vibrations and stability of axially traveling laminated beams abstract in this paper vibrations and stability of an axially traveling laminated composite beam are investigated analytically via the method of multiple scales based on classical laminated beam theory the governing equations of motion for a time variant axial speed are obtained using newton s second law of motion and constitutive relations the method of multiple scales an approximate analytical method is applied directly to the gyroscopic governing equations of motion and complex eigenfunctions and natural frequencies of the system are obtained the stability boundaries of the system near resonance are determined via the routh hurwitz criterion finally a parametric study is conducted which considers the effects of laminate type and configuration as well as the mean speed and amplitude of speed fluctuations on the vibration response natural frequencies and stability boundaries of the system

supercritical speed stability of the trivial equilibrium of an axially moving string on an elastic foundation the stability of an axially moving string supported by a discrete or distributed elastic foundation is examined analytically particular attention is directed at the distribution of the critical speeds and identifying the divergence instability of the trivial equilibrium the elastically supported string shows unique stability behavior that is considerably different from unsupported axially moving string in particular any elastic foundation discrete or distributed leads to multiple critical speeds and a single region of divergence instability above the first critical speed whereas the unsupported string has one critical speed and is stable at all supercritical speeds additionally the elastically supported string critical speeds are bounded above and the maximum critical speed is the upper bound of the divergent speed region the analysis draws on the self adjoint eigenvalue problem for the critical speeds and a perturbation analysis about the critical speeds neither numerical solution nor spatial discretization which can produce substantially incorrect results are required the system falls in the class of dispersive gyroscopic continua and its behavior provides a useful comparison for general gyroscopic systems the analytical findings also serve as a benchmark for approximate methods applied to gyroscopic continua

phase transitions and spatio temporal fluctuations in stochastic lattice lotka volterra models we study the general properties of stochastic two species models for predator prey competition and coexistence with lotka volterra type interactions defined on a d dimensional lattice introducing spatial degrees of freedom and allowing for stochastic fluctuations generically invalidates the classical deterministic mean field picture already within mean field theory however spatial constraints modeling locally limited resources lead to the emergence of a continuous active to absorbing state phase transition field theoretic arguments supported by monte carlo simulation results indicate that this transition which represents an extinction threshold for the predator population is governed by the directed percolation universality class in the active state where predators and prey coexist the classical center singularities with associated population cycles are replaced by either nodes or foci in the vicinity of the stable nodes the system is characterized by essentially stationary localized clusters of predators in a sea of prey near the stable foci however the stochastic lattice lotka volterra system displays complex correlated spatio temporal patterns of competing activity fronts correspondingly the population densities in our numerical simulations turn out to oscillate irregularly in time with amplitudes that tend to zero in the thermodynamic limit yet in finite systems these oscillatory fluctuations are quite persistent and their features are determined by the intrinsic interaction rates rather than the initial conditions we emphasize the robustness of this scenario with respect to various model perturbations

flips from 4 folds with isolated complete intersection singularities we investigate a flipping contraction g x y from a 4 fold x with at worst isolated complete intersection singularities if y has an anti bicanonical divisor bi elephant with only rational singularities then g carries an inductive structure involving a chain of blow ups which we call la torre pendente and in particular the flip exists this naturally contains reid s pagoda as an anticanonical divisor elephant and its proper transforms

some special cremona transformations in this paper we continue the study c f c k s t 1 2 of special cremona transformations i e those whose base scheme y is smooth and connected crauder and katz have completely classified these when dim y 2 our main results classify them when they are quadro quadric theorem 2 6 and when codim y 2 theorem 3 2 in the first case they are just the maps given by systems of quadrics through severi varieties by a result of zak there are just four of these the veronese surface v c p5 the segre embedding of p2 x p2 in p8 the grassmannian g 2 6 in p14 and the 16dimensional e6 variety in p26 and in the second either y is a quintic elliptic scroll in p4 or y is defined in pi by the vanishing of the n x n minors of

spectral analysis for the transverse vibration of an axially moving timoshenko beam the use of frequency dependent spectral element matrix or exact dynamic stiffness matrix in structural dynamics is known to provide very accurate solutions while reducing the number of degrees of freedom to resolve the computational and cost problems thus in the present paper the spectral element model is formulated for the axially moving timoshenko beam under a uniform axial tension the high accuracy of the present spectral element is then verified by comparing its solutions with the conventional finite element solutions and exact analytical solutions the effects of the axial velocity and axial tension on the vibration characteristics the dispersion relation and the stability of a moving timoshenko beam are analytically and numerically investigated

non linear parametric vibration and stability of axially moving visco elastic rayleigh beams abstract an axially moving visco elastic rayleigh beam with cubic non linearity is considered and the governing partial differential equation of motion for large amplitude vibration is derived through geometrical constitutive and dynamical relations by directly applying the method of multiple scales to the governing equations of motion and considering the solvability condition the linear and non linear frequencies and mode shapes of the system are analytically formulated in the presence of damping terms it can be seen that the amplitude is exponentially time dependent and as a result the non linear natural frequencies of the system will be time dependent for the resonance case through considering the solvability condition and routh hurwitz criterion the stability conditions are developed analytically eventually the effects of system parameters on the vibrational behavior stability and bifurcation points of the system are investigated through parametric studies

coupled longitudinal transverse dynamics of an axially accelerating beam abstract the coupled longitudinal transverse nonlinear dynamics of an axially accelerating beam is numerically investigated this problem is classified as a parametrically excited gyroscopic system the axial speed is assumed to be comprised of a constant mean value along with harmonic fluctuations hamilton s principle is employed to derive the equations of motion of the system which are in the form of two coupled partial differential equations the equations are discretized using the galerkin method which yields a set of coupled second order nonlinear ordinary differential equations with time dependent coefficients the sub critical dynamics of the system is examined via the pseudo arclength continuation technique while the global dynamics is investigated using direct time integration the mean axial speed and the amplitude of the speed variations are varied so as to construct the bifurcation diagrams of poincare maps the vibration specifications of the system are investigated more detailed via plotting time histories phase plane portraits and fast fourier transforms ffts

on fano manifolds of large pseudoindex abstract we describe fano manifolds of large pseudoindex that are rationally connected with respect to some numerically independent families of rational curves

stability in parametric resonance of axially moving viscoelastic beams with time dependent speed stability in transverse parametric vibration of axially accelerating viscoelastic beams is investigated the governing equation is derived from newton s second law the kelvin constitution relation and the geometrical relation when the axial speed is a constant mean speed with small harmonic variations the governing equation can be regarded as a continuous gyroscopic system under small periodically parametric excitations and a damping term the method of multiple scales is applied directly to the governing equation without discretization the stability conditions are obtained for combination and principal parametric resonance numerical examples are presented for beams with simple supports and fixed supports respectively to demonstrate the effect of viscoelasticity on the stability boundaries in both cases

critical and oscillatory behavior of a system of smart preys and predators it is shown that a system of smart preys and predators exhibits irreversible phase transitions between a regime of prey predator coexistence and an state where predator extinction is observed within the coexistence regime the system exhibits a transition between a regime where the densities of species remain constant and another with self sustained oscillations respectively this transition is located by means of a combined treatment involving finite size scaling and fourier transforms furthermore it is shown that the transition can be rationalized in terms of the standard percolation theory the existence of an oscillatory regime in the thermodynamic limit which is in contrast to previous findings of boccara et al phys rev e 50 4531 1994 may be due to subtle differences between the studied models

infinite mode analysis and truncation to resonant modes of axially accelerated beam vibrations abstract the transverse vibrations of simply supported axially moving euler bernoulli beams are investigated the beam has a time varying axial velocity with viscous damping traveling beam eigenfunctions with infinite number of modes are considered approximate analytical solutions are sought using the method of multiple scales a perturbation technique a detailed analysis of the resonances in which upto four modes of vibration involved are performed stability analysis is treated for each type of resonance approximate stability borders are given for the resonances involving only two modes for higher number of modes involved in a resonance sample numerical examples are presented for stabilities

small contractions of symplectic 4 folds we classify small contractions of holomorphically symplectic 4 folds ams msc 14e30 14j35

a general solution procedure for vibrations of systems with cubic nonlinearities and nonlinear time dependent internal boundary conditions abstract the subject of this paper is the development of a general solution procedure for the vibrations primary resonance and nonlinear natural frequency of systems with cubic nonlinearities subjected to nonlinear and time dependent internal boundary conditions this is a commonly occurring situation in the vibration analysis of continuous systems with intermediate elements the equations of motion form a set of nonlinear partial differential equations with nonlinear time dependent and coupled internal boundary conditions the method of multiple timescales an approximate analytical method is applied directly to each partial differential equation of motion as well as coupled boundary conditions i e on each sub domain and the corresponding internal boundary conditions for a continuous system with intermediate elements which ultimately leads to approximate analytical expressions for the frequency response relation and nonlinear natural frequencies of the system these closed form solutions provide direct insight into the relationship between the system parameters and vibration characteristics of the system moreover the suggested solution procedure is applied to a sample problem which is discussed in detail

combination and principal parametric resonances of axially accelerating viscoelastic beams recognition of longitudinally varying tensions abstracts nonlinear parametric vibration is investigated for axially accelerating viscoelastic beams subject to parametric excitations resulting from longitudinally varying tensions and axial speed fluctuations the effects of the longitudinally varying tension due to the axial acceleration are highlighted while the tension was assumed to be longitudinally uniform in previous studies the dependence of the tension on the finite axial support rigidity is also modeled the governing equations of coupled planar vibration and the associated boundary conditions are derived from the generalized hamilton principle and the viscoelastic constitutive relation the equation is simplified into a governing equation of transverse nonlinear vibration in small but finite stretching problems the governing equation of transverse vibration is a nonlinear integro partial differential equation with time dependent and space dependent coefficients the method of multiple scales is employed to analyze the combination and the principal parametric resonances with the focus on steady state responses in the difference resonance there is only trivial zero response which is always stable in the summation and the principal resonances the trivial responses may become unstable and bifurcate into nontrivial responses for certain excitation frequencies some numerical examples indicate that the longitudinal tension variation makes the instability frequency intervals of trivial responses small and the nontrivial response amplitudes large small in the summation principal resonance it is also found that the nontrivial responses are not sensitive to the axial support rigidity numerical solutions are calculated via the differential quadrature to support results via the method of multiple scales

transverse vibration of an axially accelerating string abstract the transverse vibration of an axially accelerating string is investigated the equation of motion is developed using hamilton s principle the resulting partial differential equations are discretized using galerkin s method assuming the axial velocity to be periodic a stability analysis is performed using floquet theory one two three four six and eight term series approximations are considered in the galerkin s method the one term approximation leads to a mathieu equation the solution of which is well known the numerical results for one term are compared with the analytical solution for the mathieu equation and they are in full agreement the two term approximation leads to gyroscopically coupled equations and the solutions differ significantly from that of the one term approximation whereas the three term approximation solutions look similar to the one term approximation solutions the analysis is carried out for higher order even approximations and the solutions are in qualitative agreement the two and four term approximation solutions are compared with the analytical results from hsu s method and are in reasonable agreement the results show that instabilities occur at much higher amplitudes and frequencies of the periodic axial velocity than that of typical devices such as tape machines and band saws

on the oscillatory dynamical behaviour of epidemic spreading in fractal media we present numerical evidence that dynamical physical processes that develop a time dependent characteristic length and take place in fractal media exhibiting spatial discrete scale invariance dsi with fundamental scaling ratio b may become coupled to the topology of the fractal leading to the observation of time dsi the hallmark of time dsi is the observation of a log periodic modulation of the dynamic or kinetic observables which is characterized by a well defined fundamental time scaling ratio both fundamental scaling ratios are linked according to b 1 z where z is the dynamic exponent characteristic of the physical process specifically we have studied the epidemic behaviour of the contact process cp in sierpinski carpets the cp exhibits second order irreversible phase transitions between an active regime and an absorbing state where the system is trapped without any escape possibility we observed that relevant dynamic observables such as the number of active sites the survival probability of the epidemics and the mean square displacement of the epidemic from the origin r2 t exhibit log periodic modulations by fitting the data we evaluate the fundamental time scaling ratio for various fractals and the corresponding dynamic exponents since at criticality one has that r2 t t2 z an independent estimation of the dynamic exponent can be performed in excellent agreement with results obtained by using the conjectured relationship for the fundamental scaling ratios b and

transition behaviour from string to beam for an axially accelerating material an approximate analytical expression for the natural frequency is given for the problem for velocity profiles harmonically varying about a mean velocity stability borders are determined analytically for fluctuation frequency versus amplitudes beam effects cause the stability boundaries to shift to higher frequency values

flocks herds and schools a quantitative theory of flocking we present a quantitative continuum theory of flocking the collective coherent motion of large numbers of self propelled organisms in agreement with everyday experience our model predicts the existence of an ordered phase of flocks in which all members of even an arbitrarily large flock move together with the same mean velocity stackrel ensuremath rightarrow v ensuremath ne 0 this coherent motion of the flock is an example of spontaneously broken symmetry no preferred direction for the motion is picked out a priori in the model rather each flock is allowed to and does spontaneously pick out some completely arbitrary direction to move in by analyzing our model we can make detailed quantitative predictions for the long distance long time behavior of this broken symmetry state the goldstone modes associated with this spontaneously broken rotational symmetry are fluctuations in the direction of motion of a large part of the flock away from the mean direction of motion of the flock as a whole these goldstone modes mix with modes associated with conservation of bird number to produce propagating sound modes these sound modes lead to enormous fluctuations of the density of the flock far larger at long wavelengths than those in e g an equilibrium gas our model is similar in many ways to the navier stokes equations for a simple compressible fluid in other ways it resembles a relaxational time dependent ginsburg landau theory for an n d component isotropic ferromagnet in spatial dimensions dg4 the long distance behavior is correctly described by a linearized theory and is equivalent to that of an unusual but nonetheless equilibrium model for spin systems for dl4 nonlinear fluctuation effects radically alter the long distance behavior making it different from that of any known equilibrium model in particular we find that in d 2 where we can calculate the scaling exponents exactly flocks exhibit a true long range ordered spontaneously broken symmetry state in contrast to equilibrium systems which cannot spontaneously break a continuous symmetry in d 2 the mermin wagner theorem we make detailed predictions for various correlation functions that could be measured either in simulations or by quantitative imaging of real flocks we also consider an anisotropic model in which the birds move preferentially in an easy e g horizontal plane and make analogous but quantitatively different predictions for that model as well for this anisotropic model we obtain exact scaling exponents for all spatial dimensions including the physically relevant case d 3

vibrations of an axially moving beam with time dependent velocity the dynamic response of an axially accelerating elastic tensioned beam is investigated the time dependent velocity is assumed to vary harmonically about a constant mean velocity these systems experience a coriolis acceleration component which renders such systems gyroscopic the equation of motion is solved by using perturbation analysis principal parametric resonances and combination resonances are investigated in detail stability boundaries are determined analytically it is found that instabilities occur when the frequency of velocity fluctuations is close to two times the natural frequency of the constant velocity system or when the frequency is close to the sum of any two natural frequencies when the velocity variation frequency is close to zero or to the difference of two natural frequencies however no instabilities are detected up to the first order of perturbation numerical results are presented for different flexural stiffness values and for the first two modes

principal parametric resonances of a general continuous system with cubic nonlinearities abstract a generalized vibrational model of cubic nonlinear continuous system with arbitrary parametric excitation is considered the method of multiple scales a perturbation method is used to find an approximate analytical solution the primary parametric resonance of the parametric excitation is considered the amplitude and phase modulation equations are derived steady state solutions and their stability are discussed the solution algorithm is applied to the problem of nonlinear vibrations of viscoelastic pipes conveying fluids natural frequencies of viscoelastic pipes are found frequency response curves and bifurcation points are drawn stable and unstable regions of trivial and nontrivial solutions are obtained

fluctuations and correlations in lattice models for predator prey interaction including spatial structure and stochastic noise invalidates the classical lotka volterra picture of stable regular population cycles emerging in models for predator prey interactions growth limiting terms for the prey induce a continuous extinction threshold for the predator population whose critical properties are in the directed percolation universality class we discuss the robustness of this scenario by considering an ecologically inspired stochastic lattice predator prey model variant where the predation process includes next nearest neighbor interactions we find that the corresponding stochastic model reproduces the above scenario in dimensions 1 d or 4 in contrast with the mean field theory which predicts a first order phase transition however the mean field features are recovered upon allowing for nearest neighbor particle exchange processes provided these are sufficiently fast

dynamic stability in parametric resonance of axially accelerating viscoelastic timoshenko beams abstract this paper investigates dynamic stability of an axially accelerating viscoelastic beam undergoing parametric resonance the effects of shear deformation and rotary inertia are taken into account by the timoshenko thick beam theory the beam material obeys the kelvin model in which the material time derivative is used the axial speed is characterized as a simple harmonic variation about the constant mean speed the governing partial differential equations are derived from newton s second law euler s angular momentum principle and the constitutive relation the method of multiple scales is applied to the equations to establish the solvability conditions in summation and principal parametric resonances the sufficient and necessary condition of the stability is derived from the routh hurvitz criterion some numerical examples are presented to demonstrate the effects of related parameters on the stability boundaries

directed percolation in 2 1 dimensions the author presents results of monte carlo simulations for directed percolation in 2 1 dimensions very close to the percolation threshold his values for pc for bond and site percolation on the bcc and simple cubic lattices are more precise than previous estimates by one to two orders of magnitude the improvement on the critical exponents describing the behaviour at pc is less impressive but they are also substantially more precise than previous ones