported by a data analysis of tracking trajectories of individual hfts in a financial market here we show the mathematical foundation for the hft model paralleling to the traditional kinetic theory in statistical physics we first derive the time evolution equation for the phase space distribution for the hft model exactly which corresponds to the liouville equation in conventional analytical mechanics by a systematic reduction of the liouville equation for the hft model the bogoliubov born green kirkwood yvon hierarchal equations are derived for financial brownian motion we then derive the boltzmann like and langevin like equations for the order book and the price dynamics by making the assumption of molecular chaos the qualitative behavior of the model is asymptotically studied by solving the boltzmann like and langevin like equations for the large number of hfts which is numerically validated through the monte carlo simulation our kinetic description highlights the parallel mathematical structure between the financial brownian motion and the physical brownian motion

asymptotic power law of moments in a random multiplicative process with weak additive noise it is well known that a random multiplicative process with weak additive noise generates a power law probability distribution it has recently been recognized that this process exhibits another type of power law the moment of the stochastic variable scales as a function of the additive noise strength we clarify the mechanism for this power law behavior of moments by treating a simple langevin type model both approximately and exactly and argue this mechanism is universal we also discuss the relevance of our findings to noisy on off intermittency and to singular spatio temporal chaos recently observed in systems of non locally coupled elements

a long range memory stochastic model of the return in financial markets abstract we present a nonlinear stochastic differential equation sde which mimics the probability density function pdf of the return and the power spectrum of the absolute return in financial markets absolute return as a measure of market volatility is considered in the proposed model as a long range memory stochastic variable the sde is obtained from the analogy with an earlier proposed model of trading activity in the financial markets and generalized within the nonextensive statistical mechanics framework the proposed stochastic model generates time series of the return with two power law statistics i e the pdf and the power spectral density reproducing the empirical data for the one minute trading return in the nyse

scaling and memory of intraday volatility return intervals in stock markets we study the return interval tau between price volatilities that are above a certain threshold q for 31 intraday data sets including the standard and poor s 500 index and the 30 stocks that form the dow jones industrial index for different threshold q the probability density function pq tau scales with the mean interval tau as formula see text similar to that found in daily volatilities since the intraday records have significantly more data points compared to the daily records we could probe for much higher thresholds and still obtain good statistics we find that the scaling function f x is consistent for all 31 intraday data sets in various time resolutions and the function is well approximated by the stretched exponential f x similar to e ax gamma with gamma 0 38 0 05 and a 3 9 0 5 which indicates the existence of correlations we analyze the conditional probability distribution pq tau tau0 for tau following a certain interval tau0 and find pq tau tau0 depends on tau0 which demonstrates memory in intraday return intervals also we find that the mean conditional interval tau tau0 increases with tau0 consistent with the memory found for pq tau tau0 moreover we find that return interval records in addition to having short term correlations as demonstrated by pq tau tau0 have long term correlations with correlation exponents similar to that of volatility records

the origin of fat tailed distributions in financial time series abstract 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 we find that destroying all correlations without changing the 1 d distribution by shuffling the order of the daily returns causes the fat tails to almost vanish for 1 d we argue that the fat tails are caused by the well known long range volatility correlations that have already been systematically studied previously 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 1 d

global well posedness for 2 d boussinesq system with the temperature dependent viscosity and supercritical dissipation abstract the present paper is dedicated to the global well posedness issue for the boussinesq system with the temperature dependent viscosity in r 2 motivated by the work abidi and zhang adv math 305 2017 1202 1249 on the critical dissipation d with 1 in the temperature equation of the system we consider the extension of their work to the supercritical dissipation for 2 3 1

modeling of financial data comparison of the truncated levy flight and the arch 1 and garch 1 1 processes we compare our results on empirical analysis of nancia l data with simulations of two stochastic models of the dynamics of stock market prices the two models are i the truncated l evy igh t recently introduced by us and ii the arch 1 and garch 1 1 processes we n d that the tlf well describes the scaling and its breakdown observed in empirical data while it is not able to properly describe the uctuation s of volatility empirically detected the arch 1 and garch 1 1 models are able to describe the probability density function of price changes at a given time horizon but both fail to describe the scaling properties of the pdfs for short time horizons c 1998 elsevier science b v all rights reserved

stochastic resonance of a periodically driven neuron under non gaussian noise abstract we investigate the first passage time statistics of the integrate fire neuron model driven by a sub threshold harmonic signal superposed with a non gaussian noise here we considered the noise as the result of a random multiplicative process displaced from the origin by an additive term such a mechanism generates a power law distributed noise whose characteristic decay exponent can be finely tuned we performed numerical simulations to analyze the influence of the noise non gaussian character on the stochastic resonance condition we found that when the noise deviates from gaussian statistics the resonance condition occurs at weaker noise intensities achieving a minimum at a finite value of the distribution function decay exponent we discuss the possible relevance of this feature to the efficiency of the firing dynamics of biological neurons as the present result indicates that neurons would require a lower noise level to detect a sub threshold signal when its statistics departs from gaussian

time evolving distribution of time lags between commercial airline disasters abstract we have studied the time lags between commercial line airplane disasters and their occurrence frequency till 2002 as obtained from a freely available website we show that the time lags seem to be well described by poisson random events where the average events rate is itself a function of time i e time dependent poisson events this is likely due to the unsteady growth of the industry the time lag distribution is compared with a truncated tsallis distribution thereby showing that the phenomenon has similarities with a brownian particle with time dependent mass we distinguish between other causes or natural causes and terrorism acts the latter amounts to about 5 but we find no drastic difference nor impact due to the latter on the overall distribution

volatility driven market in a generalized lotka voltera formalism abstract the generalized lotka voltera glv formalism has been introduced in order to explain the power law distributions in the individual wealth w i t pareto law and financial markets returns fluctuations r as a result of the auto catalytic multiplicative random character of the individual capital dynamics as long as the multiplicative random factor is extracted from the same probability distribution for all the individuals the exponent of the power laws turns out to be independent on the time variations of the average this explains also the stability over the past century of experimentally measured pareto exponent in contrast to the scaling properties of the single time unconditional probability distributions the auto correlations between observables measured at different times are not correctly reproduced by the original glv if the variance 2 of is time independent in the glv formalism the volatility r 2 auto correlations decay exponentially while the measurements in real markets indicate a power law with a very small exponent we show in the present paper that by making the variance of the individual wealth changes 2 a function of the market volatility r 2 one correctly reproduces the market volatility long range correlations moreover we show that this non trivial feedback loop between the market price volatility and the variance of the investors wealth leads to non trivial patterns in the overall market trends if the feedback is too strong it may even endanger the market stability

multifractal features of financial markets abstract we study the tick dynamical behavior of three assets in financial markets the kospi the won dollar and yen dollar exchange rates using the rescaled range r s analysis the multifractal hurst exponents with long run memory effect can be obtained from those assets and we discuss whether there exists the crossover or not for the hurst exponents at characteristic time scales particularly we find that the probability distribution of returns approaches to a lorentz distribution different from gaussian properties

on the rayleigh benard marangoni system and a related optimal control problem abstract in this paper we study a boundary control problem associated to the stationary rayleigh benard marangoni rbm system in presence of controls for the velocity and the temperature on parts of the boundary we analyze the existence uniqueness and regularity of weak solutions for the stationary rbm system in polyhedral domains of r 3 and then we prove the existence of the optimal solution by using the theorem of lagrange multipliers we derive an optimality system we also give a second order sufficient optimality condition and we establish a result of uniqueness of the optimal solution

time interval between successive trading in foreign currency market from microscopic to macroscopic abstract recently it has been shown that inter transaction interval iti distribution of foreign currency rates has a fat tail in order to understand the statistical property of the iti dealer model with n interactive agents is proposed from numerical simulations it is confirmed that the iti distribution of the dealer model has a power law tail the random multiplicative process rmp can be approximately derived from the iti of the dealer model consequently we conclude that the power law tail of the iti distribution of the dealer model is a result of the rmp

statistical properties of the moving average price in dollar yen exchange rates we introduce a weighted moving average analysis for the tick by tick data of yen dollar exchange rates the weights are determined automatically for given data by applying the yule walker formula for autoregressive model although the data are non stationary the resulting moving average gives a quite nice property that the deviation around the moving average becomes a white noise the weights decay exponentially with time scale less than 2 min implying that dealers are watching only very recent market state

power law distributions in random multiplicative processes with non gaussian colored multipliers abstract one class of universal mechanisms that generate power law probability distributions is that of random multiplicative processes in this paper we consider a multiplicative langevin equation driven by non gaussian colored multipliers we analytically derive a formula that relates the power law exponent to the statistics of the multipliers and numerically confirm its validity using multiplicative noise generated by chaotic dynamical systems and by a two valued markov process we also investigate the relationship between our treatment and the large deviation analysis of time series and demonstrate the appearance of log periodic fluctuations superimposed on the power law distribution due to the non gaussian nature of the multipliers

theoretical analysis of potential forces in markets abstract we show that random walks in a moving potential function with its center at the moving average of market prices are represented in the form of the self modulation model from this point of view we confirm the existence of non trivial autocorrelation in real market price changes by generalizing the formulation of potential function we prove that the arch model belongs to the special case of random walk in an asymmetric potential with randomly changing coefficient

a reactive lattice gas approach to economic cycles abstract a microscopic approach to macroeconomic features is intended a model for macroeconomic behavior under heterogeneous spatial economic conditions is reviewed a birth death lattice gas model taking into account the influence of an economic environment on the fitness and concentration evolution of economic entities is numerically and analytically examined the reaction diffusion model can also be mapped onto a high order logistic map the role of the selection pressure along various dynamics with entity diffusion on a square symmetry lattice has been studied by monte carlo simulation the model leads to a sort of phase transition for the fitness gap as a function of the selection pressure and to cycles the control parameter is a scalar business plan the business plan s allows for spin offs or merging and enterprise survival evolution law s whence bifurcations cycles and chaotic behavior