surface and bulk properties of deposits grown with a bidisperse ballistic deposition model we study roughness scaling of the outer surface and the internal porous structure of deposits generated with the three dimensional bidisperse ballistic deposition bbd in which particles of two sizes are randomly deposited systematic extrapolation of roughness and dynamical exponents and the comparison of roughness distributions indicate that the top surface has kardar parisi zhang kpz scaling for any ratio f of the flux between large and small particles a scaling theory predicts the characteristic time of the crossover from random to correlated growth in bbd and provides relations between the amplitudes of roughness scaling and f in the kpz regime the porosity of the deposits monotonically increases with f and scales as f 1 2 for small f which is also explained by the scaling approach and illustrates the possibility of connecting surface growth rules and bulk properties the suppression of relaxation mechanisms in bbd enhances the connectivity of the deposits when compared to other ballisticlike models so that they percolate down to f ensuremath approx 0 05 the fractal dimension of the internal surface of the percolating deposits is d f ensuremath approx 2 9 which is very close to the values in other ballistic like models and suggests universality among these systems

dynamic properties in a family of competitive growing models the properties of a wide variety of growing models generically called x rd involving the deposition of particles according to competitive processes such that a particle is attached to the aggregate with probability p following the mechanisms of a generic model x that provides the correlations and at random random deposition rd with probability 1 p are studied by means of numerical simulations and analytic developments the study comprises the following x models ballistic deposition random deposition with surface relaxation das sarma tamboronea kim kosterlitz lai das sarma wolf villain large curvature and three additional models that are variants of the ballistic deposition model it is shown that after a growing regime the interface width becomes saturated at a crossover time tx2 that by fixing the sample size scales with p according to tx2 p proportional variant p y p 0 where is an exponent also the interface width at saturation wsat scales as wsat p proportional variant p delta p 0 where delta is another exponent it is proved that in any dimension the exponents delta and y obey the following relationship delta y beta rd where beta rd 1 2 is the growing exponent for rd furthermore both exponents exhibit universality in the p 0 limit by mapping the behavior of the average height difference of two neighboring sites in discrete models of type x rd and two kinds of random walks we have determined the exact value of the exponent delta when the height difference between two neighbouring sites corresponds to a random walk that after walking steps returns to a distance from its initial position that is proportional to the maximum distance reached random walk of type a one has delta 1 2 on the other hand when the height difference between two neighboring sites corresponds to a random walk that after steps moves steps towards the initial position random walk of type b one has delta 1 finally by linking four well established universality classes namely edwards wilkinson kardar parisi zhang linear molecular beam epitaxy mbe and nonlinear mbe with the properties of type a and b of random walks eight different stochastic equations for all the competitive models studied are derived

system structure and singular control the general continuous time linear quadratic control problem is considered it is shown that recently developed linear system theoretic properties and algorithms play an important role in solving this singular control problem

growth models and the question of universality classes in the past many papers have appeared which simulated surface growth with different growth models the results showed that if models differed only slightly in their growth rules the resulting surfaces may belong to different universality classes i e they are described by different differential equations in the present paper we describe a mapping of growth rules to differential operators and give plausibility arguments for this mapping we illustrate the validity of our theory by applying it to published results

width distribution for random walk interfaces roughening of a one dimensional interface is studied under the assumption that the interface configurations are continuous periodic random walks the distribution of the square of the width of interface mathit w 2 is found to scale as p mathit w 2 mathit w 2 mathrm mathrm ensuremath 1 ensuremath phi mathit w 2 mathit w 2 where mathit w 2 is the average of mathit w 2 we calculate the scaling function ensuremath phi x exactly and compare it both to exact enumerations for a discrete slope surface evolution model and to ensuremath phi s obtained in monte carlo simulations of equilibrium and driven interfaces of chemically reacting systems

roughness distribution of multiple hit and long surface diffusion length noise reduced discrete growth models abstract conventionally the universality class of a discrete growth model is identified via the scaling of interface width this method requires large scale simulations to minimize finite size effects on the results the multiple hit noise reduction techniques m 1 nrt and the long surface diffusion length noise reduction techniques l 1 nrt have been used to promote the asymptotic behaviors of the growth models lately an alternative method involving comparison of roughness distribution in the steady state has been proposed in this work the roughness distribution of the 2 1 dimensional das sarma tamborenea dt wolf villain wv and larger curvature lc models with and without nrts are calculated in order to investigate effects of the nrts on the roughness distribution additionally effective growth exponents of the noise reduced 2 1 dimensional dt wv and lc models are also calculated our results indicate that the nrts affect the interface width both in the growth and the saturation regimes in the steady state the nrts do not seem to have any impact on the roughness distribution of the dt model but it significantly changes the roughness distribution of the wv and lc models to the normal distribution curves

existence and comparison theorems for algebraic riccati equations for continuous and discrete time systems abstract we discuss two comparison theorems for algebraic riccati equations of the form xbr 1 b x x a br 1 c a br 1 c x q c r 1 c 0 simultaneously we give sufficient conditions to obtain the existence of the maximal hermitian solution of a riccati equation from the existence of a hermitian solution of a second riccati equation further similar results are given for discrete algebraic riccati equations

kinetic roughening with power law waiting time distribution we introduce a surface growth model where the elementary events are characterized by a waiting time distribution p t exact relations to directed polymer statistics and to continuous time random walk problems are established for p t i the behaviour is similar to that of the zhang model where rare event dominated kinetic roughening occurs due to a power law noise in the surface increments a careful correction to scaling analysis of our numerical results in 1 1 dimensions indicates universality with the zhang model for fixed values of p

the crossover phenomena in surface growth models with height dependent noise abstract in this paper we consider several known growth processes with height dependent noise this type of noise is interesting from a theoretical standpoint for example it paves the way to the derivation of the exact height distribution of the kpz equation through the hopf cole transformation in addition it may have implications for experimental growth processes using numerical methods we observe that adding such a noise to different growth processes can change their universality class or ruin the scaling laws in the case of mullins herring equation a two fold cross over is observed

interface depinning in a disordered medium numerical results abstract we propose a lattice model to study the dynamics of a driven interface in a medium with random pinning forces the critical exponents characterizing the depinning transition are determined numerically in 1 1 and 2 1 dimensions our findings are compared with recent numerical and analytical results for a langevin equation with quenched noise which is expected to be in the same universality class

roughness fluctuations roughness exponents and the universality class of ballistic deposition abstract in order to estimate roughness exponents of interface growth models we propose the calculation of effective exponents from the roughness fluctuation in the steady state we compare the finite size behavior of these exponents and the ones calculated from the average roughness w 2 for two models in the 2 1 dimensional kardar parisi zhang kpz class and for a model in the 1 1 dimensional villain lai das sarma vlds class the values obtained from provide consistent asymptotic estimates eventually with smaller finite size corrections for the vlds nonlinear molecular beam epitaxy class we obtain 0 93 0 01 improving previous estimates we also apply this method to two versions of the ballistic deposition model in two dimensional substrates in order to clarify the controversy in terms of its universality class raised by numerical results and a recent derivation of its continuous equation effective exponents calculated from suggest that both versions are in the kpz class additional support for this conclusion is obtained by a comparison of the full roughness distributions of these models and the distribution of other discrete kpz models

surface growth and crossover behaviour in a restricted solid on solid model the authors describe results of numerical simulations of growth in a restricted solid on solid model they first extract the exponent beta by comparing the surface width w t approximately tbeta with a spatially averaged height correlation function g t the latter is shown to give a more accurate estimate for beta even for relatively small systems the exponent x is obtained from the saturation of the interface fluctuations in the late time regime their results lead to a conjecture of dimension dependent exponents as beta d 1 d 1 x d 2 d 2 in addition they study time dependent crossover phenomena by relaxing the local height constraint and using a noise reduction method in the model they demonstrate how the effect of such crossover effects may lead to spurious values of the growth exponents finally they discuss their results in relation to other discrete models and the continuum growth equations

symmetry based determination of space time functions in nonequilibrium growth processes we study the space time correlation and response functions in nonequilibrium growth processes described by linear stochastic langevin equations exploiting exclusively the existence of space and time dependent symmetries of the noiseless part of these equations we derive expressions for the universal scaling functions of two time quantities which are found to agree with the exact expressions obtained from the stochastic equations of motion the usefulness of the space time functions is illustrated through the investigation of two atomistic growth models the family model and the restricted family model which are shown to belong to a unique universality class in 1 1 and 2 1 space dimensions this corrects earlier studies which claimed that in 2 1 dimensions the two models belong to different universality classes

stochastic linear quadratic control via primal dual semidefinite programming we study stochastic linear quadratic lq optimal control problems over an infinite time horizon allowing the cost matrices to be indefinite we develop a systematic approach based on semidefinite programming sdp a central issue is the stability of the feedback control we show that this can be effectively examined through the complementary duality of the sdp furthermore we establish several implication relations among the sdp complementary duality the generalized riccati equation and the optimality of the lq control problem based on these relations we propose a numerical procedure that provides a thorough treatment of the lq control problem via primal dual sdp it identifies a stabilizing feedback control that is optimal or determines that the problem possesses no optimal solution for the latter case we develop an epsilon approximation scheme that is asymptotically optimal

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

kinetic roughening global quantities and fluctuation dissipation relations abstract growth processes and interface fluctuations can be studied through the properties of global quantities we here discuss a global quantity that not only captures better the roughness of an interface than the widely studied surface width but that is also directly conjugate to an experimentally accessible parameter thereby allowing us to study in a consistent way the global response of the system to a global change of external conditions exploiting the full analyticity of the linear edwards wilkinson and mullins herring equations we study in detail various two time functions related to that quantity this quantity fulfills the fluctuation dissipation theorem when considering steady state equilibrium fluctuations

linear matrix inequalities riccati equations and indefinite stochastic linear quadratic controls this paper deals with an optimal stochastic linear quadratic lq control problem in infinite time horizon where the diffusion term in dynamics depends on both the state and the control variables in contrast to the deterministic case we allow the control and state weighting matrices in the cost functional to be indefinite this leads to an indefinite lq problem which may still be well posed due to the deep nature of uncertainty involved the problem gives rise to a stochastic algebraic riccati equation sare which is however fundamentally different from the classical algebraic riccati equation as a result of the indefinite nature of the lq problem to analyze the sare we introduce linear matrix inequalities lmis whose feasibility is shown to be equivalent to the solvability of the sare moreover we develop a computational approach to the sare via a semi definite programming associated with the lmis finally numerical experiments are reported to illustrate the proposed approach

multifractal behavior of the surfaces evolved with surface relaxation a discrete model exhibiting conserved dynamics with nonconserved noise involving particles of different nature termed as linear and nonlinear is proposed here the morphology of the surface has been studied with different abundances of these particles the saturated surface slowly evolved from a lower contribution of nonlinear particles to a higher contribution of nonlinear particles splits into four distinct scaling regimes with three crossover lengths each regime is characterized by different scaling property it is shown that when the contribution of the nonlinear particles crosses a critical value the surface morphology shows a linear nonlinear phase transition the roughness exponent in a nonlinear regime is well compared with that of the continuum nonlinear equation in a molecular beam epitaxy mbe class as well as a mbe motivated discrete model

phase separation in a single step growth model with surface diffusion we consider a one dimensional solid on solid growth model in which the nearest neighbour height differences are restricted to take the values deposition occurs at local minima with probability f while diffusion moves of single adatoms within a layer occur with probability 1 f interlayer transport and detachment from step edges is suppressed for the stationary distribution of the model is known hence the growth induced surface current can be computed analytically for small diffusion rates in the opposite diffusion dominated limit a description in terms of step flow is possible for slopes larger than a critical slope for smaller slopes the surface phase separates into regions of slope the stationary domain size diverges for as where we suggest that the large scale behaviour in this limit can be described by the noisy kuramoto sivashinsky equation in its noise dominated regime

a direct mapping between eden growth model and directed polymers in random media on the basis of preserving required symmetries and capturing the essential ingredients the scaling properties of the frontier of eden model clusters 1961 have been suggested by kardar et al 1986 to be governed in the continuum limit by a burger s equation with noise the authors show that such a correspondence is exact by mapping explicitly the eden model onto the problem of the conformation of a directed polymer in a random medium at zero temperature the latter model has been shown to be itself in correspondence with burgers equations in addition this mapping allows them to have access to the distribution of noise to be included in burgers equation to exactly reproduce the eden growth model finally this implies that the eden model always shows the same universal behaviour in contrast to a recently found breakdown of universality for the directed polymer problem in a very disordered medium

surface pattern formation and scaling described by conserved lattice gases we extend our 2 1 dimensional discrete growth model odor et al phys rev e 79 021125 2009 with conserved local exchange dynamics of octahedra describing surface diffusion a roughening process was realized by uphill diffusion and curvature dependence by mapping the slopes onto particles two dimensional nonequilibrium binary lattice model emerges in which the smoothing or roughening surface diffusion can be described by attracting or repelling motion of oriented dimers the binary representation allows simulations on very large size and time scales we provide numerical evidence for mullins herring or molecular beam epitaxy class scaling of the surface width the competition of inverse mullins herring diffusion with a smoothing deposition which corresponds to a kardar parisi zhang kpz process generates different patterns dots or ripples we analyze numerically the scaling and wavelength growth behavior in these models in particular we confirm by large size simulations that the kpz type of scaling is stable against the addition of this surface diffusion hence this is the asymptotic behavior of the kuramoto sivashinsky equation as conjectured by field theory in two dimensions but has been debated numerically if very strong normal surface diffusion is added to a kpz process we observe smooth surfaces with logarithmic growth which can describe the mean field behavior of the strong coupling kpz class we show that ripple coarsening occurs if parallel surface currents are present otherwise logarithmic behavior emerges

lq control of descriptor systems by cancelling structure at infinity this paper presents results concerning lq control of arbitrary descriptor systems and a numerical algorithm for achieving it the algorithm consists of two steps the first step is using the silverman algorithm orthogonal version transformation of the problem of lq control of descriptor system into a problem of lq control of a strictly proper system with singular or non singular new matrix 22 if new 22 is singular we perform the second step i e solving the lq singular control problem using again the silverman algorithm regarding the existing results on the lq singular control problem we have new results a counter example that this problem may not have a stable solution most general solvability conditions with or without stability and a new numerical algorithm based on using orthogonal matrices when stabilizability conditions are satisfied the algorithm places simultaneously stable poles in the closed loop system we show that the traditional riccati equation associated to this proble

the role of the dissipation matrix in singular optimal control the optimal cost in the regular stationary linear quadratic optimal control problem is given by the maximal solution of an algebraic riccati equation this solution minimizes the rank of a certain matrix which we call the dissipation matrix the rank minimization problem is also meaningful in the singular case does it provide the optimal cost for the singular control problem this question was posed by j c willems in 1971 the answer is yes

dynamic scaling in thin film growth with irreversible step edge attachment we study dynamic scaling in a model with collective diffusion cd of isolated atoms in terraces and irreversible aggregation at step edges simulations are performed in two dimensional substrates with several diffusion to deposition ratios r identical with d f data collapse of scaled roughness distributions confirms that this model is in the class of the fourth order nonlinear growth equation by villain lai and das sarma vlds with negligible finite size effects while estimates of scaling exponents show some discrepancies this result is consistent with the prediction of a recent renormalization group approach and improves previous numerical works on related models the roughness follows dynamic scaling as w lalpha r1 2f xi l with correlation length xi rt 1 z where z is the dynamic exponent we also propose a limited mobility lm model where the incident atom executes up to g steps before a new atom is adsorbed and irreversibly aggregates at step edges this model is also shown to belong to the vlds class the size of the plateaus in the film surface increases as g1 2 and the lateral correlation scales as g1 2t1 z the time evolution of the roughness reproduces that of the cd model if an equivalent parameter g approximately r2 z is chosen this suggests the possibility of using lm models with tunable diffusion length to simulate processes with simultaneous diffusion of many atoms a scaling approach is used to justify exponent values and dynamic relations for both models including the significant decrease of surface roughness as r or g increases

nonuniversal effects in mixing correlated growth processes with randomness interplay between bulk morphology and surface roughening to construct continuum stochastic growth equations for competitive nonequilibrium surface growth processes of the type rd x that mixes random deposition rd with a correlated growth process x we use a simplex decomposition of the height field a distinction between growth processes x that do and do not create voids in the bulk leads to the definition of the effective probability p eff of the process x that is a measurable property of the bulk morphology and depends on the activation probability p of x in the competitive process rd x the bulk morphology is reflected in the surface roughening via nonuniversal prefactors in the universal scaling of the surface width that scales in p eff the equation and the resulting scaling are derived for x in either a kardar parisi zhang or edwards wilkinson universality class in 1 1 dimensions and are illustrated by an example of x being a ballistic deposition we obtain full data collapse on its corresponding universal scaling function for all p 0 1 we outline the generalizations to 1 n dimensions and to many component competitive growth processes

cluster structure of the eden model and directed polymers in a random potential the cluster structures of the eden model and directed polymers in a random potential are described the heights hs and widths ws of each cluster grows as hs approximately sv and ws approximately sv perpendicular to with v sub z d 1 z and vperpendicular to 1 d 1 z in d dimensions where s is the size of the cluster and z is the dynamic critical exponent generalization to include the cluster size distribution is discussed

interface growth with competing surface currents the authors examine the dynamics of interface growth under the combined influence of a stabilizing and a destabilizing surface current in 1 1 dimensions it has been shown that the surface is weakly stabilized if a newly deposited particle can move locally to maximize the total number of nearest neighbour contacts with the surface curvature driven current the introduction of a weak destabilizing surface tension term results in an almost periodic grooved surface the width of the surface grows linearly in time and does not reach a steady state it appears that such a formation cannot be described by a continuous langevin equation

renormalization of stochastic lattice models basic formulation we describe a general method for the multiscale analysis of stochastic lattice models beginning with a lattice langevin formulation of site fluctuations we derive stochastic partial differential equations by regularizing the transition rules of the model subsequent coarse graining is accomplished by calculating renormalization group rg trajectories from initial conditions determined by the regularized atomistic models the rg trajectories correspond to hierarchies of continuum equations describing lattice models over expanding length and time scales these continuum equations retain a quantitative connection over different scales as well as to the underlying atomistic dynamics this provides a systematic method for the derivation of continuum equations from the transition rules of lattice models for any length and time scales as an illustration we consider the one dimensional 1d wolf villain wv model europhys lett 13 389 1990 the rg analysis of this model which we develop in detail is generic and can be applied to a wide range of conservative lattice models the rg trajectory of the 1d wv model shows a complex crossover sequence of linear and nonlinear stochastic differential equations which is in excellent agreement with kinetic monte carlo simulations of this model we conclude by discussing possible applications of the multiscale method described here to other nonequilibrium systems

non equilibrium critical behaviour on fractal lattices a simple one component surface reaction model exhibiting a critical point has been studied on deterministic fractal lattices with fractal dimension 1 df 2 results from time dependent simulations show a change in the value of the critical exponents with df two of the exponents interpolate very nicely between the values in one and two dimensions

a primal dual semi definite programming approach to linear quadratic control we study a deterministic linear quadratic lq control problem over an infinite horizon without the restriction that the control cost matrix r or the state cost matrix q be positive definite we develop a general approach to the problem based on semi definite programming sdp and related duality analysis we show that the complementary duality condition of the sdp is necessary and sufficient for the existence of an optimal lq control under a certain stability condition which is satisfied automatically when q is positive definite when the complementary duality does hold an optimal state feedback control is constructed explicitly in terms of the solution to the primal sdp

numerical study of discrete models in the class of the nonlinear molecular beam epitaxy equation we study numerically some discrete growth models belonging to the class of the nonlinear molecular beam epitaxy equation or the villain lai das sarma vlds equation the conserved restricted solid on solid model crsos with maximum height differences delta h max 1 and delta h max 2 was analyzed in substrate dimensions d 1 and d 2 the das sarma and tamborenea dt model and a competitive model involving random deposition and crsos deposition were studied in d 1 for the crsos model with delta h max 1 we obtain the more accurate estimates of scaling exponents in d 1 roughness exponent alpha 0 94 0 02 and dynamical exponent z 2 88 0 04 these estimates are significantly below the values of one loop renormalization for the vlds theory which confirms janssen s proposal of the existence of higher order corrections the roughness exponent in d 2 is very near the one loop result alpha 2 3 in agreement with previous works the moments w n of orders n 2 3 4 of the height distribution were calculated for all models and the skewness s triple bond w3 w 3 2 2 and the kurtosis q triple bond w4 w 2 2 3 were estimated at the steady states the crsos models and the competitive model have nearly the same values of s and q in d 1 which suggests that these amplitude ratios are universal in the vlds class the estimates for the dt model are different possibly due to their typically long crossover to asymptotic values results for the crsos models in d 2 also suggest that those quantities are universal

nonlinear conditions for weighted composition operators between lipschitz algebras abstract let t lip 0 x lip 0 y be a surjective map between pointed lipschitz algebras where x and y are compact metric spaces on the one hand we prove that if t satisfies the non symmetric norm multiplicativity condition t f t g 1 f g 1 f g lip 0 x then t is of the form t f f 1 f f lip 0 x where and are functions on y such that y 0 1 and y k 1 and y x is a base point preserving lipschitz homeomorphism on the other hand if t satisfies the weakly peripherally multiplicativity condition ran f g ran t f t g f g lip 0 x where ran f denotes the peripheral range of f then t can be expressed as t f f f lip 0 x with and as above as a consequence we obtain similar descriptions for surjective maps between lipschitz algebras lip x

unital and multiplicatively spectrum preserving surjections between semi simple commutative banach algebras are linear and multiplicative abstract let t be a surjective map from a unital semi simple commutative banach algebra a onto a unital commutative banach algebra b suppose that t preserves the unit element and the spectrum f g of the product of any two elements f and g in a coincides with the spectrum t f t g then b is semi simple and t is an isomorphism the condition that t is surjective is essential an example of a non linear and non multiplicative unital map from a commutative c algebra into itself such that t f t g f g holds for every f g are given we also show an example of a surjective unital map from a commutative c algebra onto itself which is neither linear nor multiplicative such that t f t g f g holds for every f g

generalizations of weakly peripherally multiplicative maps between uniform algebras abstract let a and b be uniform algebras on first countable compact hausdorff spaces x and y respectively for f a the peripheral spectrum of f denoted by f f f is the set of spectral values of maximum modulus a map t a b is weakly peripherally multiplicative if t f t g f g for all f g a we show that if t is a surjective weakly peripherally multiplicative map then t is a weighted composition operator extending earlier results furthermore if t 1 t 2 a b are surjective mappings that satisfy t 1 f t 2 g f g for all f g a then t 1 f t 2 1 t 1 1 t 2 f for all f a and the map f t 1 f t 2 1 is an isometric algebra isomorphism

generalized survival in equilibrium step fluctuations we investigate the dynamics of a generalized survival probability s t r defined with respect to an arbitrary reference level r rather than the average in equilibrium step fluctuations the exponential decay at large time scales of the generalized survival probability is numerically analyzed s t r is shown to exhibit simple scaling behavior as a function of system size l sampling time ensuremath delta t and the reference level r the generalized survival time scale ensuremath tau s r associated with s t r is shown to decay exponentially as a function of r

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

maps which preserve norms of non symmetrical quotients between groups of exponentials of lipschitz functions let explip x1 explip x2 be a surjective mapping where x1x1 and x2x2 are compact metric spaces we prove that if satisfies the non symmetric quotient norm condition for the uniform norm gf 1 g f 1 f g explip x1 then is of the form f y 1 y f y if y k 1 y f y if y x2 k f explip x1 where x2 x1 x2 x1 is a homeomorphism and k is a closed open subset of x2x2 on the other hand if satisfies the non symmetric quotient norm condition for the lipschitz algebra norm gf 1 gf 1 l g f 1 g f 1 l f g explip x1 we show that is of the form f y 1 y f y y x2 f explip x1 or f y 1 y f y y x2 f explip x1 where x2 x1 x2 x1 is a surjective isometry

conserved growth in a restricted solid on solid model the surface dynamics of conserved growth in a restricted solid on solid rsos model is described a randomly deposited particle is allowed to migrate to the nearest site satisfying the rsos condition the surface width the correlation function and the structure factor measurements are consistent with the lai and das sarma 1991 and villain 1991 equation delta h delta t nu del 4h lambda del 2 del h 2 eta the physical origin of the nonlinearity is also discussed

derivation of continuum stochastic equations for discrete growth models we present a formalism to derive the stochastic differential equations sdes for several solid on solid growth models our formalism begins with a mapping of the microscopic dynamics of growth models onto the particle systems with reactions and diffusion we then write the master equations for these corresponding particle systems and find the sdes for the particle densities finally by connecting the particle densities with the growth heights we derive the sdes for the height variables applying this formalism to discrete growth models we find the edwards wilkinson equation for the symmetric body centered solid on solid bcsos model the kardar parisi zhang equation for the asymmetric bcsos model and the generalized restricted solid on solid rsos model and the villain lai das sarma equation for the conserved rsos model in addition to the consistent forms of equations for growth models we also obtain the coefficients associated with the sdes

singular optimal control a geometric approach linear quadratic singular optimal control problem is solved for nonminimum phase and noninvertible systems a state space decomposition is obtained and a reduced order nonsingular subproblem is solved the optimal stabilizing input of the singular problem has been found when there are no transmission zeros on the imaginary axis

technical communique indefinite linear quadratic optimal control problem for singular discrete time system with multiple input delays an indefinite linear quadratic ilq optimal control problem is discussed for singular discrete time varying linear systems with multiple input delays the problem is transformed to the one for standard systems by normalizability decomposition an explicit controller is obtained by computing the gain of the smoothing estimation of dual systems necessary and sufficient conditions guaranteeing the existence of unique solution are given simultaneously a numerical example illustrates the presented method

stochastic equation for conserved growth in a restricted solid on solid model we apply the master equation method naturally extended for the nonlocal growth process to directly deriving the continuum stochastic equation for a conserved growth model with a restricted solid on solid condition the villain lai das sarma growth equation we obtain for the model is consistent with the result of recent numerical simulations furthermore we find that only the relaxation of the deposited particles up to the nearest neighborhood for n51 condition or the next nearest neighborhood for n 1 condition determines the scaling property and the universality class of the model and the higher neighbor hopping processes play no essential role the choice of the regularization scheme in the derivation procedure is also discussed s1063 651x 98 07604 1

roughening of the interfaces in 1 1 dimensional two component surface growth with an admixture of random deposition we simulate competitive two component growth on a one dimensional substrate of l sites one component is a poisson type deposition that generates kardar parisi zhang kpz correlations the other is random deposition rd we derive the universal scaling function of the interface width for this model and show that the rd admixture acts as a dilatation mechanism to the fundamental time and height scales but leaves the kpz correlations intact this observation is generalized to other growth models it is shown that the flat substrate initial condition is responsible for the existence of an early nonscaling phase in the interface evolution the length of this initial phase is a nonuniversal parameter but its presence is universal we introduce a method to measure the length of this initial nonscaling phase in application to parallel and distributed computations the important consequence of the derived scaling is the existence of the upper bound for the desynchronization in a conservative update algorithm for parallel discrete event simulations it is shown that such algorithms are generally scalable in a ring communication topology

maximal and minimal height distributions of fluctuating interfaces maximal and minimal height distributions mahd mihd of two dimensional interfaces grown with the nonlinear equations of kardar parisi zhang kpz second order and of villain lai das sarma vlds fourth order are shown to be different two universal curves may be mahd or mihd of each class depending on the sign of the relevant nonlinear term which is confirmed by results of several lattice models in the kpz and vlds classes the difference between mahd and midh is connected with the asymmetry of the local height distribution a simple exactly solvable deposition erosion model is introduced to illustrate this feature the average extremal heights scale with the same exponent of the average roughness in contrast to other correlated systems generalized gumbel distributions do not fit those mahd and mihd nor those of edwards wilkinson growth

numerical study of roughness distributions in nonlinear models of interface growth we analyze the shapes of roughness distributions of discrete models in the kardar parisi and zhang kpz and in the villain lai and das sarma vlds classes of interface growth in one and two dimensions three kpz models in d 2 confirm the expected scaling of the distribution and show a stretched exponential tail approximately as exp x0 8 with a significant asymmetry near the maximum conserved restricted solid on solid models belonging to the vlds class were simulated in d 1 and d 2 the tail in d 1 has the form exp x2 and in d 2 has a simple exponential decay but is quantitatively different from the distribution of the linear fourth order mullins herring theory it is not possible to fit any of the above distributions to those of 1 f alpha noise interfaces in contrast with recently studied models with depinning transitions

parameter free scaling relation for nonequilibrium growth processes we discuss a parameter free scaling relation that yields a complete data collapse for large classes of nonequilibrium growth processes we illustrate the power of this scaling relation through various growth models such as the competitive growth model with random deposition and random deposition with surface diffusion or the restricted solid on solid model with different nearest neighbor height differences as well as through a deposition model with temperature dependent diffusion the scaling relation is compared to the familiar family vicsek relation and the limitations of the latter are highlighted

scaling in the crossover from random to correlated growth in systems where deposition rates are high compared to diffusion desorption and other mechanisms that generate correlations a crossover from random to correlated growth of surface roughness is expected at a characteristic time t0 this crossover is analyzed in lattice models via scaling arguments with support from simulation results presented here and in other works we argue that the amplitudes of the saturation roughness and of the saturation time t x scale as t0 1 2 and t0 respectively for models with lateral aggregation which typically are in the kardar parisi zhang kpz class we show that t0 approximately p 1 where p is the probability of the correlated aggregation mechanism to take place however t0 approximately p 2 is obtained in solid on solid models with single particle deposition attempts this group includes models in various universality classes with numerical examples being provided in the edwards wilkinson ew kpz and villain lai das sarma nonlinear molecular beam epitaxy classes most applications are for two component models in which random deposition with probability 1 p competes with a correlated aggregation process with probability p however our approach can be extended to other systems with the same crossover such as the generalized restricted solid on solid model with maximum height difference s for large s moreover the scaling approach applies to all dimensions in the particular case of one dimensional kpz processes with this crossover we show that t0 approximately nu 1 and nu approximately lambda 2 3 where nu and lambda are the coefficients of the linear and nonlinear terms of the associated kpz equations the applicability of previous results to models in the ew and kpz classes is discussed

surface growth on percolation networks by a conserved noise restricted solid on solid growth model surface growth by the conserved noise restricted solid on solid model is investigated on diluted lattices i e on percolation networks that are embedded in two spatial dimensions the growth exponent and the roughness exponent are defined respectively by the mean square surface width via w 2 t t 2 and the mean square saturated width via w sat 2 l l 2 where l is the system size these are measured on both an infinite network and a backbone network and the results are compared with power counting predictions obtained using the fractional langevin equation while the monte carlo results on deterministic fractal substrates show excellent agreement with the predictions d h kim and j m kim phys rev e 84 011105 2011 the results on critical percolation networks deviate by 8 12 from these predictions