a smoothing property of a hyperbolic system and boundary controllability abstract we investigate a method with which one can deduce controllability results from smoothing properties previous applications of the method were for partial differential equations like the euler bernoulli beam equation petrowski hyperbolic in this paper we study the method s applicability to a strictly hyperbolic system by considering the boundary controllability of a vibrating timoshenko beam with physical characteristics that may vary along the length of the beam two cases are considered a beam which is clamped at one end the other end being controlled by a torque and transverse force and a beam which is hinged at one end where a control torque is applied and free at the other end where a control force is applied

growth of self affine surfaces abstract growing rough surfaces are a natural illustration of self affinity a term coined some years ago by benoit mandelbrot the eden model ballistic deposition and polynucleation growth are well known examples where such structures emerge using the concept of the intrinsic surface width associated with the physical lower cutoff we explain important corrections to scaling and show how anomalous roughening at morphological transitions develops

anisotropy and scaling of eden clusters in two and three dimensions for two dimensional eden clusters grown on flat substrates the way the perimeter per unit length and the surface width depend on the orientation of the substrate with respect to the lattice is measured the evolution of the perimeter per unit length during growth is shown to be independent of the substrate length for the surface width strong corrections to scaling are observed the anisotropy of three dimensional eden clusters and its implications for the scaling of the surface width are investigated the largest two and three dimensional clusters studied are more than one order of magnitude larger than in previous simulations

dynamic boundary control of the timoshenko beam abstract we consider a clamped free timoshenko beam to stabilize the beam vibrations we propose a dynamic boundary control law applied at the free end of the beam we prove that with the proposed control law the beam vibrations uniformly and exponentially decay to zero the proof uses a lyapunov functional based on the energy of the system

boundary control of the timoshenko beam it is shown that the timoshenko beam can be uniformly stabilized by means of a boundary control a numerical study on the spectrum is also presented

a dynamic control law for the wave equation abstract we consider a system described by the one dimensional linear wave equation in a bounded domain with appropriate boundary conditions to stabilize the system we propose a dynamic boundary controller applied at the free end of the system the transfer function of the proposed controller is restricted to be a positive real function which could be strictly proper we then show that if the transfer function of the controller is strictly proper then the resulting closed loop system is asymptotically stable and if proper but not strictly proper then the resulting closed loop system is exponentially stable

universality class of interface growth with reflection symmetry we investigate interface dynamics in 1 1 dimensions respecting reflection symmetry in the continuum approach of kardar parisi and zhang the leading nonlinearity is then of the form ht 3 on the basis of monte carlo simulations for a driven lattice gas we argue that the nonlinearity is marginally irrelevant thus the universality class is the one of equilibrium interfaces with a purely relaxational bulk dynamics

multiparticle biased diffusion limited aggregation with surface diffusion a comprehensive model of electrodeposition we present a complete study of the multiparticle biased diffusion limited aggregation mbdla model supplemented with surface diffusion sd focusing on the relevance and effects of the latter transport mechanism by comparing different algorithms we show that mbdla 1 sd is a very good qualitative model for electrodeposition in essentially the whole range of current intensities provided one introduces sd in the model in the proper fashion we have found that the correct procedure involves simultaneous bulk diffusion and sd introducing a time scale arising from the ratio of the rates of the two processes we discuss in detail the different morphologies obtained and compare them to the available experimental data with very satisfactory results we also characterize the aggregates thus obtained by means of the dynamic scaling exponents of the interface height allowing us to distinguish several regimes in the mentioned interface growth our asymptotic scaling exponents are again in good agreement with recent experiments we conclude by discussing a global picture of the influence and consequences of sd in electrodeposition

orientation and stabilization of a flexible beam attached to a rigid body planar motion the author considers a flexible structure modeled as a rigid body which rotates in inertial space a light flexible beam is clamped to the rigid body at one end and free one is clamped at the other it is assumed that the flexible beam performs only planar motion the equations of motion are obtained by using free body diagrams two control problems are posed namely the orientation and stabilization of the system it is shown that suitable boundary controls applied to the free end of the beam and suitable control torques applied to the rigid body solve the problems posed above the proofs are obtained by using the energy of the system as a lyapunov functional

persistence in nonequilibrium surface growth persistence probabilities of the interface height in 1 1 and 2 1 dimensional atomistic solid on solid stochastic models of surface growth are studied using kinetic monte carlo simulations with emphasis on models that belong to the molecular beam epitaxy mbe universality class both the initial transient and the long time steady state regimes are investigated we show that for growth models in the mbe universality class the nonlinearity of the underlying dynamical equation is clearly reflected in the difference between the measured values of the positive and negative persistence exponents in both transient and steady state regimes for the mbe universality class the positive and negative persistence exponents in the steady state are found to be 0 66 0 02 and 0 78 0 02 respectively in 1 1 dimensions and 0 76 0 02 and 0 85 0 02 respectively in 2 1 dimensions the noise reduction technique is applied on some of the 1 1 dimensional models in order to obtain accurate values of the persistence exponents we show analytically that a relation between the steady state persistence exponent and the dynamic growth exponent found earlier to be valid for linear models should be satisfied by the smaller of the two steady state persistence exponents in the nonlinear models our numerical results for the persistence exponents are consistent with this prediction we also find that the steady state persistence exponents can be obtained from simulations over times that are much shorter than that required for the interface to reach the steady state the dependence of the persistence probability on the system size and the sampling time is shown to be described by a simple scaling form

scaling properties of the surface of the eden model in d 2 3 4 the surface of the eden model is investigated numerically by finite size scaling using a strip geometry three different versions are studied and it shows that the one mostly used previously exhibits strong finite size corrections in two dimensions it is found that the surface thickness simply grows as the square root of the width of the strip for infinitely long strips this result as well as the results in d 3 and d 4 suggest that the surface of the eden shares some properties with the equilibrium models used to describe the roughening transition moreover it is found that the surface thickness scales differently with the height of the cluster for infinitely large strips

is it really possible to grow isotropic on lattice diffusion limited aggregates in a recent paper bogoyavlenskiy v a 2002 j phys a math gen 35 2533 an algorithm aiming to generate isotropic clusters of the on lattice diffusion limited aggregation dla model was proposed the procedure consists of aggregation probabilities proportional to the squared number of occupied sites k2 in the present work we analysed this algorithm using the noise reduced version of the dla model and large scale simulations in the noiseless limit instead of isotropic patterns a 45 30 rotation in the anisotropy directions of the clusters grown on square triangular lattices was observed a generalized algorithm in which the aggregation probability is proportional to k was proposed the exponent has a nonuniversal critical value c for which the patterns generated in the noiseless limit exhibit the original axial anisotropy for c the values c 1 395 0 005 and c 0 82 0 01 were found for square and triangular lattices respectively moreover large scale simulations show that there is a nontrivial relation between the noise reduction and anisotropy direction the case 2 bogoyavlenskiy s rule is an example where the patterns exhibit the axial anisotropy for small and the diagonal one for large noise reduction

solving second order matrix differential equations with regular singular points avoiding the increase of the problem dimension in this paper we propose a method for solving second order matrix differential systems of the form t 2x ta t x b t x 0 where a and b are analytic matrix functions in a neighborhood of t 0 series solutions of the problem are constructed without increasing the problem dimension by introducing the concept of a fundamental set of solutions of the above equation an analogous result to the frobenius theorem to solve the corresponding scalar equation is presented

anomalous scaling in a nonlocal growth model in the kardar parisi zhang universality class we study the interface dynamics of a discrete model previously shown a s anchez m j bernal and j m riveiro phys rev e 50 r2427 1994 to quantitatively describe electrochemical deposition experiments the model allows for a finite density of biased random walkers which irreversibly stick onto a substrate there is no surface diffusion extensive numerical simulations indicate that the interface dynamics is unstable at early times but asymptotically displays the scaling of the kardar parisi zhang universality class during the time interval in which the surface is unstable its power spectrum is anomalous hence the behaviors at length scales smaller than or comparable with the system size are described by different roughness exponents these results are expected to apply to a wide range of electrochemical deposition experiments

stochastic equations for simple discrete models of epitaxial growth we derive continuous stochastic equations governing the asymptotic behavior of growth from a master equation for discrete growth models with local relaxation we consider several simple models of epitaxial growth the family the wolf villain and the das sarma tamborenea models and their modifications i n 1 11 dimensions we derive for each model the corresponding langevin equation and identify leading terms that determine the universality class our results for models with local relaxation are in agreement with recent computer simulations the applicability of the method in 211 dimensions is demonstrated in the case of the family model problems of the procedure in particular regularization in the continuous limit are discussed s1063 651x 96 00710 6

noise reduction in eden models ii surface structure and intrinsic width for pt i see ibid vol 20 p 257 1987 the authors suggest a picture of the intrinsic surface width in eden models and show that it is a major source of corrections to scaling of the surface roughness using the multiple hit noise reduction method they can control the intrinsic width and thereby improve the scaling behaviour systematically as is demonstrated in detailed calculations on the square lattice they calculate the number of excess perimeter sites as a function of time and find that its asymptotic value decays with a power law as a function of increasing hitting number substrate effects and anisotropy become more apparent if noise reduction is applied

analytic solutions of coupled second order delay differential equations abstract in this paper initial value problems for systems of second order delay differential equations with variable coefficients are treated by means of a combined use of the method of steps and the method of frobenius the analytic solution of the problem is constructed

explicit solution of systems of second order differential difference equations abstract in this paper systems of second order differential difference equations are studied by using the concept of co solution of certain associated algebraic matrix equations an explicit solution of initial value problems for second order differential difference systems is constructed

noise reduction in eden models i the authors adapt the multiple hit method of noise reduction introduced earlier for diffusion limited growth to eden models a and c on the square lattice the dynamic scaling is improved considerably they obtain 0 33 or 0 015 model a for the dynamic exponent beta of surface roughening with relatively small computing effort results for model c support universality

the behavior of solutions of second order delay differential equations in this paper we study the behavior of solutions of second order delay differential equation y t p1y t p2y t q1y t q2y t where p1 p2 q1 q2 are real numbers is positive real number a basic theorem on the behavior of solutions is established as a consequence of this theorem a stability criterion is obtained

stochastic boundary control design for timoshenko beams with large motions abstract this paper considers modeling and boundary control of timoshenko beams with large motions under both deterministic and stochastic external loads the original nonlinear partial differential equations governing motion of the beams are derived and used in the control design the control design is based on the lyapunov direct method the proposed controllers guarantee globally practically k exponentially p stability of the beam motions at the reference state well posedness and stability are analyzed based on a lyapunov type theorem developed to study well posedness and stability for a class of stochastic evolution systems in hilbert space simulation results are included to illustrate the effectiveness of the proposed control design

boundary control of a timoshenko beam system with input dead zone in this paper boundary control is designed for a timoshenko beam system with the input dead zone by the hamilton s principle the dynamics of the timoshenko beam system is represented by a distributed parameter model with two partial differential equations and four ordinary differential equations the bounded part is separated from the input dead zone and then forms the disturbance like term together with the boundary disturbance which finally acts on the timoshenko beam system boundary control based on the lyapunov s direct method is proposed to ensure the timoshenko beam converge into a small neighbourhood of zero where stability of the system is also analysed besides the existence and uniqueness of the solution of the timoshenko beam system are proved simulations are provided to reveal the applicability and effectiveness of the proposed control scheme

on the solutions of a system of linear retarded and advanced differential equations by the bessel collocation approximation in this study we present a numerical approximation for the solutions of the system of high order linear retarded and advanced differential equations with variable coefficients under the mixed conditions this method is based on taking the truncated bessel expansion of the functions in the retarded and advanced differential equation system by the aid of the matrix operations and the collocation points the problem is transformed into a matrix equation with the unknown bessel coefficients by solving this matrix equation the unknown coefficients of the approximate solutions are computed in addition examples that illustrate the pertinent features of the method are presented and the results of this investigation are discussed

wulff construction and anisotropic surface properties of two dimensional eden clusters a relation between the shape of eden clusters and the number of perimeter sites per unit area of the surface is derived which is analogous to the wulff construction of equilibrium shapes in thermodynamic systems new data are presented for the surface width and the surface skewness of eden clusters grown on a square lattice the width depends on the average orientation of the surface with respect to the underlying lattice its corrections to scaling are discussed the skewness has unexpected changes of sign

stabilization of exact nonlinear timoshenko beams in space by boundary feedback abstract boundary feedback controllers are designed to stabilize timoshenko beams with large translational and rotational motions in space under external disturbances the exact nonlinear partial differential equations governing motion of the beams are derived and used in the control design the designed controllers guarantee globally practically asymptotically and locally practically exponentially stability of the beam motions at the reference state the control design well posedness and stability analysis are based on various relationships between the earth fixed and body fixed coordinates sobolev embeddings and a lyapunov type theorem developed to study well posedness and stability for a class of evolution systems in hilbert space simulation results are included to illustrate the effectiveness of the proposed control design

monte carlo approach to dendritic growth the connection between diffusion limited aggregation and the equations of dendritic growth is critically examined a different type of monte carlo simulation is proposed and used to construct two dimensional dendrite like patterns the wavelength occurring for short times is in good agreement with the linear stability analysis the time dependence of the characteristic wavelengths is also determined

scaling cumulant ratios and height distribution of ballistic deposition in 3 1 and 4 1 dimensions we investigate the origin of the scaling corrections in ballistic deposition models in high dimensions using the method proposed by alves et al phys rev e 90 052405 2014 in d 2 1 dimensions where the intrinsic width associated with the fluctuations of the height increments during the deposition processes is explicitly taken into account in the present work we show that this concept holds for d 3 1 and 4 1 dimensions we have found that growth and roughness exponents and dimensionless cumulant ratios are in agreement with other models presenting small finite time corrections to the scaling that in principle belong to the kardar parisi zhang kpz universality class in both d 3 1 and 4 1 our results constitute further evidence that the upper critical dimension of the kpz class if it exists is larger than 4

stabilisation of timoshenko beam system with a tip payload under the unknown boundary external disturbances this paper is concerned with the boundary stabilisation of a timoshenko beam with a tip payload under the boundary external disturbances nonlinear feedback control laws are designed to reduce the effects of the external disturbances since the controlled system is nonlinear the well posedness of the nonlinear closed loop system is investigated using the theory of nonlinear maximal monotone operators and the variational principle in addition we show the exponential stability of the nonlinear controlled system using the lyapunov direct method in the end the numerical simulations are displayed to illustrate the effectiveness of the proposed boundary controls

morphology of the interfacial patterns growing from unstable initial states in crystal growth models using the walsh fourier transform of the interface function the author introduces a new method for the analysis of the morphology of the complex interfacial patterns evolving with time on discrete lattices in a wide class of physical systems including crystal growth models for the crystal growth models he also generalises an old technique for characterising the interfacial patterns on small length scales to patterns evolving from initial states far from equilibrium

stochastic burgers and kpz equations from particle systems we consider two strictly related models a solid on solid interface growth model and the weakly asymmetric exclusion process both on the one dimensional lattice it has been proven that in the diffusive scaling limit the density field of the weakly asymmetric exclusion process evolves according to the burgers equation and the fluctuation field converges to a generalized ornstein uhlenbeck process we analyze instead the density fluctuations beyond the hydrodynamical scale and prove that their limiting distribution solves the non linear burgers equation with a random noise on the density current for the solid on solid model we prove that the fluctuation field of the interface profile if suitably rescaled converges to the kardar parisi zhang equation this provides a microscopic justification of the so called kinetic roughening i e the non gaussian fluctuations in some non equilibrium processes our main tool is the cole hopf transformation and its microscopic version we also develop a mathematical theory for the macroscopic equations

morphology and dynamic scaling analysis of cell colonies with linear growth fronts the growth of linear cell colony fronts is investigated from the morphology of cell monolayer colonies the cell size and shape distribution the front displacement velocity and the dynamic scaling analysis of front roughness fluctuations at the early growth stages colony patterns consist of rather ordered compact domains of small cells whereas at advanced stages an uneven distribution of cells sets in and some large cells and cells exhibiting large filopodia are produced colony front profiles exhibit overhangs and behave as fractals with the dimension d f 1 25 0 05 the colony fronts shift at 0 22 0 02 m min 1 average constant linear velocity and their roughness w increases with time t dynamic scaling analysis of experimental and overhang corrected growth profile data shows that w versus system width l log log plots collapse to a single curve when l exceeds a certain threshold value l o a width corresponding to the average diameter of few cells then the influence of overhangs on the roughness dynamics becomes negligible and a growth exponent 0 33 0 02 is derived from the structure factor analysis of overhang corrected profiles a global roughness exponent s 0 50 0 05 is obtained for l 200 m this set of exponents fulfills the family vicsek relationship it is consistent with the predictions of the continuous kardar parisi zhang model

exact and approximate solutions of second order including function delay differential equations with variable coefficients by means of the method of steps and the method of power series the exact solution of the initial value problem for coupled second order delay differential equations with variable coefficients is constructed then in a bounded domain a finite analytic solution with error bounds is provided

possible origin for the experimental scarcity of kpz scaling in non conserved surface growth abstract the kardar parisi zhang kpz equation is generically expected to describe the scaling properties of rough surfaces growing in the absence of conservation laws however very few experimental realizations are known of this universality class here we focus on the role of instabilities whether of diffusional origin or other as physical mechanisms hindering the observation of kpz scaling examples are drawn from various growth processes such as electrochemical deposition ecd chemical vapor deposition cvd and erosion by ion beam sputtering we moreover consider an interface equation which starting from the corresponding constitutive equations can be derived to describe growth by either ecd or cvd depending on the interpretation of the quantities appearing this approach makes contact with phenomenological parameters and suggests that a more generic description of non conserved growth may be provided by the kuramoto sivashinsky equation and generalizations thereof in this case the experimental scarcity of kpz scaling would be due to exceedingly long transients determined by the instabilities that occur

dynamic scaling and phase transitions in interface growth abstract the dynamic scaling approach is an effective tool for understanding the temporal evolution of fluctuating interfaces the surface width w obeys the scaling form w l t l t l where and are exponents which characterize how the surface width grows with the length scale l and the time t applications of dynamic scaling to a number of surface growth models are discussed the results of a large scale simulation of the ballistic deposition model in three dimensions are presented and compared with recent conjectures the question of universality in interface growth is addressed and a finite temperature generalization of the restricted solid on solid model is studied this model appears to undergo a phase transition from the usual rough phase at high temperatures to a new phase at low temperatures numerical solutions of the generalized langevin equation indicate that there is no phase transition in 2 1 dimensions thus the relation between the continuum equation and the discrete models is still an open question

modeling stabilization and control of serially connected beams many flexible structures consist of a large number of components coupled end to end in the form of a chain in this paper we consider the simplest type of such structures which is formed by n seri

the surface statistics of a granular aggregate the problem of the surface fluctuations in a settled granular material is posed a simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of langevin equations for the fourier modes of the surface are derived these equations imply that the fourier amplitudes behave like the velocities of a set of independent brownian particles we show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random the divergence being removed by a more accurate description of the settling material for example by having the granules fall through a sieve

numerical solution of the kardar parisi zhang equation in one two and three dimensions abstract on a course grained level a family of microscopic growth processes may be described by a stochastic differential equation which is solved numerically for surface dimensions d 1 2 and 3 dimensional analysis shows that the spatial discretization parameter has the meaning of an effective coupling constant the numerical stability of the euler integration scheme is discussed for the strong coupling exponents defined by surface width time the following effective values were obtained d 1 0 330 0 004 and d 2 0 24 0 005 considering the width and its ensemble fluctuations at constant dimensionless time the transition between strong and weak coupling phases is located in d 3 for the largest coupling for which reliable data are available we obtain an effective exponent close to the best estimates on discrete models d 3 0 17