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To fulfill their killing functions, cytotoxic T lymphocytes (CTLs) need to migrate to search for their target cells in complex biological microenvironments, a key component of which is extracellular matrix (ECM). The mechanisms underlying CTL's navigation are not well understood so far. Here we use a collagen assay as a model for the ECM and analyze the migration trajectories of primary human CTLs in collagen matrices with different concentrations. We observe different migration patterns for individual T cells. Three different motility types can be distinguished: slow, fast and mixed motilities. Slow CTLs remain nearly stationary within the collagen matrix and show slightly anti-persistent motility, while the fast ones move quickly and persistent (i.e. with not too large turning angles). The dynamics of the mixed type consists of periods of slow and fast motions; both states are persistent, but they have different persistencies. The dynamics can be well described by a two-state persistent random walk model. We extract the parameters of the model by analyzing experimental data. The mean square displacements predicted by the model and those measured experimentally are in very good agreement, without any fitting parameter. Potential reasons for the observed two-state motility are discussed. T cells dig the collagen during their migration and form channels, which facilitate the movement of other CTLs in the collagen network., Comment: 9 pages, 9 figures, 4 tables

Experimental realizations of disorder in optical lattices generate a distribution of the Bose-Hubbard (BH) parameters, like on-site potentials, hopping strengths, and interaction energies. We analyze this distribution for bosons in a bichromatic quasi-periodic potential by determining the generalized Wannier functions and calculating the corresponding BH parameters. Using a local mean-field cluster analysis, we study the effect of the corresponding disorder on the phase diagrams. We find a substantial amount of disorder in the hopping strengths, which produces strong deviations from the phase diagram of the disordered BH model with solely random on-site potentials.

Domain walls, optimal droplets and disorder chaos at zero temperature are studied numerically for the solid-on-solid model on a random substrate. It is shown that the ensemble of random curves represented by the domain walls obeys Schramm's left passage formula with kappa=4 whereas their fractal dimension is d_s=1.25, and therefore is NOT described by "Stochastic-Loewner-Evolution" (SLE). Optimal droplets with a lateral size between L and 2L have the same fractal dimension as domain walls but an energy that saturates at a value of order O(1) for L->infinity such that arbitrarily large excitations exist which cost only a small amount of energy. Finally it is demonstrated that the sensitivity of the ground state to small changes of order delta in the disorder is subtle: beyond a cross-over length scale L_delta ~ 1/delta the correlations of the perturbed ground state with the unperturbed ground state, rescaled by the roughness, are suppressed and approach zero logarithmically., Comment: 23 pages, 11 figures

A theoretical model based on the molecular interactions between a growing tumor and a dynamically evolving blood vessel network describes the transformation of the regular vasculature in normal tissues into a highly inhomogeneous tumor specific capillary network. The emerging morphology, characterized by the compartmentalization of the tumor into several regions differing in vessel density, diameter and necrosis, is in accordance with experimental data for human melanoma. Vessel collapse due to a combination of severely reduced blood flow and solid stress exerted by the tumor, leads to a correlated percolation process that is driven towards criticality by the mechanism of hydrodynamic vessel stabilization., Comment: 4 pages, 3 figures (higher resolution at http://www.uni-saarland.de/fak7/rieger/HOMEPAGE/flow.eps)

The transformation of the regular vasculature in normal tissue into a highly inhomogeneous tumor specific capillary network is described by a theoretical model incorporating tumor growth, vessel cooption, neo-vascularization, vessel collapse and cell death. Compartmentalization of the tumor into several regions differing in vessel density, diameter and in necrosis is observed for a wide range of parameters in agreement with the vessel morphology found in human melanoma. In accord with data for human melanoma the model predicts, that microvascular density (MVD, regarded as an important diagnostic tool in cancer treatment, does not necessarily determine the tempo of tumor progression. Instead it is suggested, that the MVD of the original tissue as well as the metabolic demand of the individual tumor cell plays the major role in the initial stages of tumor growth., Comment: 30 pages, 11 figures (higher resolution at http://www.uni-saarland.de/fak7/rieger/HOMEPAGE/BJ0.pdf)

A microscopic model for the diluted spin-mixed compounds (R_xY_(1-x))_2BaNiO_5 (R=magnetic rare-earth) is studied using Quantum Monte Carlo (QMC). The ordering temperature is shown to be a universal function of the impurity concentration x and the intrinsic Ni-chain correlation length. An effective model for the critical modes is derived. The possibility of a quantum critical point driven by the rare earth-concentration and the existence of a Griffiths phase in the high dilution limit is investigated. Several possible experimental approaches to verify the results are put forward., Comment: 4 pages, 3 figures

We review recent findings on spin glass models. Both the equilibrium properties and the dynamic properties are covered. We focus on progress in theoretical, in particular numerical, studies, while its relationship to real magnetic materials is also mentioned., Comment: Chapter 6 in ``Frustrated Spin Systems'' edited by H.T.Diep

We reconsider the random bond antiferromagnetic spin-1/2 chain for weak disorder and demonstrate the existence of crossover length scale x_W that diverges with decreasing strength of the disorder. Recent DMRG calculations [Phys. Rev. Lett. 89, 127202 (2002); cond-mat/0111027] claimed to have found evidence for a non-universal behavior in this model and found no indications of a universal infinite randomness fixed point (IRFP) scenario. We show that these data are not in the asymptotic regime since the system sizes that have been considered are of the same order of magnitude or much smaller than the crossover length x_W. We give a scaling form for the xx-spin-correlation function that takes this crossover length into account and that is compatible with the IRFP scenario and a random singlet phase., Comment: 1 page RevTeX, eps-fig included

The effect of quenched disorder on the low-energy and low-temperature properties of various two- and three-dimensional Heisenberg models is studied by a numerical strong disorder renormalization group method. For strong enough disorder we have identified two relevant fixed points, in which the gap exponent, omega, describing the low-energy tail of the gap distribution, P(Delta) ~ Delta^omega is independent of disorder, the strength of couplings and the value of the spin. The dynamical behavior of non-frustrated random antiferromagnetic models is controlled by a singlet-like fixed point, whereas for frustrated models the fixed point corresponds to a large spin formation and the gap exponent is given by omega ~ 0. Another type of universality classes is observed at quantum critical points and in dimerized phases but no infinite randomness behavior is found, in contrast to one-dimensional models., Comment: 11 pages RevTeX, eps-figs included, language revised

We study the anti-ferromagnetic six-state clock model with nearest neighbor interactions on a triangular lattice with extensive Monte-Carlo simulations. We find clear indications of two phase transitions at two different temperatures: Below $T_I$ a chirality order sets in and by a thorough finite size scaling analysis of the specific heat and the chirality correlation length we show that this transition is in the Ising universality class (with a non-vanishing chirality order parameter below $T_I$). At $T_{KT}(

The effect of quenched disorder on the low-energy properties of various antiferromagnetic spin ladder models is studied by a numerical strong disorder renormalization group method and by density matrix renormalization. For strong enough disorder the originally gapped phases with finite topological or dimer order become gapless. In these quantum Griffiths phases the scaling of the energy, as well as the singularities in the dynamical quantities are characterized by a finite dynamical exponent, z, which varies with the strength of disorder. At the phase boundaries, separating topologically distinct Griffiths phases the singular behavior of the disordered ladders is generally controlled by an infinite randomness fixed point., Comment: 11 pages, 15 figures, PRB accepted for publication

The out-of-equilibrium low-frequency complex susceptibility of the orientational glass methanol(73%)-beta-hydrochinone-clathrate is studied using temperature-stop protocols in aging experiments . Although the material does not have a sharp glass transition aging effects including rejuvenation and memory are found at low temperatures. However, they turn out to be much weaker, however, than in conventional magnetic spin glasses., Comment: 5 pages RevTeX, 6 eps-figures included

Monolayers of the halomethane CF$_3$Br adsorbed on graphite have been investigated by x-ray diffraction. The layers crystallize in a commensurate triangular lattice. On cooling they approach a three-sublattice antiferroelectric pattern of the in-plane components of the dipole moments. The ordering is not consistent with a conventional phase transition, but points to Kosterlitz-Thouless behavior. It is argued that the transition is described by a 6-state clock model on a triangular lattice with antiferromagnetic nearest neighbor interactions which is studied with Monte-Carlo simulations. A finite-size scaling analysis shows that the ordering transition is indeed in the KT universality class., Comment: 4 pages, 5 figures

We discuss with the aid of random walk arguments and exact numerical computations the magnetization properties of one-dimensional random field chains. The ground state structure is explained in terms of absorbing and non-absorbing random walk excursions. At low temperatures, the magnetization profiles follow those of the ground states except at regions where a local random field fluctuation makes thermal excitations feasible. This follows also from the non-absorbing random walks, and implies that the magnetization length scale is a product of these two scales. It is not simply given by the Imry-Ma-like ground state domain size nor by the scale of the thermal excitations., Comment: 7 pages LaTeX, 8 eps-figures included

We study the critical behavior of Ising quantum magnets with broadly distributed random couplings (J), such that $P(\ln J) \sim |\ln J|^{-1-\alpha}$, $\alpha>1$, for large $|\ln J|$ (L\'evy flight statistics). For sufficiently broad distributions, $\alpha<\alpha_c$, the critical behavior is controlled by a line of fixed points, where the critical exponents vary with the L\'evy index, $\alpha$. In one dimension, with $\alpha_c=2$, we obtaind several exact results through a mapping to surviving Riemann walks. In two dimensions the varying critical exponents have been calculated by a numerical implementation of the Ma-Dasgupta-Hu renormalization group method leading to $\alpha_c \approx 4.5$. Thus in the region $2<\alpha<\alpha_c$, where the central limit theorem holds for $|\ln J|$ the broadness of the distribution is relevant for the 2d quantum Ising model., Comment: 10pages, 13figures, final form

The competing effect of a periodic pinning potential and random point disorder is studied for arrays of elastic lines or directed polymers. The groundstates are investigated by exact combinatorial optimization. In both two and three dimensions a phase diagram is found with two or three distinct phases: a strictly flat phase if the disorder is bounded and weak, a weakly fluctuating phase for intermediate valleys depths, where the lines roughen individually on a scale smaller than the line-line distance, and a rough phase for strong disorder, where the roughness follows the scaling with pure point disorder. The line wandering in the transverse direction leads in the three-dimensional, rough phase to an entangled state with a complicated topology., Comment: 4 pages RevTeX, 6 eps-figure included

Joint ground states of two directed polymers in a random medium are investigated. Using exact min-cost flow optimization the true two-line ground-state is compared with the single line ground state plus its first excited state. It is found that these two-line configurations are (for almost all disorder configurations) distinct implying that the true two-line ground-state is non-separable, even with 'worst-possible' initial conditions. The effective interaction energy between the two lines scales with the system size with the scaling exponents 0.39 and 0.21 in 2D and 3D, respectively., Comment: 19 pages RevTeX, figures included

We consider the non-stationary quantum relaxation of the Ising spin chain in a transverse field of strength h. Starting from a homogeneously magnetized initial state the system approaches a stationary state by a process possessing quasi long range correlations in time and space, independent of the value of $h$. In particular the system exhibits aging (or lack of time translational invariance on intermediate time scales) although no indications of coarsening are present., Comment: 4 pages RevTeX, 2 eps-figures included

The quantum critical behavior and the Griffiths-McCoy singularities of random quantum Ising ferromagnets are studied by applying a numerical implementation of the Ma-Dasgupta-Hu renormalization group scheme. We check the procedure for the analytically tractable one-dimensional case and apply our code to the quasi-one-dimensional double chain. For the latter we obtain identical critical exponents as for the simple chain implying the same universality class. Then we apply the method to the two-dimensional case for which we get estimates for the exponents that are compatible with a recent study in the same spirit., Comment: 10 pages LaTeX, eps-figures and PTP-macros included. Proceedings of the ICCP5, Kanazawa (Japan), 1999

By means of molecular dynamics simulations we examine the aging process of a strong glass former, a silica melt modeled by the BKS potential. The system is quenched from a temperature above to one below the critical temperature, and the potential energy and the scattering function C(t_w,t+t_w) for various waiting times t_w after the quench are measured. We find that both qualitatively and quantitatively the results agree well with the ones found in similar simulations of a fragile glass former, a Lennard-Jones liquid., Comment: 5 pages LaTeX, eps-figures and JPSJ-macros included. Proceedings of the workshop 'Frontiers in Magnetism', Kyoto, Oct. 1999

We study XY and dimerized XX spin-1/2 chains with random exchange couplings by analytical and numerical methods and scaling considerations. We extend previous investigations to dynamical properties, to surface quantities and operator profiles, and give a detailed analysis of the Griffiths phase. We present a phenomenological scaling theory of average quantities based on the scaling properties of rare regions, in which the distribution of the couplings follows a surviving random walk character. Using this theory we have obtained the complete set of critical decay exponents of the random XY and XX models, both in the volume and at the surface. The scaling results are confronted with numerical calculations based on a mapping to free fermions, which then lead to an exact correspondence with directed walks. The numerically calculated critical operator profiles on large finite systems (L<=512) are found to follow conformal predictions with the decay exponents of the phenomenological scaling theory. Dynamical correlations in the critical state are in average logarithmically slow and their distribution show multi-scaling character. In the Griffiths phase, which is an extended part of the off-critical region average autocorrelations have a power-law form with a non-universal decay exponent, which is analytically calculated. We note on extensions of our work to the random antiferromagnetic XXZ chain and to higher dimensions., Comment: 19 pages RevTeX, eps-figures included

We study random XY and (dimerized) XX spin-1/2 quantum spin chains at their quantum phase transition driven by the anisotropy and dimerization, respectively. Using exact expressions for magnetization, correlation functions and energy gap, obtained by the free fermion technique, the critical and off-critical (Griffiths-McCoy) singularities are related to persistence properties of random walks. In this way we determine exactly the decay exponents for surface and bulk transverse and longitudinal correlations, correlation length exponent and dynamical exponent., Comment: 4 pages RevTeX, 1 eps-figure included

We study the effect of spatial correlations in the quenched disorder on random quantum magnets at and near a quantum critical point. In the random transverse field Ising systems disorder correlations that decay algebraically with an exponent rho change the universality class of the transition for small enough rho and the off-critical Griffiths-McCoy singularities are enhanced. We present exact results for 1d utilizing a mapping to fractional Brownian motion and generalize the predictions for the critical exponents and the generalized dynamical exponent in the Griffiths phase to d>=2., Comment: 4 pages RevTeX, 1 eps-figure included

We present a new microscopic stochastic model for an ensemble of interacting investors that buy and sell stocks in discrete time steps via limit orders based on individual forecasts about the price of the stock. These orders determine the supply and demand fixing after each round (time step) the new price of the stock according to which the limited buy and sell orders are then executed and new forecasts are made. We show via numerical simulation of this model that the distribution of price differences obeys an exponentially truncated Levy-distribution with a self similarity exponent mu~5., Comment: 14 pages RevTeX, 5 eps-figures included

The vortex glass model for a disordered high-T_c superconductor in an external magnetic field is studied in the strong screening limit. With exact ground state (i.e. T=0) calculations we show that 1) the ground state of the vortex configuration varies drastically with infinitesimal variations of the strength of the external field, 2) the minimum energy of global excitation loops of length scale L do not depend on the strength of the external field, however 3) the excitation loops themself depend sensibly on the field. From 2) we infer the absence of a true superconducting state at any finite temperature independent of the external field., Comment: 6 pages RevTeX, 5 eps-figures included

We study the quantum phase transition in the two-dimensional random Ising model in a transverse field by Monte Carlo simulations. We find results similar to those known analytically in one-dimension. At the critical point, the dynamical exponent is infinite and the typical correlation function decays with a stretched exponential dependence on distance. Away from the critical point there are Griffiths-McCoy singularities, characterized by a single, continuously varying exponent, z', which diverges at the critical point, as in one-dimension. Consequently, the zero temperature susceptibility diverges for a RANGE of parameters about the transition., Comment: 4 pages RevTeX, 3 eps-figures included

We consider the paramagnetic phase of the random transverse-field Ising spin chain and study the dynamical properties by numerical methods and scaling considerations. We extend our previous work [Phys. Rev. B 57, 11404 (1998)] to new quantities, such as the non-linear susceptibility, higher excitations and the energy-density autocorrelation function. We show that in the Griffiths phase all the above quantities exhibit power-law singularities and the corresponding critical exponents, which vary with the distance from the critical point, can be related to the dynamical exponent z, the latter being the positive root of [(J/h)^{1/z}]_av=1. Particularly, whereas the average spin autocorrelation function in imaginary time decays as [G]_av(t)~t^{-1/z}, the average energy-density autocorrelations decay with another exponent as [G^e]_av(t)~t^{-2-1/z}., Comment: 8 pages RevTeX, 8 eps-figures included

We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the transverse-field Ising model with inhomogeneous couplings we obtain many new analytical results for the random walk problem. In the absence of global bias the qualitative behavior of the diffusive motion of the particle and the corresponding persistence probability strongly depend on the fluctuation properties of the environment. In environments with bounded fluctuations the particle shows normal diffusive motion and the diffusion constant is simply related to the persistence probability. On the other hand in a medium with unbounded fluctuations the diffusion is ultra-slow, the displacement of the particle grows on logarithmic time scales. For the borderline situation with marginal fluctuations both the diffusion exponent and the persistence exponent are continuously varying functions of the aperiodicity. Extensions of the results to disordered media and to higher dimensions are also discussed., Comment: 11 pages, RevTex

We study the first passage time properties of an integrated Brownian curve both in homogeneous and disordered environments. In a disordered medium we relate the scaling properties of this center of mass persistence of a random walker to the average persistence, the latter being the probability P_pr(t) that the expectation value of the walker's position after time t has not returned to the initial value. The average persistence is then connected to the statistics of extreme events of homogeneous random walks which can be computed exactly for moderate system sizes. As a result we obtain a logarithmic dependence P_pr(t)~{ln(t)}^theta' with a new exponent theta'=0.191+/-0.002. We note on a complete correspondence between the average persistence of random walks and the magnetization autocorrelation function of the transverse-field Ising chain, in the homogeneous and disordered case., Comment: 6 pages LaTeX, 3 postscript figures included

A new numerical method to calculate exact ground states of multi-fluxline systems with quenched disorder is presented, which is based on the minimum cost flow algorithm from combinatorial optimization. We discuss several models that can be studied with this method including their specific implementations, physically relevant observables and results: 1) the N-line model with N fluxlines (or directed polymers) in a d-dimensional environment with point and/or columnar disorder and hard or soft core repulsion; 2) the vortex glass model for a disordered superconductor in the strong screening limit and 3) the Sine-Gordon model with random pase shifts in the strong coupling limit., Comment: 4 pages RevTeX, 3 eps-figures included

We study the three-dimensional gauge glass model in the limit of strong screening by using a minimum cost flow algorithm, enabling us to obtain EXACT ground states for systems of linear size L<=48. By calculating the domain-wall energy, we obtain the stiffness exponent theta = -0.95+/-0.03, indicating the absence of a finite temperature phase transition, and the thermal exponent nu=1.05+/-0.03. We discuss the sensitivity of the ground state with respect to small perturbations of the disorder and determine the overlap length, which is characterized by the chaos exponent zeta=3.9+/-0.2, implying strong chaos., Comment: 4 pages RevTeX, 2 eps-figures included

In a recent letter [PRL 80 (1998) 3539] Fisher, Le Doussal and Monthus report new predictions for the persistence properties of Sinai's model, which they obtain by using an approximate real space renormalization group scheme. In this comment we show that these predictions can be derived in a rigorous and more transparent way by reducing the quantities of interest to particular statistical properties of a simple random walk in a homogeneous environment. We also point out that they are valid in a much more general context: our results are neither restricted to the random force model but are valid for any asymmetric hopping model, nor to the vicinity of the critical point., Comment: 1 pages RevTeX

We consider cooperative processes (quantum spin chains and random walks) in one-dimensional fluctuating random and aperiodic environments characterized by fluctuating exponents omega>0. At the critical point the random and aperiodic systems scale essentially anisotropically in a similar fashion: length (L) and time (t) scales are related as t ~ log^{1/omega}. Also some critical exponents, characterizing the singularities of average quantities, are found to be universal functions of omega, whereas some others do depend on details of the distribution of the disorder. In the off-critical region there is an important difference between the two types of environments: in aperiodic systems there are no extra (Griffiths)-singularities., Comment: 13 pages RevTeX, 10 eps-figures included

Using exact expressions for the persistence probability and for the leading eigenvalue of the Focker-Planck operator of a random walk in a random environment we establish a fundamental relation between the statistical properties of anomalous diffusion and the critical and off-critical behavior of random quantum spin chains. Many new exact results are obtained from this correspondence including the space and time correlations of surviving random walks and the distribution of the gaps of the corresponding Focker-Planck operator. In turn we derive analytically the dynamical exponent of the random transverse-field Ising spin chain in the Griffiths-McCoy region., Comment: 4 pages RevTeX, 1 eps-figures included

The sensitivity of the random field Ising model to small random perturbations of the quenched disorder is studied via exact ground states obtained with a maximum-flow algorithm. In one and two space dimensions we find a mild form of chaos, meaning that the overlap of the old, unperturbed ground state and the new one is smaller than one, but extensive. In three dimensions the rearrangements are marginal (concentrated in the well defined domain walls). Implications for finite temperature variations and experiments are discussed., Comment: 4 pages RevTeX, 6 eps-figures included

In a recent letter [PRL 78 (1997) 4581] Kob and Barrat reported results of their molecular dynamics simulation of the non-equilibrium dynamics of a binary Lennard-Jones glass. They propose an aging scenario in this system that is close to a t/t_w scaling behavior. In this comment we present new results and show that a different aging scenario, known under the name activated dynamics scaling [i.e. log((t+t_w)/tau)/log(t_w/tau)], describes the aging regime of this kind of glassy systems much better., Comment: 1 page RevTex, 1 eps-figure included

The site-diluted transverse field Ising model in two dimensions is studied with Quantum-Monte-Carlo simulations. Its phase diagram is determined in the transverse field (Gamma) and temperature (T) plane for various (fixed) concentrations (p). The nature of the quantum Griffiths phase at zero temperature is investigated by calculating the distribution of the local zero-frequency susceptibility. It is pointed out that the nature of the Griffiths phase is different for small and large Gamma., Comment: 21 LaTeX (JPSJ macros included), 12 eps-figures included

A cluster algorithm formulated in continuous (imaginary) time is presented for Ising models in a transverse field. It works directly with an infinite number of time-slices in the imaginary time direction, avoiding the necessity to take this limit explicitly. The algorithm is tested at the zero-temperature critical point of the pure two-dimensional (2d) transverse Ising model. Then it is applied to the 2d Ising ferromagnet with random bonds and transverse fields, for which the phase diagram is determined. Finite size scaling at the quantum critical point as well as the study of the quantum Griffiths-McCoy phase indicate that the dynamical critical exponent is infinite as in 1d., Comment: 4 pages RevTeX, 3 eps-figures included

We study the critical and off-critical (Griffiths-McCoy) regions of the random transverse-field Ising spin chain by analytical and numerical methods and by phenomenological scaling considerations. Here we extend previous investigations to surface quantities and to the ferromagnetic phase. The surface magnetization of the model is shown to be related to the surviving probability of an adsorbing walk and several critical exponents are exactly calculated. Analyzing the structure of low energy excitations we present a phenomenological theory which explains both the scaling behavior at the critical point and the nature of Griffiths-McCoy singularities in the off-critical regions. In the numerical part of the work we used the free-fermion representation of the model and calculated the critical magnetization profiles, which are found to follow very accurately the conformal predictions for different boundary conditions. In the off-critical regions we demonstrated that the Griffiths-McCoy singularities are characterized by a single, varying exponent, the value of which is related through duality in the paramagnetic and ferromagnetic phases., Comment: 18 pages RevTeX (multicolumn), eps-figures included

According to the Harris-Luck criterion the relevance of a fluctuating interaction at the critical point is connected to the value of the fluctuation exponent omega. Here we consider different types of relevant fluctuations in the quantum Ising chain and investigate the universality class of the models. At the critical point the random and aperiodic systems behave similarly, due to the same type of extreme broad distribution of the energy scales at low energies. The critical exponents of some averaged quantities are found to be a universal function of omega, but some others do depend on other parameters of the distribution of the couplings. In the off-critical region there is an important difference between the two systems: there are no Griffiths singularities in aperiodic models., Comment: 4 pages RevTeX, 2 eps-figures included

An introduction to the application of combinatorial optimization methods to ground state calculations of frustrated, disordered systems is given. We discuss the interface problem in the random bond Ising ferromagnet, the random field Ising model, the diluted antiferromagnet in an external field, the spin glass problem, the solid-on-solid model with a disordered substrate and other convex cost flow problems occurring in superconducting flux line lattices and traffic flow networks. On the algorithmic side we present a concise introduction to a number of elementary algorithms in combinatorial optimization, in particular network flows: the shortest path algorithm, the maximum-flow algorithms and minimum-cost-flow algorithms. We present a short glance at the minimum weighted matching and branch-and-cut algorithms., Comment: 40 pages LaTeX, uses Springer macros (lamuphys.sty included), 4 postscript-figures included. Manuscript of a lecture given on the Eotvos summer school in Physics: Advances in Computer Simulations, Budapest, July 16-20, 1996

Dynamical correlations of the spin and the energy density are investigated in the critical region of the random transverse-field Ising chain by numerically exact calculations in large finite systems (L<=128). The spin-spin autocorrelation function is found to decay proportional to (log t)^{-2x_m} and (log t)^{-2x_m^s} in the bulk and on the surface, respectively, with x_m and x_m^s the bulk and surface magnetization exponents, respectively. On the other hand the critical energy-energy autocorrelation functions have a power law decay, which are characterized by novel critical exponents eta_e~2.2 in the bulk and eta_e^s~2.5 at the surface, respectively. The numerical results are compared with the predictions of a scaling theory., Comment: 12 pages LaTeX (RevTeX), 6 postscript-figures included

We present a one dimensional model for diffusion on a hierarchical tree structure. It is shown that this model exhibits aging phenomena although no disorder is present. The origin of aging in this model is therefore the hierarchical structure of phase space., Comment: 10 pages LaTeX, 4 postscript-figures included

We investigate the Bose glass phase and the insulator-to-superfluid transition in the two-dimensional disordered boson Hubbard model in the Villain representation via Monte Carlo simulations. In the Bose glass phase the probability distribution of the local susceptibility is found to have a $1/ \chi^2$ tail and the imaginary time Green's function decays algebraically $C(\tau) \sim \tau^{-1}$, giving rise to a divergent global susceptibility. By considering the participation ratio it is shown that the excitations in the Bose glass phase are fully localized and a scaling law is established. For commensurate boson densities we find a direct Mott insulator to superfluid transition without an intervening Bose glass phase for weak disorder. For this transition we obtain the critical exponents $z=1, \nu=0.7\pm 0.1$ and $\eta = 0.1 \pm 0.1$, which agree with those for the classical three-dimensional XY model without disorder. This indicates that disorder is irrelevant at the tip of the Mott-lobes and that here the inequality $\nu\ge2/d$ is violated., Comment: 15 pages RevTeX, 18 postscript-figures included