vibration of an axially moving string with geometric non linearity and translating acceleration the vibration of an axially moving string is studied when the string has geometric non linearity and translating acceleration based upon the von karman strain theory the equations of motion are derived considering the longitudinal and transverse deflections the equation for the longitudinal vibration is linear and uncoupled while the equation for the transverse vibration is non linear and coupled between the longitudinal and transverse deflections these equations are discretized by the galerkin method after they are transformed into the variational equations i e the weak forms so that the admissible and comparison functions can be used for the bases of the longitudinal and transverse deflections respectively with the discretized equations the natural frequencies the time histories of the deflections and the distributions of the deflection and stress are investigated in addition comparisons between the results of linear and non linear theories are provided

normal modes for non linear vibratory systems a methodology is presented which extends to non linear systems the concept of normal modes of motion which is well developed for linear systems the method is constructive for weakly non linear systems and provides the physical nature of the normal modes along with the non linear differential equations which govern their dynamics it also provides the non linear co ordinate transformation which relates the original system co ordinates to the modal co ordinates using this transformation we demonstrate how an approximate non linear version of superposition can be employed to reconstruct the overall motion from the individual non linear modal dynamics the results presented herein for non linear systems reduce to modal analysis for the linearized system when non linearities are neglected even though the approach is entirely different from the traditional one the tools employed are from the theory of invariant manifolds for dynamical systems and were inspired by the center manifold reduction technique in this paper the basic ideas are outlined a few examples are presented and some natural extensions and applications of the method are briefly described in the conclusions

inequalities involving modified bessel functions of the first kind ii the intrinsic properties including logarithmic convexity concavity of the modified bessel functions of the first kind and some other related functions are obtained several inequalities involving functions under discussion are established

on resonances and the applicability of galerkin s truncation method for an axially moving string with time varying velocity abstract in this paper an initial boundary value problem for a linear homogeneous equation describing an axially moving string is investigated the time dependent velocity is assumed to vary harmonically about a constant mean velocity with a small fluctuation amplitude the two timescales perturbation method and the laplace transform method have been employed to the equation of motion in search of infinite mode approximate solutions all resonance cases are investigated in detail it will be shown that galerkin s truncation method cannot be applied to this problem in all cases to obtain approximations valid on long timescales

sharp bounds for cumulative distribution functions abstract ratios of integrals can be bounded in terms of ratios of integrands under certain monotonicity conditions this result related to l hopital s monotone rule can be used to obtain sharp bounds for cumulative distribution functions we consider the case of noncentral cumulative gamma and beta distributions three different types of sharp bounds for the noncentral gamma distributions also called marcum functions are obtained in terms of modified bessel functions and one additional type of function a second modified bessel function two error functions or one incomplete gamma function for the noncentral beta case the bounds are expressed in terms of kummer functions and one additional kummer function or an incomplete beta function these bounds improve previous results with respect to their range of application and or its sharpness

nonlinear vibration analysis of axially moving strings based on gyroscopic modes decoupling abstract a novel idea that applies the multiple scale analysis to a discretized decoupled system of gyroscopic continua is introduced and an axial moving string is treated as an example first the invariant manifold method is applied to the discretized ordinary differential equations of the axially moving string complex gyroscopic mode functions that agree well with true analytical results are obtained the gyroscopic modes are subsequently used for the discretized ordinary differential equations with gyroscopic and nonlinear coupling terms that yield a gyroscopically decoupled system further the method of multiple scales is used to obtain the equations at a slow scale this novel procedure is compared to solutions obtained by directly applying the classical multiple scale analysis to the gyroscopically coupled system without decoupling the modal decoupled system analysis yields better frequency with comparing to the classic method the proposed methodology provides a novel alternative for nonlinear dynamic analysis of gyroscopic continua

new bounds for the marcum q function new bounds are proposed for the marcum q function which is defined by an integral expression where the 0th order modified bessel function appears the proposed bounds are derived by suitable approximations of the 0th order modified bessel function in the integration region of the marcum q function they prove to be very tight and outperform bounds previously proposed in the literature in particular the proposed bounds are noticeably good for large values of the parameters of the marcum q function where previously introduced bounds fail and where exact computation of the function becomes critical due to numerical problems

generalized superstatistics of nonequilibrium markovian systems abstract the paper is devoted to the construction of the superstatistical description for nonequilibrium markovian systems it is based on kirchhoff s diagram technique and the assumption on the system under consideration to possess a wide variety of cycles with vanishing probability fluxes the latter feature enables us to introduce equivalence classes called channels within which detailed balance holds individually then stationary probability as well as flux distributions are represented as some sums over the channels the latter construction actually forms the superstatistical description which however deals with a certain superposition of equilibrium subsystems rather than a formal expansion of the nonequilibrium steady state distribution into terms of the boltzmann type

multicanonical distribution statistical equilibrium of multiscale systems a multicanonical formalism is introduced to describe the statistical equilibrium of complex systems exhibiting a hierarchy of time and length scales where the hierarchical structure is described as a set of nested internal heat reservoirs with fluctuating temperatures the probability distribution of states at small scales is written as an appropriate averaging of the large scale distribution the boltzmann gibbs distribution over these effective internal degrees of freedom for a large class of systems the multicanonical distribution is given explicitly in terms of generalized hypergeometric functions as a concrete example it is shown that generalized hypergeometric distributions describe remarkably well the statistics of acceleration measurements in lagrangian turbulence

computing the generalized marcum q function a modified version of the method of saddlepoint integration is shown to compute the generalized marcum q function accurately over a broad range of parameters bounds on the truncation error incurred by stopping the numerical quadrature at a certain point are presented

multifractal analysis of fluid particle accelerations in turbulence the probability density function pdf of accelerations in turbulence is derived analytically with the help of the multifractal analysis based on generalized entropy i e the tsallis or the renyi entropy it is shown that the derived pdf explains quite well the one obtained by bodenschatz et al in the measurement of fluid particle accelerations in the lagrangian frame at r 690 and the one by gotoh et al in the dns with the mesh size 10243 at r 380

universal recurrence algorithm for computing nuttall generalized marcum and incomplete toronto functions and moments of a noncentral χ 2 random variable abstract this article proposes a novel recurrence algorithm for computing nuttall generalized marcum and incomplete toronto functions as well as truncated and raw moments of any real order for a noncentral 2 random variable the numerical results highlight that the proposed recurrence method offers an excellent speed accuracy trade off for a wide variety of meaningful and relevant applications ranging from the operations management and industrial engineering fields to problems encountered in the financial engineering industry

galerkin methods for natural frequencies of high speed axially moving beams in this paper natural frequencies of planar vibration of axially moving beams are numerically investigated in the supercritical ranges in the supercritical transport speed regime the straight equilibrium configuration becomes unstable and bifurcate in multiple equilibrium positions the governing equations of coupled planar is reduced to two nonlinear models of transverse vibration for motion about each bifurcated solution those nonlinear equations are cast in the standard form of continuous gyroscopic systems by introducing a coordinate transform the natural frequencies are investigated for the beams via the galerkin method to truncate the corresponding governing equations without nonlinear parts into an infinite set of ordinary differential equations under the simple support boundary numerical results indicate that the nonlinear coefficient has little effects on the natural frequency and the three models predict qualitatively the same tendencies of the natural frequencies with the changing parameters and the integro partial differential equation yields results quantitatively closer to those of the coupled equations

experimental lagrangian acceleration probability density function measurement abstract we report experimental results on the acceleration component probability distribution function at r 690 to probabilities of less than 10 7 this is an improvement of more than an order of magnitude over past measurements and allows us to conclude that the fourth moment converges and the flatness is approximately 55 we compare our probability distribution to those predicted by several models inspired by non extensive statistical mechanics we also look at acceleration component probability distributions conditioned on a velocity component for conditioning velocities as high as three times the standard deviation and find them to be highly non gaussian

exponential type bounds on the generalized marcum q function with application to error probability analysis over fading channels strict upper and lower bounds of exponential type are derived for the generalized mth order marcum q function which enable simple evaluation of a tight upper bound on the average bit error probability performance of a wide class of noncoherent and differentially coherent communication systems operating over generalized fading channels for the case of frequency selective fading with arbitrary statistics per independent fading path the resulting upper hound on performance is expressed in the form of a product of moment generating functions of the instantaneous power random variables that characterize these paths

inequalities for the generalized marcum q function abstract in this paper we consider the generalized marcum q function of order 0 real defined by q a b 1 a 1 b t e t 2 a 2 2 i 1 at d t where a b 0 i stands for the modified bessel function of the first kind and the right hand side of the above equation is replaced by its limiting value when a 0 our aim is to prove that the function q a b is strictly increasing on 0 for each a 0 b 0 and to deduce some interesting inequalities for the function q moreover we present a somewhat new viewpoint of the generalized marcum q function by showing that satisfies the new is better than used nbu property which arises in economic theory

bounds for modified struve functions of the first kind and their ratios abstract we obtain a simple two sided inequality for the ratio l x l 1 x in terms of the ratio i x i 1 x where l x is the modified struve function of the first kind and i x is the modified bessel function of the first kind this result allows one to use the extensive literature on bounds for i x i 1 x to immediately deduce bounds for l x l 1 x we note some consequences and obtain further bounds for l x l 1 x by adapting techniques used to bound the ratio i x i 1 x we apply these results to obtain new bounds for the condition numbers x l x l x the ratio l x l y and the modified struve function l x itself amongst other results we obtain two sided inequalities for x l x l x and l x l y that are given in terms of x i x i x and i x i y respectively which again allows one to exploit the substantial literature on bounds for these quantities the results obtained in this paper complement and improve existing bounds in the literature

on new conditions for evaluate long time scales in superstatistical time series in this article we introduce an additional condition for the criterion previously presented in order to extract the update time scale of the intensive parameter in superstatistical time series with these modifications such criterion is capable of evaluating the actual long time scale in addition the criterion permits a valuable way to verify whether the process under study is superstatistical or not

new bounds for the generalized marcum q function in this paper we study the generalized marcum q function q nu a b where a nu 0 and b ges 0 our aim is to extend the results of corazza and ferrari ieee trans inf theory vol 48 pp 3003 3008 2002 to the generalized marcum q function in order to deduce some new tight lower and upper bounds the key tools in our proofs are some monotonicity properties of certain functions involving the modified bessel function of the first kind and some classical inequalities i e the cauchy buniakowski schwarz and chebyshev integral inequalities these bounds are shown to be very tight for large b i e the relative errors of our bounds converge to zero as b increases both theoretical analysis and numerical results are provided to show the tightness of our bounds

time domain analysis of the fractional order weighted distributed parameter maxwell model in this paper we derive in time domain the fundamental solution and relevant properties of the fractional order weighted distributed parameter maxwell model fowdpmm the weight function is replaced by the truncated fourier series which is leading to three basic fractional order distributed parameter elements the inverse laplace transforms of the distributed parameter operators are derived by cutting the complex plane and computing the complex path integral along the hankel path the asymptotic property and boundary problem are discussed by using the inverse laplace transform the energy of the weight function and the band width of the fourier series the relaxation modulus of fowdpmm is solved as well which is closely related to some other viscoelastic phenomena as creep precondition and hysteresis a number of novel characteristics of fowdpmm such as power law decay and intermediate phenomenon are concluded as well several illustrated examples are provided to validate the concepts

modal analysis of a continuous gyroscopic second order system with nonlinear constraints abstract a method for the modal analysis of continuous gyroscopic systems with nonlinear constraints is developed this method assumes that the nonlinear constraint can be expressed as a piecewise linear force deflection profile located at an arbitrary position within the domain using this assumption the mode shapes and natural frequencies are first found for each state then a mapping method based on the inner product of the mode shapes is developed to map the displacement of the system between the in contact and out of contact states to illustrate this method a model for the vibration of a traveling string in contact with a piecewise linear constraint is developed as an analog of the interaction between magnetic tape and a guide in data storage systems five design parameters of the guide are considered flange clearance flange stiffness symmetry of the force deflection profile in terms of flange stiffness and offset and the guide s position along the length of the string there are critical bifurcation thresholds below which the system exhibits no chaotic behavior and is dominated by period one symmetric behavior and above which the system contains asymmetric higher periodic motion with windows of chaotic behavior these bifurcation thresholds are particularly pronounced for the transport speed flange clearance symmetry of the force deflection profile and guide position the stability of the system is sensitive to the system s velocity and compared to stationary systems more mode shapes are needed to accurately model the dynamics of the system

non linear normal modes and invariant manifolds small amplitude motions of dynamic systems structural fluid control etc about an equilibrium state are modeled by linear differential equations which have constant coefficients these are typically obtained by a taylor series expansion of the forces about the equilibrium point under quite general circumstances these equations admit a set of special solutions called normal mode motions in which each system component moves with the same frequency and with a fixed ratio amongst the displacements of the components for a conservative system for a non conservative system all displacements and velocities are linearly related to a single displacement velocity pair

estimation of the kolmogorov constant by large eddy simulation in the stable pbl abstract in this paper is evaluated the inertial subrange kolmogorov constant c 0 in a stable boundary layer the importance of the constant c 0 is well known as predictions of turbulent dispersion by means of lagrangian stochastic models depend upon its value different values of the c 0 constant has been proposed along the years most of them determined at low reynolds number and or under different techniques here we estimate the constant c 0 by tracking an ensemble of lagrangian particles injected in a stable planetary boundary layer simulated with a large eddy simulation model and analyzing the ensemble averaged lagrangian velocity structure function in the inertial subrange our estimative of c 0 w is 3 7 which is consistent with values found in literature the evaluation of c 0 u and c 0 v cannot be easily accomplished since it is difficult to identify an inertial subrange for the wind field horizontal components

bounds for the generalized marcum q function abstract in this paper we consider the generalized marcum q function of order 0 real defined by q a b 1 a 1 b t e t 2 a 2 2 i 1 at dt where a 0 b 0 and i stands for the modified bessel function of the first kind our aim is to extend some results on the first order marcum q function to the generalized marcum q function in order to deduce some new lower and upper bounds moreover we show that the proposed bounds are very tight for the generalized marcum q function of integer order and we deduce some new inequalities for the more general case of real order the chief tools in our proofs are some monotonicity properties of certain functions involving the modified bessel function of the first kind which are based on a criterion for the monotonicity of the quotient of two maclaurin series

analytic expressions and bounds for special functions and applications in communication theory this paper is devoted to the derivation of novel analytic expressions and bounds for a family of special functions that are useful in wireless communication theory these functions are the well known nuttall q function incomplete toronto function rice ie function and incomplete lipschitz hankel integrals capitalizing on the offered results useful identities are additionally derived between the above functions and humbert phi 1 function as well as for specific cases of the kampede feriet function these functions can be considered as useful mathematical tools that can be employed in applications relating to the analytic performance evaluation of modern wireless communication systems such as cognitive radio cooperative and free space optical communications as well as radar diversity and multiantenna systems as an example new closed form expressions are derived for the outage probability over nonlinear generalized fading channels namely alpha eta mu alpha lambda mu and alpha kappa mu as well as for specific cases of the eta mu and lambda mu fading channels furthermore simple expressions are presented for the channel capacity for the truncated channel inversion with fixed rate and corresponding optimum cutoff signal to noise ratio for single antenna and multiantenna communication systems over rician fading channels the accuracy and validity of the derived expressions is justified through extensive comparisons with respective numerical results

tight bounds for the generalized marcum q function abstract in this paper we study the generalized marcum q function of order 0 real defined by q a b 1 a 1 b t e t 2 a 2 2 i 1 a t dt where a 0 b 0 and i stands for the modified bessel function of the first kind our aim is to improve and extend some recent results of wang to the generalized marcum q function in order to deduce some sharp lower and upper bounds in both cases b a and b a we give the best possible upper bound for q a b the key tools in our proofs are some monotonicity properties of certain functions involving the modified bessel function of the first kind these monotonicity properties are deduced from some results on modified bessel functions which have been used in wave mechanics and finite elasticity

conditional lagrangian acceleration statistics in turbulent flows with gaussian distributed velocities the random intensity of noise approach to the one dimensional laval dubrulle nazarenko type model having deductive support from the three dimensional navier stokes equation is used to describe lagrangian acceleration statistics of a fluid particle in developed turbulent flows intensity of additive noise and cross correlation between multiplicative and additive noises entering a nonlinear langevin equation are assumed to depend on random velocity fluctuations in an exponential way we use an exact analytic result for the acceleration probability density function obtained as a stationary solution of the associated fokker planck equation we give a complete quantitative description of the available experimental data on conditional and unconditional acceleration statistics within the framework of a single model with a single set of fit parameters the acceleration distribution and variance conditioned on lagrangian velocity fluctuations and the marginal distribution calculated by using independent gaussian velocity statistics are found to be in a good agreement with the recent high reynolds number lagrangian experimental data the fitted conditional mean acceleration is very small that is in agreement with direct numerical simulations and increases for higher velocities but it departs from the experimental data which exhibit anisotropy of the studied flow

monotonicity properties and bounds for the chi square and gamma distributions a sharp analysis of the convexity properties of marcum functions is performed monotonicity properties for ratios of consecutive marcum functions are obtained the new bounds for marcum functions improve previous bounds in large regions new and improved monotonicity properties are obtained in the central case the combined bounds obtained for the central case are superior to previous bounds the generalized marcum functions q x y and p x y have as particular cases the non central 2 and gamma cumulative distributions which become central distributions incomplete gamma function ratios when the non centrality parameter x is set to zero we analyze monotonicity and convexity properties for the generalized marcum functions and for ratios of marcum functions of consecutive parameters differing in one unity and we obtain upper and lower bounds for the marcum functions these bounds are proven to be sharper than previous estimations for a wide range of the parameters additionally we show how to build convergent sequences of upper and lower bounds the particularization to incomplete gamma functions together with some additional bounds obtained for this particular case lead to combined bounds which improve previously existing inequalities

superstatistical generalizations of wishart laguerre ensembles of random matrices using beck and cohen s superstatistics we introduce in a systematic way a family of generalised wishart laguerre ensembles of random matrices with dyson index 1 2 and 4 the entries of the data matrix are gaussian random variables whose variancesfluctuate from one sample to another according to a certain probability density f and a single deformation parameter three superstatistical classes for f are usually considered 2 inverse 2 and log normal distributions while the first class already considered by two of the authors leads to a power law decay of the spectral density we here introduce and solve exactly a superposition of wishart laguerre ensembles with inverse 2 distribution the corresponding macroscopic spectral density is given by a deformation of the semi circle and marcenko pastur laws on a non compact support with exponential tails after discussing in detail the validity of wigner s surmise in the wishart laguerre class we introduce a generalised dependent surmise with stretched exponential tails which well approximates the individual level spacing distribution in the bulk the analytical results are in excellent agreement with numerical simulations to illustrate our findings we compare the 2 and inverse 2 class to empirical data from financial covariance matrices