weak commutation relations of unbounded operators and applications four possible definitions of the commutation relation s t 11 of two closable unbounded operators s t are compared the weak sense of this commutator is given in terms of the inner product of the hilbert space h where the operators act some consequences on the existence of eigenvectors of two numberlike operators are derived and the partial o algebra generated by s t is studied some applications are also considered

self similarity of the branching structure in very large dla clusters and other branching fractals we study the branching structure of very large dla clusters of up to 100 million particles the horton strahler ordering of the branches in these clusters shows a relaxation towards a state with the stream numbers forming a geometric series this behaviour is compared with those of several self similar trees it indicates that dla clusters converge to topologically self similar objects

non self adjoint hamiltonians defined by riesz bases we discuss some features of non self adjoint hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a riesz basis of hilbert space among other things we give conditions under which these hamiltonians can be factorized in terms of generalized lowering and raising operators

deterministic model for left sided multifractality in generalized diffusion limited aggregation an exactly solvable deterministic model on a hierarchical lattice is presented for the left sided multifractality of the growth probability distribution in a generalized diffusion limited aggregation eta model the exactly renormalizable growth probability is given by a multiplicative process it predicts the tip behaviour the maximum growth probability is a power law and the fjord behaviour the minimum growth probability has a logarithmic singularity an analytical form of a left sided generalized dimension d q is shown for any eta

contact with friction in multi material arbitrary lagrangian eulerian formulations using x fem a contact method with friction for the multi dimensional lagrangian step in multi material arbitrary lagrangian eulerian ale formulations is presented in our previous research the extended finite element method x fem was used to create independent fields i e velocity strain rate force mass etc for each material in the problem to model contact without friction the research presented here includes the extension to friction and improvements to the accuracy and robustness of our previous study the accelerations of the multi material nodes are obtained by coupling the material force and mass fields as a function of the prescribed contact similarly the velocities of the multi material nodes are recalculated using the conservation of momentum when the prescribed contact requires it the coupling procedures impose the same nodal velocity on the coupled materials in the direction normal to their interface during the time step update as a result the overlap of materials is prevented and unwanted separation does not occur three different types of contacts are treated perfectly bonded frictionless slip and slip with friction example impact problems are solved and the numerical solutions are presented copyright 2008 john wiley sons ltd

generalized bogoliubov transformations versus d pseudo bosons we demonstrate that not all generalized bogoliubov transformations lead to d pseudo bosons and prove that a correspondence between the two can only be achieved with the imposition of specific constraints on the parameters defining the transformation for certain values of the parameters we find that the norms of the vectors in sets of eigenvectors of two related apparently non selfadjoint number like operators possess different types of asymptotic behavior we use this result to deduce further that they constitute bases for a hilbert space albeit neither of them can form a riesz base when the constraints are relaxed they cease to be hilbert space bases but remain d quasibases

a particle level set based sharp interface cartesian grid method for impact penetration and void collapse an eulerian sharp interface cartesian grid method is developed for the numerical simulation of the response of materials to impact shocks and detonations the mass momentum and energy equations are solved along with evolution equations for deviatoric stresses and equivalent plastic strain these equations are cast in eulerian conservation law form the mie gruneisen equation of state is used to obtain pressure and the material is modeled as a johnson cook solid the eno scheme is employed to capture shocks in combination with a hybrid particle level set technique to evolve sharp immersed boundaries the numerical technique is able to handle collisions between multiple materials and can accurately compute the dynamics of the immersed boundaries results of calculations for axisymmetric taylor bar impact and penetration of a tungsten rod into steel plate show good agreement with moving finite element solutions and experimental results qualitative agreement with theory is shown for the void collapse phenomenon in an impacted material containing a spherical void

an extended finite element formulation for contact in multi material arbitrary lagrangian eulerian calculations a contact method for the multi dimensional lagrangian step in multi material arbitrary lagrangian eulerian ale formulations is presented the extended finite element method x fem is used to create independent fields i e velocity strain rate force mass etc for each material in the problem the accelerations of the multi material nodes are obtained by coupling the material force and mass fields as a function of the prescribed contact similarly the velocities of the multi material nodes are recalculated using the conservation of momentum when the prescribed contact requires it the coupling procedures impose the same nodal velocity on the coupled materials in the direction normal to their interface during the time step update as a result the overlap of materials is prevented and unwanted separation does not occur three different contacts are treated perfectly bonded frictionless slip and slip with friction example impact problems are solved and the numerical solutions are presented

contact in a multi material eulerian finite element formulation in a multi material eulerian formulation for problems in solid mechanics the default interaction between the surfaces of adjacent materials is perfect bonding in contrast for the lagrangian formulation the surfaces don t interact and may pass through each other freely unless a contact algorithm is introduced to enforce the contact inequality constraints sophisticated contact algorithms have been developed for lagrangian calculations and are routinely used in large deformation applications such as automobile crashworthiness in comparison the eulerian finite element method lags far behind the lagrangian finite element method in modeling contact a natural application for the eulerian formulation is machining which includes large deformations material failure and contact of a tool with a workpiece making its simulation a challenging problem the simulation of the isolated chips involving material failure due to shear bands is used as a test problem to investigate the strength and weakness of the different approaches to implementing contact in multi material eulerian calculations

a meshfree contact detection algorithm a new contact detection algorithm is proposed which is based on the moment matrix of the meshfree interpolation this new contact detection algorithm has several advantages over conventional contact detection algorithms they are ease of implementation accuracy in detection it is scalable in parallel computations and applicable to a wide variety of problems because the moment matrix is computed in constructing meshfree approximation the algorithm is very suitable for meshfree computations though it can be used in finite element computations as well moreover such contact detection algorithm can be conveniently implemented to detect self contact both algorithmic and mathematical aspects of the contact algorithm are discussed in the paper to validate the proposed contact algorithm the taylor bar problem is computed using both meshfree method and finite element method fem to simulate a viscoplastic projectile impacting with a rigid target at high speed numerical results obtained with the meshfree contact algorithm show that this new contact algorithm can accurately predict the contact as well as separation of projectile and target in addition the numerical results obtained show distinct and detailed shear band formations occurring in the impact event

treatment of contact separation in eulerian high speed multimaterial dynamic simulations summary a frictionless contact separation treatment in a sharp interface eulerian framework is presented to handle the general situation of high speed impact and separation of materials the algorithm has been developed for an established eulerian based cartesian grid multimaterial flow code in which the interfaces are tracked in a sharp manner using a standard narrow band level set approach boundary conditions have been applied using a modified ghost fluid method for elasto plastic materials the sharp interface treatment maintains the distinct interacting interfaces without smearing the contact zone while also removing the difficulties associated with lagrangian moving mesh entities in contact separation situations the algorithm has been tested and verified against experimental and numerical results for three different problems in the high strain rate regime which involve contact separation and sliding of materials copyright 2014 john wiley sons ltd

a mixture theory for contact in multi material eulerian formulations abstract multi material eulerian methods are attractive for solving a broad range of highly nonlinear problems in solid mechanics because they permit arbitrarily large deformations and automatically allow new free surfaces to evolve many of these problems involve the contact and separation of surfaces there is an extensive literature for including contact inequality constraints in lagrangian finite element methods but little consideration has been given to contact in eulerian methods the contact forces between adjacent bodies are governed by the mixture theory in the eulerian formulation making the mixture theory the natural starting point in the treatment of the contact inequalities a mixture theory that equilibrates the traction across the material interface and limits the shear stress according to a coulomb friction law is developed

appearances of pseudo bosons from black scholes equation it is a well known fact that the black scholes equation admits an alternative representation as a schrodinger equation expressed in terms of a non self adjoint hamiltonian we show how pseudo bosons linear or not naturally arise in this context and how they can be used in the computation of the pricing kernel

evolution implementation and application of level set and fast marching methods for advancing fronts abstract a variety of numerical techniques are available for tracking moving interfaces in this review we concentrate on techniques that result from the link between the partial differential equations that describe moving interfaces and numerical schemes designed for approximating the solutions to hyperbolic conservation laws this link gives rise to computational techniques for tracking moving interfaces in two and three space dimensions under complex speed laws we discuss the evolution of these techniques the fundamental numerical approximations involved implementation details and applications in particular we review some work on three aspects of materials sciences semiconductor process simulations seismic processing and optimal structural topology design

intertwining operators for non self adjoint hamiltonians and bicoherent states this paper is devoted to the construction of what we will call exactly solvable models i e of quantum mechanical systems described by an hamiltonian h whose eigenvalues and eigenvectors can be explicitly constructed out of some minimal ingredients in particular motivated by pt quantum mechanics we will not insist on any self adjointness feature of the hamiltonians considered in our construction we also introduce the so called bicoherent states we analyze some of their properties and we show how they can be used for quantizing a system some examples both in finite and in infinite dimensional hilbert spaces are discussed

two families of superintegrable and isospectral potentials in two dimensions as an extension of the intertwining operator idea an algebraic method which provides a link between supersymmetric quantum mechanics and quantum super integrability is introduced by realization of the method in two dimensions two infinite families of superintegrable and isospectral stationary potentials are generated the method makes it possible to perform darboux transformations in such a way that in addition to the isospectral property they acquire the superintegrability preserving property symmetry generators are second and fourth order in derivatives and all potentials are isospectral with one of the smorodinsky winternitz potentials explicit expressions of the potentials their dynamical symmetry generators and the algebra they obey as well as their degenerate spectra and corresponding normalizable states are presented

random self similar river networks and derivations of generalized horton laws in terms of statistical simple scaling recent data analyses of a dozen or so large networks support the presence of simple scaling in the probability distributions of many topologic geometric and hydraulic geometric variables we have labeled them generalized horton laws in contrast to traditional horton laws which are stated only in terms of means these data sets also show that horton s bifurcation ratios are significantly larger than 4 which can not be predicted by the well known random model motivated by the need to understand these data analyses of large river networks within a common theoretical framework a new class of models with statistically self similar network topology is introduced the network construction process can be viewed as a statistical generalization of the type of a recursive process which generates many fractal geometrical objects unlike the well known random model our random channel networks do not belong to the class of binary galton watson stochastic branching processes the generalized horton laws are predicted in the limit of large horton strahler order as a scale parameter for a subclass of random self similar network models a derivation of horton s law of stream numbers as a consequence of the simple scaling of distributions of basin magnitude gives it a new theoretical significance a further subclass also exhibits tokunga self similarity which is an average property of the side tributary structure in river networks comparisons with empirical observations for three large basins analyzed here show that the generalized horton laws are well predicted by this new class of random self similar network models and analytically predicted relationships between topologic and geometric horton ratios are also seen in data

non self adjoint hamiltonians defined by generalized riesz bases bagarello inoue and trapani j math phys 55 033501 2014 investigated some operators defined by the riesz bases these operators connect with quasi hermitian quantum mechanics and its relatives in this paper we introduce a notion of generalized riesz bases which is a generalization of riesz bases and investigate some operators defined by the generalized riesz bases by changing the frameworks of the operators defined in the work of bagarello inoue and trapani

more mathematics for pseudo bosons we propose an alternative definition for pseudo bosons this simplifies the mathematical structure minimizing the required assumptions some physical examples are discussed as well as some mathematical results related to the biorthogonal sets arising out of our framework we also briefly extend the results to the so called nonlinear pseudo bosons

definition of new equivalent indices of horton strahler ratios for the derivation of the geomorphological instantaneous unit hydrograph 1 the horton strahler concept has been important in river basin geomorphology it describes scaling properties and identifies giuh but has also attracted criticisms because it depends on the threshold area s which is used to extract the channel network from digital elevation models dem on the position of the outlet and on the few number of ratios used to identify the scaling laws to overcome these limitations this paper proposes new indices independently of s and which have similar properties than the horton strahler ratios applications were conducted on seven french basins the methodology consists on analyzing the morphometric properties such as the drained area the number of sources and the length of the channel network as a function of s the results show that horton strahler ratios vary considerably with s particularly while the order length l is a staircase function of s results show that the channel network is articulated around two main nodes independent of s which are descriptors of l then we compared the properties of horton strahler laws to those obtained from self similarity analysis which enables to define new indices independent of s these indices are calculated automatically from dem have similar properties as the horton strahler ratios and are used to calculate the giuh independently of s the four new descriptors rbe rle rae and le which have similar properties as rb rl ra and l respectively are equivalent to those of horton strahler s laws and can be used as indicators of hydrological similarity for catchment comparison and regionalization

regular biorthogonal pairs and pseudo bosonic operators the first purpose of this paper is to show a method of constructing a regular biorthogonal pair based on the commutation rule ab ba i for a pair of operators a and b acting on a hilbert space h with inner product here sequences n and n in a hilbert space h are biorthogonal if n m nm n m 0 1 and they are regular if both d span n and d span n are dense in h indeed the assumptions to construct the regular biorthogonal pair coincide with the definition of pseudo bosons as originally given in f bagarello pseudobosons riesz bases and coherent states j math phys 51 023531 2010 furthermore we study the connections between the pseudo bosonic operators a b a b and the pseudo bosonic operators defined by a regular biorthogonal pair n n and an onb e of h in h inoue general theory of regular biorthogonal pairs and its physical applications e print arxiv math ph 1604 01967 the second purpose is to define and study the notion of d p

hamiltonians defined by biorthogonal sets in some recent papers studies on biorthogonal riesz bases have found renewed motivation because of their connection with pseudo hermitian quantum mechanics which deals with physical systems described by hamiltonians that are not self adjoint but may still have real point spectra also their eigenvectors may form riesz not necessarily orthonormal bases for the hilbert space in which the model is defined those riesz bases allow a decomposition of the hamiltonian as already discussed in some previous papers however in many physical models one has to deal not with orthonormal bases or with riesz bases but just with biorthogonal sets here we consider the more general concept of quasi basis and we show a series of conditions under which a definition of non self adjoint hamiltonian with purely point real spectra is still possible

nonlinear pseudo bosons in a series of recent papers the author has introduced the notion of regular pseudo bosons showing in particular that two number like operators whose spectra are n0 n 0 can be naturally introduced here we extend this construction to operators with rather more general spectra of course this generalization can be applied to many more physical systems we discuss several examples of our framework

weak commutation relations of unbounded operators nonlinear extensions we continue our analysis of the consequences of the commutation relation s t 1 where s and t are two closable unbounded operators the weak sense of this commutator is given in terms of the inner product of the hilbert space h where the operators act we also consider what we call adopting a physical terminology a nonlinear extension of the above commutation relations

geometrical multifractality of growing structures the authors study the mass distribution of fractal objects growing by subsequent addition of units to the structure it is demonstrated that in the limit of very large sizes such structures generally exhibit multifractal properties without defining a singular measure on the fractal support using the mass as a measure on the fractal for a few simple deterministic processes they give the spectrum of corresponding fractal dimensions exactly according to their results such geometrical multifractals should be very common and consist of parts which have a varying local fractal scaling of mass different from that of the whole object they demonstrate the variation of multifractal properties as a function of the increasing size in this way establishing for the calculation of multifractality an approach common in the studies of fractal properties of growing clusters

evaluation of multifidelity surrogate modeling techniques to construct closure laws for drag in shock particle interactions abstract meta or surrogate models constructed from meso scale simulations can be used in place of empirical correlations to close macro scale equations in shocked particulate flows surrogate models for drag are constructed as functions of shock mach number ma particle volume fraction reynolds number re etc the computational cost of the high fidelity meso scale simulations is a challenge in construction of surrogates in such hierarchical multi scale frameworks here multifidelity surrogate modeling techniques are evaluated as inexpensive alternatives to high fidelity surrogate models for obtaining closure laws for drag in shock particle interactions preliminary surrogates for drag as a function of ma and are constructed from ensembles of low fidelity coarse grid mesoscale computations the low fidelity surrogates are subsequently corrected using only a few n h f high fidelity computations to obtain multifidelity surrogate models the paper evaluates three different methods for correcting an initial low fidelity surrogate space mapping sm radial basis functions rbf and modified bayesian kriging mbkg of these methods mbkg is found to provide the best multi fidelity surrogate model simultaneously minimizing the computational cost and error in the constructed surrogate

fractal relation of mainstream length to catchment area in river networks institute of hydraulics university of genoa italymandelbrot s 1982 hypothesis that river length is fractal has been recently substantiated byhjelmfelt 1988 using eight rivers in missouri the fractal dimension of river length d is derived herefrom the horton s laws of network composition this results in a simple function of stream length andstream area ratios that is d max 1 2 log rl og ra three case studies are reported showing thisestimate to be coherent with measurements of d obtained from map analysis the scaling properties ofthe network as a whole are also investigated showing the fractal dimension of river network d todepend upon bifurcation and stream area ratios according to d min 2 2 log rb log ra theseresults provide a linkage between quantitative analysis of drainage network composition and scalingproperties of river networks

harmonic measure around a linearly self similar tree the authors use the concept of random multiplicative processes to help describe and understand the distribution of the harmonic measure on growing fractal boundaries the laplacian potential around a linearly self similar square koch tree is studied in detail the multiplicative nature of this potential and the consequent multifractality of the harmonic measure are discussed on prefractal stages the density d mu of the harmonic measure and the corresponding holder alpha ln d mu are well defined along the boundary except in the folds where the tangent is undefined a regularization scheme is introduced to eliminate these local effects they then consider the probability distributions p alpha d alpha of successive stages and discuss their collapse into an f alpha curve both the left and right hand sides of this curve show good convergence other studies indicate that for dla the right hand tail does not converge a brief comparison is made between the multifractality of these two cases

a reformulation of horton s laws for large river networks in terms of statistical self similarity the well known horton s laws are empirical observations on how the means of measurements for river networks and basins vary with horton strahler order it is now known that these laws are a consequence of an average sense self similarity in the bifurcation structure of river networks in this paper we present a reformulation of horton s laws which generalizes the familiar scaling of first moments or means to scaling of entire distributions we also present extensive data analysis which supports this reformulation and show that this feature is also exhibited by shreve s well known random topology model

directed recursion models for fractal growth fractals constructed by recursive processes are introduced to model growth phenomena these fractals are simultaneously directed and self similar in analogy with patterns growing under diffusion limited conditions the multifractal nature of the harmonic measure associated with laplacian interfaces is qualitatively interpreted using the models calculation of the largest singularity exponent allows one to make conclusions about the behaviour of diffusion limited aggregates

pseudo bosons for the d2 type quantum calogero model abstract in the first part of this paper we show how a simple system a 2 dimensional quantum harmonic oscillator can be described in terms of pseudo bosonic variables this apparently strange choice is useful when the natural hilbert space of the system l 2 r 2 in this case is for some reason not the most appropriate this is exactly what happens for the d 2 type quantum calogero model considered in the second part of the paper where the hilbert space l 2 r 2 appears to be an unappropriate choice since the eigenvectors of the relevant hamiltonian are not square integrable then we discuss how a certain intertwining operator arising from the model can be used to fix a different hilbert space more useful

general theory of regular biorthogonal pairs and its physical operators in this paper we introduce a general theory of regular biorthogonal sequences and its physical operators biorthogonal sequences n and n in a hilbert space h are said to be regular if span n and span n are dense in h the first purpose is to show that there exists a non singular positive self adjoint operator tf in h defined by an orthonormal basis onb f fn in h such that n tffn and n tf 1fn n 0 1 and such an onb f is unique the second purpose is to define and study the lowering operators af and bf the raising operators bf and af and the number operators nf and nf determined by the non singular positive self adjoint operator tf these operators connect with quasi hermitian quantum mechanics and its relatives this paper clarifies and simplifies the mathematical structure of this framework and minimizes the required assumptions

ghost fluid method for strong shock interactions part 2 immersed solid boundaries numerical simulation of shock waves interacting with multimaterial interface is immensely challenging particularly when the embedded interface is retained as a sharp entity the challenge lies in accurately capturing and representing the interface dynamics and the wave patterns at the interface in this regard the ghost fluid method has been successfully used to capture the interface conditions for both fluid fluid and solid fluid interfaces however the ghost fluid method results in over underheating errors when shocks impact interfaces and hence must be supplemented with numerical corrective measures to mitigate these errors such corrections typically fail for strong shock applications variants and extensions ofthe ghost fluid method have been proposed to remedy its shortcomings with mixed success in this paper the performance of approaches based on the ghost fluid method in the case of strong shocks impinging on immersed solid boundaries in compressible flows is evaluated it is found that from the viewpoint of simplicity robustness and accuracy a reflective boundary condition used in conjunction with a local riemann solver at the interface proves to be a good choice the method is found to be stable accurate and robust for wide range problems involving strong shocks interacting with embedded solid objects

some invariant biorthogonal sets with an application to coherent states abstract we show how to construct out of a certain basis invariant under the action of one or more unitary operators a second biorthogonal set with similar properties in particular we discuss conditions for this new set to be also a basis of the hilbert space and we apply the procedure to coherent states we conclude the paper considering a simple application of our construction to pseudo hermitian quantum mechanics

self similarity of the loop structure of diffusion limited aggregates the structure of fjords in diffusion limited aggregation dla clusters can be described in terms of the loop size distribution nr x which is the normalised number of loops with a neck to depth ratio x within a circle of radius r centred at the origin of the cluster the authors find from the numerical study of very large off lattice aggregates that nr x converges quickly to a limiting distribution with a well defined smallest ratio xmin larger than zero indicating the self similarity of the loop structure if the fjords are self similar i e they do not have long tube like structures one does not expect a phase transition in the multifractal spectrum of growth probabilities of typical dla clusters generated on the plain their study is essentially statistical and they cannot rule out the possibility of such rare events e g the occurrence of a few loops with anomalously small x which may result in a qualitatively different behaviour concerning the multifractal spectrum

multifractals in diffusion and aggregation abstract the origin of the multifractal features which appear in several random systems is discussed it is shown that for random fractals the multifractal features in the probability density of the diffusion can be derived rigorously and therefore its origin can be fully understood for the growth probabilities in dla it is shown that a novel self similar model for the structure of the branches of dla leads to a multifractal behavior for the positive moments and a logarithmic singularity for the minimum growth probability this behavior is strongly supported by recent numerical simulations

new results for self similar trees with applications to river networks in a little known series of papers beginning in 1966 tokunaga introduced an infinite class of tree graphs based on the strahler ordering scheme as recognized by tokunaga 1984 these trees are characterized by a self similarity property so we will refer to them as self similar trees or ssts ssts are defined in terms of a generator matrix which acts as a blueprint for constructing different trees many familiar tree constructions are absorbed as special cases however in tokunaga s work an additional assumption is imposed which restricts from ssts to a much smaller class we will refer to this subclass as tokunaga s trees this paper presents several new and unifying results for ssts in particular the conditions under which ssts have well defined horton strahler stream ratios are given as well as a general method for computing these ratios it is also shown that the diameters of ssts grow like m where m is the number of leaves in contrast to many other tree constructions here need not equal 1 2 thus ssts offer an explanation for hack s law finally it is demonstrated that large discrepancies exist between the predictions of shreve s well known model and detailed measurements for large river networks while other ssts fit the data quite well other potential applications of the sst framework include diffusion limited aggregation dla lightning bronchial passages neural networks and botanical trees

vector coherent states from plancherel s theorem clifford algebras and matrix domains as a substantial generalization of the technique for constructing canonical and the related nonlinear and q deformed coherent states we present here a method for constructing vector coherent states vcs in the same spirit these vcs may have a finite or an infinite number of components the resulting formalism which involves an assumption on the existence of a resolution of the identity is broad enough to include all the definitions of coherent states existing in the current literature subject to this restriction as examples we first apply the technique to construct vcs using the plancherel isometry for groups and vcs associated with clifford algebras in particular quaternions as physical examples we discuss vcs for a quantum optical model and finally apply the general technique to build vcs over certain matrix domains

phase transitions in scheidegger and eden networks we study multifractal scaling and phase transitions in scheidegger and eden networks in the plane on several lattices the horton constants and are found not to depend on the lattice the scaling exponent in the integrated area distribution function is found to be consistent with the relation the exponent defines a phase transition point in the multifractal spectrum of the area distribution the approach to this phase transition is slow and controlled by where m is the number of lattice points for the scheidegger model we are able to calculate the exact probability distribution p a for small areas a and thus to study the finite size scaling

behaviour of the harmonic measure at the bottom of fjords diffusion limited aggregates are among many important fractal shapes that involve deep indentations usually called fjords to estimate the harmonic measure at the bottom of a fjord seems a prohibitive task but the authors find that a new mathematical equality due to beurling carleson and jones makes it easy they find that the harmonic measure at the bottom of a fjord as a function of its euclidean depth can exhibit a wide range of behaviours they introduce an infinite family of model fjords for which the equality takes a very simple form in this family the decay of the harmonic measure at their bottoms can be for example power law semi exponential stretched exponential and exponentially stretched exponential they show that self affinity or randomness can lead to faster than power law decays of the minimal growth probability on boundaries

evaluation of kriging based surrogate models constructed from mesoscale computations of shock interaction with particles abstract macro scale computations of shocked particulate flows require closure laws that model the exchange of momentum energy between the fluid and particle phases closure laws are constructed in this work in the form of surrogate models derived from highly resolved mesoscale computations of shock particle interactions the mesoscale computations are performed to calculate the drag force on a cluster of particles for different values of mach number and particle volume fraction two kriging based methods viz the dynamic kriging method dkg and the modified bayesian kriging method mbkg are evaluated for their ability to construct surrogate models with sparse data i e using the least number of mesoscale simulations it is shown that if the input data is noise free the dkg method converges monotonically convergence is less robust in the presence of noise the mbkg method converges monotonically even with noisy input data and is therefore more suitable for surrogate model construction from numerical experiments this work is the first step towards a full multiscale modeling of interaction of shocked particle laden flows

local isotropy and geometry of particle flux lines in diffusion limited aggregation we present a theoretical description of the branch orientation and the geometry of walker flux lines in diffusion limited aggregation dla it is based on the self similarity and non directedness of the branch structure and explains recent numerical results on the probability distribution of the branch orientation and the angle of particle attachment our results support the idea that asymptotically large off lattice dla clusters are locally isotropic and every individual walker flux line exhibits a certain type of self similarity

regular pseudo bosons versus bosons we discuss in which sense the so called regular pseudo bosons recently introduced by trifonov and analyzed in some detail by the author are related to ordinary bosons we repeat the same analysis for pseudo bosons and analyze the role played by certain intertwining operators which may be bounded or not

implications of losing hermiticity in quantum mechanics abstract in this note we revisit a system of one self interacting boson described by a non hermitian hamiltonian h acting on an infinite dimensional hilbert space h we determine the eigenfunctions of the hamiltonian and of its adjoint which constitute complete biorthogonal sets the probabilistic interpretation of quantum mechanics is not compatible with the metric inherited from h and attempts to overcome this problem are presented consequences of losing self adjointness in the quantum mechanical context are discussed and the necessity of a careful mathematical analysis of unbounded operators is emphasized

fractal models for diffusion controlled aggregation a two dimensional fractal model is constructed for diffusion controlled deposition on a surface the fractal geometry of the deposit and the power law behaviour of the quantities characterising the non equilibrium cluster size distribution are shown to be consequences of the competition generally present in a nonlinear growth process a qualitative agreement with previous numerical results is found and the scaling laws for the critical exponents of the problem are shown to be satisfied exactly

biorthogonal vectors sesquilinear forms and some physical operators continuing the analysis undertaken in previous articles we discuss some features of non self adjoint operators and sesquilinear forms which are defined starting from two biorthogonal families of vectors like the so called generalized riesz systems enjoying certain properties in particular we discuss what happens when they forms two d quasi bases

reexamining the determination of the fractal dimension of river networks in analyzing the literature on the fractal nature of river networks one can recognize several points that require clarification or additional investigations for instance many interpretations with different conclusions have been given to the important empirical results found in the previous literature on river geomorphology similarly the argument concerning a possible more likely value of the fractal dimensions of river networks has not yet found a convincing answer in an attempt to shed more light on the topic particularly on the latter point we have reexamined the basic aspects related to selfsimilarity in river networks using uniquely the fundamental concepts of fractal geometry this approach leads to relations for the determination of the fractal dimensions which hold exactly for deterministic self similar trees and are compatible with related findings reported in literature results obtained from application of these relations to several river networks in southern italy indicate very low variability around the average values of about 1 7 1 5 and 1 1 for the fractal dimensions of the whole river network of its topological equivalent and of its individual streams respectively this outcome in addition to comparable results taken from the literature provides new arguments to the hypothesis that natural networks tend to have the same fractal dimensions

power law distribution of discharge in ideal networks data for several river networks show algebraically decaying distribution functions for the mean annual discharge and the dissipation rate rodriguez iturbe et al 1992 we derive a relation between the exponent a in the integrated mean annual discharge distribution p q q q and the topological dimension dt of the network 1 1 dt using the experimentally determined value dt 1 8 tarboton et al 1988 we find 0 45 in good agreement with the data of rodriguez iturbe et al 1992 for the random model shreve 1967 1969 smart and werner 1974 we find an exponent of 1 2

fractal structure and properties of stream networks this paper studies the fractal structure and properties of stream networks through a comparison between stream networks and loopless random aggregate trees five fractal dimensions are recognized for stream networks namely topological dimension dt minimum path dimension dm fractal dimension of stream networks as a whole df diffusion dimension dw and spectral dimension ds mathematical definitions and derivations of the fractal dimensions are proposed which provide a theoretical basis for some recognized empirical relationships in drainage basin geomorphology relationships among the fractal dimensions are examined and the average values of the fractal dimensions for natural stream networks are estimated the hydrological implications of the fractal dimensions of stream networks are also discussed

multiscaling analysis of large scale off lattice dla abstract an improved algorithm has been used to simulate off lattice diffusion limited aggregation dla in two dimensions this enables us to grow clusters of up to 6 106 particles which are the largest such clusters made up to now the density profile in two dimensions is analyzed for the scaling form multiscaling g r r r d d x c x with x r r where r is the radius of gyration and r is the distance from the cluster origin in contrast with previous studies the dimension d x shows no symmetric tendency to drop at values of x but only fluctuates around the global fractal dimension d 1 712 0 003

an extended eulerian method for contacts in godunov formulations summary this paper offers a new method to treat contacts in eulerian godunov formulations the inadequacy of classic eulerian formulations to describe contacts behavior is identified in the lack of degrees of freedom this limitation is overcome by employing a set of state variables per material for the calculation of multi material elements and faces the extra state variables allow for the independent analysis of the materials present in the problem materials interactions are characterized by introducing contact constraints in the formulation the locality of the method limits the memory burden copyright 2012 john wiley sons ltd

intertwined isospectral potentials in an arbitrary dimension the method of intertwining with n dimensional nd linear intertwining operator l is used to construct nd isospectral stationary potentials it has been proven that the differential part of l is a series in euclidean algebra generators integrability conditions of the consistency equations are investigated and the general form of a class of potentials respecting all these conditions have been specified for each n 2 3 4 5 the most general forms of 2d and 3d isospectral potentials are considered in detail and construction of their hierarchies is exhibited the followed approach provides coordinate systems which make it possible to perform separation of variables and to apply the known methods of supersymmetric quantum mechanics for 1d systems it has been shown that in choice of coordinates and l there are a number of alternatives increasing with n that enlarge the set of available potentials some salient features of higher dimensional extension as well as some applications of the results are presented

fracture patterns and scaling laws abstract fracture is determined by the growth of cracks and can be described as a moving boundary problem similar to dielectric breakdown or viscous fingering the vectorial nature of the elastic medium allows however for a much larger variety of boundary conditions and growth rules than in the scalar electrostatic analogue giving rise to a number of new effects one can model this problem on a square lattice and it is found that the patterns of cracks can be fractal even without including noise due only to the interplay of anisotropy and memory the shapes of the cracks can be compared to the ones found experimentally for stress corrosion an effect that can be mimicked by a damage memory on the surface of the crack a quantity of experimental interest in the breaking characteristics force vs displacement in a model with quenched disorder and the possibility that several cracks be present in the system one finds scaling laws in the system size for the breaking characteristics just before the system breaks fully apart the distribution of local strain is multifractal this means that the volume fraction responsible for the final cracking goes to zero in the thermodynamic limit the scaling and multiscaling laws seem to be quite universal

first passage time survival probability and propagator on deterministic fractals the first passage time density psi r t defined as the probability density for the time spent by a random walker to travel for the first time the distance r that separates the starting site from its nearest neighbours and the survival probability s r t i e the probability that a random walker who starts at a site has not been absorbed by traps located on its nearest neighbours at distance r in the time interval 0 t were calculated for the class of deterministic fractals in which sites are isolated from the rest of the lattice by their nearest neighbours the large xi identical to r square root 2dt 1dw asymptotic expressions for these quantities are psi r t approximately a xi nu 2 dw exp c xi nu and h r t 1 s r t approximately a c dw 1 xi nu 2 exp c xi nu with v dw dw 1 a and c being characteristic constants for each fractal the asymptotic expression for s r t is used to justify that for this class of deterministic fractals the propagator or green function is given asymptotically by p r t t ds 2 xi alpha exp c xi nu for large xi with alpha nu 2 df this value of alpha differs from others proposed recently

area and width functions of river networks new results on multifractal properties 1 this paper investigates the multiscale statistical structure of the area and width functions of simulated and real river networks via state of the art wavelet based multifractal mf formalisms first several intricacies in performing mf analysis of these signals are discussed and a robust framework for accurate estimation of the mf spectrum is presented second it considers the following three questions 1 does the topology of river networks leave a unique signature on the mf spectrum of area and width functions 2 how different are the mf properties of commonly used simulated trees and those of real river networks and 3 are there differences between the mf properties of width and area functions and what can these tell us about the topology of hillslope versus channelized drainage patterns in a river basin the results indicate discrepancies between the statistical scaling of the area functions of real networks found to be multifractal with a considerable spread of local singularities and the most prevailing singularity ranging from 0 4 to 0 8 and that of several commonly used stochastic self similar networks found to be monofractal with a single singularity exponent h in the range of 0 5 0 65 moreover differences are found between the mf properties of width and area functions of the same basin these differences may be the result of distinctly different branching topologies in the hillslope versus channelized drainage paths and need to be further investigated

geometry of river networks ii distributions of component size and number the structure of a river network may be seen as a discrete set of nested subnetworks built out of individual stream segments these network components are assigned an integral stream order via a hierarchical and discrete ordering method exponential relationships known as horton s laws between stream order and ensemble averaged quantities pertaining to network components are observed we extend these observations to incorporate fluctuations and all higher moments by developing functional relationships between distributions the relationships determined are drawn from a combination of theoretical analysis analysis of real river networks including the mississippi amazon and nile and numerical simulations on a model of directed random networks underlying distributions of stream segment lengths are identified as exponential combinations of these distributions form single humped distributions with exponential tails the sums of which are in turn shown to give power law distributions of stream lengths distributions of basin area and stream segment frequency are also addressed the calculations identify a single length scale as a measure of size fluctuations in network components this article is the second in a series of three addressing the geometry of river networks

multifractality of flow distribution in the river network model of scheidegger the multifractal structure of flow distribution is investigated in the river network model of scheidegger bull iash 12 15 1967 it is shown that the partition function z q mathit tsum mathit i mathit i mathit i mathit q scales as z q ensuremath approxeq mathit l mathrm ensuremath zeta mathit q where mathit i mathit i is the flow of water passing over the bond i within the river network the summation ranges over all bonds and l is the size of the river network in the limit of a sufficiently large q ensuremath zeta q q gives the exponent of the drainage basin of a river the exponent also equals to the fractal dimension mathit d mathit f of a single river the f ensuremath alpha spectrum of the normalized flow distribution is calculated it is found that the fractal dimension mathit d mathit f of a river is exactly given by mathit d mathit f 2 ensuremath alpha ensuremath infty the flow distribution shows a characteristic multifractal structure for the river network the river width distribution also shows the multifractality if the width w of a river scales as w ensuremath approxeq mathit i mathrm ensuremath beta