Forthcoming papers

Published papers

• E. Heinsalu, M. Patriarca, and F. Marchesoni
  Stochastic Resonance in a surface dipole
  Chemical Physics 375 (2010) 410
    [BibTex]   [abstract]
  
  @article{Heinsalu2010a,
  author = {E. Heinsalu and M. Patriarca and F. Marchesoni},
  title = {Stochastic Resonance in a surface dipole},
  journal = {Chemical Physics},
  volume = {375},
  pages = {410},
  year = {2010}}
  The dynamics of a neutral dipole diffusing on a one-dimensional symmetric periodic substrate is numerically investigated in the presence of an ac electric field. It is observed that the amplitude of the forced oscillations of the dipole can be enhanced by tuning the noise strength, i.e., the substrate temperature. Such a manifestation of stochastic resonance turns out to be extremely sensitive to the mechanical properties of the dipole. This phenomenon has immediate applications in surface physics and nanodevice technology.


• M. Patriarca, E. Heinsalu and A. Chakraborti
  Basic kinetic wealth-exchange models: common features and open problems
  Eur. Phys. J. B 73, (2010) 145
  [arxiv:physics/0611245]   [BibTex]   [abstract]
  
  @article{Patriarca2010a,
  author = {M. Patriarca, E. Heinsalu and A. Chakraborti},
  title = {Basic kinetic wealth-exchange models: common features and open problems},
  journal = {Eur. Phys. J. B},
  volume = {73},
  pages = {145},
  year = {2010}}
  We review the basic kinetic wealth-exchange models of Angle [J. Angle, Social Forces 65, 293 (1986); J. Math. Sociol. 26, 217 (2002)], Bennati [E. Bennati, Rivista Internazionale di Scienze Economiche e Commerciali 35, 735 (1988)], Chakraborti and Chakrabarti [A. Chakraborti, B. K. Chakrabarti, Eur. Phys. J. B 17, 167 (2000)], and of Dragulescu and Yakovenko [A. Dragulescu, V.M. Yakovenko, Eur. Phys. J. B 17, 723 (2000)]. Analytical fitting forms for the equilibrium wealth distributions are proposed. The influence of heterogeneity is investigated, the appearance of the fat tail in the wealth distribution and the relaxation to equilibrium are discussed. A unified reformulation of the models considered is suggested.


• A. Chakraborti and M. Patriarca
  Variational principle for the Pareto power law
  Phys. Rev. Lett. 103 (2009) 228701
  [arxiv:cond-mat/0605325]   [BibTex]   [abstract]
  
  @article{Chakraborti2009a,
  author = {A. Chakraborti and M. Patriarca},
  title = {A variational principle for the {P}areto power law},
  journal = {Phys. Rev. Lett.},
  volume = {103},
  pages = {228701},
  year = {2009}}
  A mechanism is proposed for the appearance of power-law distributions in various complex systems. It is shown that in a conservative mechanical system composed of subsystems with different numbers of degrees of freedom a robust power-law tail can appear in the equilibrium distribution of energy as a result of certain superpositions of the canonical equilibrium energy densities of the subsystems. The derivation only uses a variational principle based on the Boltzmann entropy, without assumptions outside the framework of canonical equilibrium statistical mechanics. Two examples are discussed, free diffusion on a complex network and a kinetic model of wealth exchange. The mechanism is illustrated in the general case through an exactly solvable mechanical model of a dimensionally heterogeneous system.


• E. Heinsalu, M. Patriarca, I. Goychuk and P. Hänggi
  Fractional Fokker-Planck subdiffusion in alternating fields
  Phys. Rev. E 79 (2009) 041137
  [arxiv.org:0902.3878]   [BibTex]   [abstract]
  
  @article{Heinsalu2009b,
  author = {E. Heinsalu and M. Patriarca and I. Goychuk and P. H\"anggi},
  title = {{F}ractional {F}okker-{P}lanck subdiffusion in alternating fields},
  journal = {submitted},
  volume = {},
  pages = {},
  year = {2009}}
  The fractional Fokker-Planck equation for subdiffusion in time-dependent force fields is derived from the underlying continuous time random walk. Its limitations are discussed and it is then applied to the study of subdiffusion under the influence of a time-periodic rectangular force. As a main result, we show that such a force does not affect the universal scaling relation between the anomalous current and diffusion when applied to the biased dynamics: in the long time limit subdiffusion current and anomalous diffusion are immune to the driving. This is in sharp contrast with the unbiased case when the subdiffusion coefficient can be strongly enhanced, i.e. a zero-frequency response to a periodic driving is present.


• E. Heinsalu, M. Patriarca and F. Marchesoni
  Stochastic resonance in confining potentials. On the role of confinement
  Eur. Phys. J. B 69 (2009) 19
  [arxiv.org:0901.2523]   [BibTex]   [abstract]
  
  @article{Heinsalu2009a,
  author = {E. Heinsalu and M. Patriarca and F. Marchesoni},
  title = {Stochastic resonance in confining potentials. On the role of confinement},
  journal = {Eur. J. Phys. B, in press},
  volume = {},
  pages = {},
  year = {2009}}
  We study the effects of the confining conditions on the occurrence of stochastic resonance (SR) in continuous bistable systems. We model such systems by means of double-well potentials that diverge like |x |^q for |x | going to infinite. For super-harmonic (hard) potentials with q > 2 the SR peak sharpens with increasing q, whereas for sub-harmonic (soft) potentials, q < 2, it gets suppressed.


• M. Patriarca and E. Heinsalu
  Influence of geography on language competition
  Physica A 388 (2009) 174
  [arxiv.org:0807.3100]   [BibTex]   [abstract]
  
  @article{Patriarca2008a,
  author = {Marco Patriarca and Els Heinsalu},
  title = {Influence of geography on language competition},
  journal = {Physica A},
  volume = {388},
  pages = {174-186},
  year = {2008}}
  Competition between languages or cultural traits diffusing in the same geographical area is studied combining the model of Abrams and Strogatz with a model of human dispersal on an inhomogeneous substrate. Also, the effect of population growth is discussed. It is shown through numerical simulations that the final configuration of the languages can be strongly affected by geographical and historical factors. These factors are not related to the dynamics of culture transmission, but rather to initial population distributions as well as geographical boundaries and inhomogeneities, which modulate the diffusion process.


• A. Chakraborty and M. Patriarca
  Gamma-distribution and Income inequality
  Pramana J. Phys. 71 (2008) 233
  [arxiv.org:0802.4410]   [BibTex]   [abstract]
  
  @article{Chakraborti2008a,
  author = {A. Chakraborti and M. Patriarca},
  title = {Gamma-distribution and Wealth inequality},
  journal = {Pramana J. Phys, in press},
  volume = {71},
  pages = {233},
  year = {2008}}
  We discuss the equivalence between kinetic wealth-exchange models, in which agents exchange wealth during trades and mechanical models of particles, exchanging energy during collisions. The universality of the underlying dynamics is shown both through a variational approach based on the minimization of the Boltzmann entropy and a microscopic analysis of the collision dynamics of molecules in a gas. In various relevant cases, the equilibrium distribution is well-approximated by a gamma-distribution with suitably defined temperature and number of dimensions. This in turn allows one to quantify the inequalities observed in the wealth distributions and suggests that their origin should be traced back to very general underlying mechanisms, for instance, the fact that smaller the fraction of the relevant quantity (e.g. wealth) that agent can exchange during an interaction, the closer the corresponding equilibrium distribution is to a fair distribution.


• E. Heinsalu, M. Patriarca and F. Marchesoni
  Dimer diffusion in a washboard potential
  Phys. Rev. E 77, 021129 (2008)
  [arxiv.org:0708.2858]   [BibTex]   [abstract]
  
  @article{Heinsalu2008a,
  author = {Els Heinsalu and Marco Patriarca and Fabio Marchesoni},
  title = {Dimer diffusion in a washboard potential},
  journal = {Phys. Rev. E},
  volume = {77},
  pages = {021129},
  year = {2008}}
  The transport of a dimer, consisting of two Brownian particles bounded by a harmonic potential, moving on a periodic substrate is investigated both numerically and analytically. The mobility and diffusion of the dimer center of mass present distinct properties when compared with those of a monomer under the same transport conditions. Both the average current and the diffusion coefficient are found to be complicated nonmonotonic functions of the driving force. The influence of dimer equilibrium length, coupling strength and damping constant on the dimer transport properties are also examined in detail.


• A. Chakraborti, M. Patriarca and M.S. Santhanam
  Financial time-series analysis: A brief overview
  in Econophysics and Sociophysics of Markets and Networks, A. Chatterjee and B. K. Chakrabarti Eds., Springer, 2007, pp. 51-67.
  [arxiv.org:0704.1738]   [BibTex]   [abstract]
  
  @article{Chakraborti2007a,
  Author = {A. Chakraborti and M. Patriarca and M.S. Santhanam},
  Title = {Financial time-series analysis: A brief overview},
  Booktitle = {Econophysics and Sociophysics of Markets and Networks},
  Editor = {A. Chatterjee and B. K. Chakrabarti},
  Publisher = {Springer},
  Address = {},
  Year = {2007}}
  Prices of commodities or assets produce what is called time-series. Different kinds of financial time-series have been recorded and studied for decades. Nowadays, all transactions on a financial market are recorded, leading to a huge amount of data available, either for free in the Internet or commercially. Financial time-series analysis is of great interest to practitioners as well as to theoreticians, for making inferences and predictions. Furthermore, the stochastic uncertainties inherent in financial time-series and the theory needed to deal with them make the subject especially interesting not only to economists, but also to statisticians and physicists 1. While it would be a formidable task to make an exhaustive review on the topic, with this review we try to give a flavor of some of its aspects.


• E. Heinsalu, M. Patriarca, I. Goychuk and P. Hänggi
  Use and abuse of a fractional Fokker- Planck dynamics for time-dependent driving
  Phys. Rev. Lett. 99 (2007) 120602
  [arxiv.org:cond-mat/0703420]   [BibTex]   [abstract]
  
  @article{Heinsalu2007b,
  Author = {Heinsalu, E. and Patriarca, M. and Goychuk, I. and H\"anggi, P.},
  Journal = {Phys. Rev. Lett.},
  Volume = {99},
  Pages = {120602},
  Title = {Use and Abuse of a Fractional {F}okker-{P}lanck Dynamics for Time-Dependent Driving},
  Year = {2007}}
  We investigate a subdiffusive, fractional Fokker-Planck dynamics occurring in time-varying potential landscapes and thereby disclose the failure of the fractional Fokker-Planck equation (FFPE) in its commonly used form when generalized in an ad hoc manner to time-dependent forces. A modified FFPE (MFFPE) is rigorously derived, being valid for a family of dichotomously alternating force fields. This MFFPE is numerically validated for a rectangular time-dependent force with zero average bias. For this case, subdiffusion is shown to become enhanced as compared to the force free case. We question, however, the existence of any physically valid FFPE for arbitrary varying time-dependent fields that differ from this dichotomous varying family.


• M. Patriarca, E. Heinsalu, A. Chakraborti and G. Germano
  Relaxation in Statistical Many-agent Economy Models
  Eur. Phys. J. B 57 (2007) 219
  [arxiv.org:physics/0608174]   [BibTex]   [abstract]
  
  @article{Patriarca2007a,
  Author = {Patriarca, Marco and Chakraborti, Anirban and Heinsalu, Els and Germano, Guido},
  Title = {Relaxation in statistical many-agent economy models},
  Journal = {Eur. J. Phys. B},
  Pages = {219},
  Volume = {57},
  Year = {2007}}
  We review some statistical many-agent models of economic and social systems inspired by microscopic molecular models and discuss their stochastic interpretation. We apply these models to wealth exchange in economics and study how the relaxation process depends on the parameters of the system, in particular on the saving propensities that define and diversify the agent profiles.


• E. Heinsalu, M. Patriarca, I. Goychuk and P. Hänggi
  Fractional diffusion in periodic potentials
  J. Phys.: Condensed Matter 19 (2007) 065114
  [arxiv.org:cond-mat/0604269]   [BibTex]   [abstract]
  
  @article{Heinsalu2007a,
  Author = {Heinsalu, E. and Patriarca, M. and Goychuk, I. and H\"anggi, P.},
  Journal = {J. Phys.:Condens. Matter},
  Title = {Fractional diffusion in periodic potentials},
  Pages = {065114},
  Volume = {19},
  Year = {2007}}
  Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two quadratures. This theoretical result is corroborated by numerical simulations for different shapes of the periodic potential. Normal and fractional spreading processes are contrasted via the time evolution of the corresponding probability densities in state space. While there are distinct differences occurring at small evolution times, a re-scaling of time yields a mutual matching between the long-time behaviours of normal and fractional diffusion.


• M. Patriarca, A. Kuronen, M. Robles and K. Kaski
  Three dimensional interactive Molecular Dynamics program for the study of defect dynamics in crystals
  Comp. Phys. Comm. 176 (2007) 38
  Comp. Phys. Comm. Program Library, Catalogue Identifier: ADYJ_v1_0
  Home Page of ALINE (aka boundary3D)   [BibTex]   [abstract]
  
  @article{Patriarca2007b,
  Author = {Patriarca, M. and Kuronen, A. and Robles, M. and Kaski, K.},
  Journal = {Comp. Phys. Comm.},
  Pages = {38},
  Title = {Three-dimensional interactive {M}olecular {D}ynamics program for the study of defect dynamics in crystals},
  Volume = {176},
  Year = {2007}}
  The study of crystal defects and the complex processes underlying their formation and time evolution has motivated the development of the program ALINE for interactive molecular dynamics experiments. This program couples a molecular dynamics code to a Graphical User Interface and runs on a UNIX-X11 Window System platform with the MOTIF library, which is contained in many standard Linux releases. ALINE is written in C, thus giving the user the possibility to modify the source code and, at the same time, provides an effective and user-friendly framework for numerical experiments, in which the main parameters can be interactively varied and the system visualized in various ways. We illustrate the main features of the program through some examples of detection and dynamical tracking of point-defects, linear defects and planar defects, such as stacking faults in lattice-mismatched heterostructures.


• E. Heinsalu, M. Patriarca, I. Goychuk, G. Schmid and P. Hänggi
  Fractional Fokker-Planck dynamics: Numerical algorithm and simulations
  Phys. Rev. E 73 (2006) 020101
  [arxiv.org:cond-mat/0603516]   [BibTex]   [abstract]
  
  @article{Heinsalu2006a,
  Author = {Heinsalu, E. and Patriarca, M. and Goychuk, I. and Schmid, G. and H{\"a}nggi, P.},
  Title = {Fractional {F}okker-{P}lanck dynamics: Numerical algorithm and simulations},
  Journal = {Phys. Rev. E},
  Pages = {046133},
  Volume = {73},
  Year = {2006}}
  Anomalous transport in a tilted periodic potential is investigated numerically within the framework of the fractional Fokker-Planck dynamics via the underlying continuous-time random walk. An efficient numerical algorithm is developed which is applicable for an arbitrary potential. This algorithm is then applied to inves- tigate the fractional current and the corresponding nonlinear mobility in different washboard potentials. Normal and fractional diffusion are compared through their time evolution of the probability density in state space. Moreover, we discuss the stationary probability density of the fractional current values.


• M. Patriarca, A. Chakraborti, K. Kaski and G. Germano
  Influence of saving propensity on the power-law tail of wealth distribution
  Physica A 369 (2006) 723
  [arxiv.org:physics/0506028]   [BibTex]   [abstract]
  
  @article{Patriarca2006a,
  Author = {Patriarca, M. and Chakraborti, A. and Germano, G.},
  Title = {Influence of saving propensity on the power law tail of wealth distribution},
  Journal = {Physica A},
  Pages = {723},
  Volume = {369},
  Year = {2006}}
  Some general features of statistical multi-agent economic models are reviewed, with particular attention to the dependence of the equilibrium wealth distribution on the agents’ saving propensities. It is shown that in a finite system of agents with a continuous saving propensity distribution a power-law tail with Pareto exponent a α = 1 can appear also when agents do not have saving propensities distributed over the whole interval between zero and one. Rather, a power-law can be observed in a finite interval of wealth, whose lower and upper ends are shown to be determined by the lower and upper cutoffs, respectively, of the saving propensity distribution. It is pointed out that a cutoff of the power-law tail can arise also through a different mechanism, when the number of agents is small enough. Numerical simulations have been carried out by implementing a procedure for assigning saving propensities homogeneously, which results in a smoother wealth distributions and correspondingly wider power-law intervals than other procedures based on random algorithms.


• I. Goychuk, E. Heinsalu, M. Patriarca, G. Schmid and P. Hänggi
  Current and universal scaling in anomalous transport
  Phys. Rev. E 73 (2006) 020101
  [arxiv.org:cond-mat/0509172]   [BibTex]   [abstract]
  
  @article{Goychuk2006a,
  Author = {Goychuk, I. and Heinsalu, E. and Patriarca, M. and Schmid, G. and H{\"a}nggi, P.},
  Journal = {Phys. Rev. E},
  Pages = {020101},
  Title = {Universal scaling in anomalous transport},
  Volume = {73},
  Year = {2006}}
  Anomalous transport in tilted periodic potentials is investigated within the framework of the fractional Fokker-Planck dynamics and the underlying continuous time random walk. The analytical solution for the stationary, anomalous current is obtained in closed form. We derive a universal scaling law for anomalous diffusion occurring in tilted periodic potentials. This scaling relation is corroborated with precise numerical studies covering wide parameter regimes and different shapes for the periodic potential, being either symmetric or ratchetlike.


• M. Patriarca, A. Chakraborti, K. Kaski and G. Germano
  Kinetic theory models for the distribution of wealth: power law from overlap of exponentials,
  in Econophysics of Wealth Distributions (Econophys-Kolkata I), A. Chatterjee, S.Yarlagadda and B. K. Chakrabarti Eds., Springer 2005, pp. 93-110.
  [arxiv.org:physics/0504153]   [BibTex]   [abstract]
  
  @inproceedings{Patriarca2005a,
  Author = {Patriarca, M. and Chakraborti, A. and Kaski, K. and Germano, G.},
  Title = {Kinetic theory models for the distribution of wealth: Power law from overlap of exponentials},
  Booktitle = {Econophysics of Wealth Distributions},
  Editor = {Chatterjee, A. and S.Yarlagadda and Chakrabarti, B. K.},
  Publisher = {Springer},
  Pages = {93},
  Year = {2005}}
  Various multi-agent models of wealth distributions defined by microscopic laws regulating the trades, with or without a saving criterion, are reviewed. We discuss and clarify the equilibrium properties of the model with constant global saving propensity, resulting in Gamma distributions and their equivalence to the Maxwell-Boltzmann kinetic energy distribution for a system of molecules in an effective number of dimensions D_λ, related to the saving propensity λ M. Patriarca, A. Chakraborti and K. Kaski, Phys. Rev. E 70 (2004) 016104. We use these results to analyze the model in which the individual saving propensities of the agents are quenched random variables and the tail of the equilibrium wealth distribution exhibits a Pareto law f ( x ) ~ x ^{- α - 1} with an exponent α = 1 A. Chatterjee, B. K. Chakrabarti and S. S. Manna, Physica Scripta T106 (2003) 367. Here, we show that the observed Pareto power law can be explained as arising from the overlap of the Maxwell-Boltzmann distributions associated to the various agents, which reach an equilibrium state characterized by their individual Gamma distributions. We also consider the influence of different types of saving propensity distributions on the equilibrium state.


• P. Szelestey, M. Patriarca and K. Kaski
  Computational study of a screw dislocation interacting with a stacking fault tetrahedron in nickel
  Modelling Simul. Mater. Sci. Eng. 13 (2005) 541
  [BibTex]   [abstract]
  
  @article{Szelestey2005b,
  Author = {Szelestey, P. and Patriarca, M. and Kaski, K.},
  Title = {Computational Study of a dislocation interacting with a stacking fault tetrahedron in nickel},
  Journal = {Mod. Simul. Mater. Sci. Eng.},
  Pages = {541},
  Volume = {13},
  Year = {2005}}
  A numerical simulation study of the intersection process of a moving ½ 110 screw dislocation with a perfect stacking-fault tetrahedron (SFT) in an fcc nickel crystal is carried out using molecular dynamics for different many-body potentials. When the glide plane of the screw dislocation coincides with one of the planes of the SFT, the interaction involves several dislocation reactions, jog line formation and bending of dislocation segments. The complex atomic processes are illustrated in detail and are shown to depend on the relative orientation of the defect and moving dislocation. In most cases, the jogs disappear quickly, but in special cases the jog lines in the dissociated dislocation remain even after the interaction process with the SFT, dragging some vacancies away. While in this geometrical set-up the main effect of the intersection is the ledge formation on the SFT, when the moving dislocation intersects the SFT in the middle part, it leads to slip and the separation of the SFT into two parts. Finally, if the screw dislocation passes at non-zero distance from the SFT the elastic interaction does not lead to any deformation of the SFT.


• A. Kuronen and M. Patriarca
  Atomistic modeling of hetero-structures,
  in Handbook of Theoretical and Computational Nanotechnology, M. Rieth and W. Schommers Editors, ASP, 2005
  BibTex   [abstract]
  
  @inproceedings{Kuronen2005a,
  Address = {Stevenson Ranch},
  Author = {Kuronen, A. and Patriarca, M.},
  Title = {Atomistic modeling of strain relaxation in heterostructures},
  Booktitle = {Handbook of Theoretical and Computational Nanotechnology},
  Editor = {Rieth, Michael and Schommers, Wolfram},
  Pages = {589},
  Publisher = {American Scientific Publishers},
  Volume = {2},
  Year = {2005}}
  Atomistic methods used in the studies of hetero- and nanostructures are reviewed. Modern semiempirical potential models used in atomistic simulations are shortly described. Application of the molecular dynamics method in structural and dynamical studies of nanostructures is reviewed. Kinetic Monte Carlo method is described and its application to simulation of growth of heteroepitaxial systems is reviewed. Finally, some recently developed advanced methods are described that allow to accelerate the conventional atomistic simulation methods.


• M. Patriarca
  Feynman-Vernon model for a moving thermal environment
  Physica E 29 (2005) 243
  BibTex   [abstract]
  
  @article{Patriarca2005c,
  Author = {Patriarca, M.},
  Journal = {Physica E},
  Pages = {243},
  Title = {{F}eynman-{V}ernon model of a moving thermal environment},
  Volume = {29},
  Year = {2005}}
  The formulation of the Feynman-Vernon model of linear dissipative systems, taking into account space and time invariance properties of a thermal environment, is reviewed. In this formulation the classical limit is consistently recovered and no infinite quantities appear at any step of the calculations. The model easily lends itself to be generalized to other types of environments. The case of a thermal environment moving with a time-dependent velocity with respect to the laboratory frame is studied. The corresponding classical Langevin equation and the influence functional of the quantum path integral formulation are derived.


• M. Patriarca, P. Szelestey and E. Heinsalu
  Brownian Model of Dissociated Dislocations
  Acta Physica Polonica B 36 (2005) 1745
  BibTex   [abstract]
  
  @article{Patriarca2005b,
  Author = {Patriarca, M. and Szelestey, P. and Heinsalu, E.},
  Title = {{B}rownian model of dissociated dislocations},
  Journal = {Acta Physica Polonica B},
  Pages = {1745},
  Volume = {36},
  Year = {2005}}
  Starting from the Volterra model of dissociated dislocations, a dislocation dissociated into two Shockley partials under the action of the periodic Peierls potential and a general external stress is modeled as a pair of coupled Brownian particles in a washboard potential. It is found that mobility shows a sensitive dependence on the parameters of the interaction between partials. In particular, a resonant-like behavior of the average velocity, for equilibrium separation distances close to half-integer multiples of the period of the Peierls potential, is observed.


• P. Szelestey, M. Patriarca and K. Kaski
  Dissociated dislocations in nickel: A computational study
  Mater. Sci. Eng. A 390 (2004) 393
  BibTex   [abstract]
  
  @article{Szelestey2005a,
  Author = {Szelestey, P. and Patriarca, M. and Kaski, K.},
  Title = {Dissociated dislocations in nickel: A computational study},
  Journal = {Mat. Sci. Eng. A},
  Pages = {390},
  Volume = {393},
  Year = {2004}}
  We present a systematic computational study of the behavior of a ½ <110> dissociated screw dislocation in fcc nickel, in which atomic interactions are described through an EAM potential. A suitable external stress is applied on the system, both for modifying the equilibrium separation distance d and moving the dislocation complex. We study the structure of the dislocation and its corresponding changes during the motion, in the framework of the two-dimensional Peierls model, for different values of the ratio d/a, where a is the period of the Peierls potential. We find that the distance between the edge and screw components of the partials, as well their widths, undergo a modulation with period a, as the dislocation moves. The amplitudes of such oscillations are shown to depend on d/a. We also analyze the effective stress acting on the dislocation and estimate the critical resolved shear stress for different values of d/a.


• M. Patriarca, A. Chakraborti and K. Kaski
  A statistical model with a standard gamma distribution
  Phys. Rev. E 70, (2004) 016104
  [arxiv.org:cond-mat/0402200]   BibTex   [abstract]
  
  @article{Patriarca2004a,
  Author = {Patriarca, M. and Chakraborti, A. and Kaski, K.},
  Title = {Statistical model with a standard gamma distribution},
  Journal = {Phys. Rev. E},
  Pages = {016104},
  Volume = {70},
  Year = {2004}}
  We study a statistical model consisting of N basic units which interact with each other by exchanging a physical entity, according to a given microscopic random law, depending on a parameter λ. We focus on the equilibrium or stationary distribution of the entity exchanged and verify through numerical fitting of the simulation data that the final form of the equilibrium distribution is that of a standard Gamma distribution. The model can be interpreted as a simple closed economy in which economic agents trade money and a saving criterion is fixed by the saving propensity λ. Alternatively, from the nature of the equilibrium distribution, we show that the model can also be interpreted as a perfect gas at an effective temperature T(λ), where particles exchange energy in a space with an effective dimension D(λ).


• M. Patriarca, A. Chakraborti and K. Kaski
  Gibbs versus non-Gibbs distributions in money dynamics
  Physica A 340 (2004) 334
  [arxiv.org:cond-mat/0312167]   BibTex   [abstract]
  
  @article{Patriarca2004b,
  Author = {Patriarca, M. and Chakraborti, A. and Kaski, K.},
  Title = {{G}ibbs versus non-{G}ibbs distributions in money dynamics},
  Journal = {Physica A},
  Pages = {334},
  Volume = {340},
  Year = {2004}}
  We review a simple model of closed economy, where the economic agents make money transactions and a saving criterion is present. We observe the Gibbs distribution for zero saving propensity and non-Gibbs distributions otherwise. While the exact solution in the case of zero saving propensity is already known to be given by the Gibbs distribution, here we provide the explicit analytical form of the equi- librium distribution for the general case of nonzero saving propensity. We verify it through comparison with numerical data and show that it can be cast in the form of a Poisson distribution.


• M. Patriarca and T. Leppänen
  Modelling language competition
  Physica A 338 (2004) 296
  BibTex   [abstract]
  
  @article{Patriarca2004c,
  Author = {Patriarca, M. and Lepp{\"a}nen, T.},
  Title = {Modeling language competition},
  Journal = {Physica A},
  Pages = {296},
  Volume = {338},
  Year = {2004}}
  We consider a model introduced recently Nature 424(2003)900, for describing competition between two languages, which in typical situations predicts the extinction of one of them. We generalize it by introducing a spatial dependence in terms of a reaction–diffusion equation. We show that in this generalized model both languages can survive, each mostly concentrated in a different geographical area.


• P. Szelestey, M. Patriarca and K. Kaski
  Computational study of core structure and Peierls stress of dissociated dislocations in nickel
  Modelling Simul. Mater. Sci. Eng. 11 (2003) 883
  BibTex   [abstract]
  
  @article{Szelestey2003a,
  Author = {Szelestey, P. and Patriarca, M. and Kaski, K.},
  Title = {Computational study of core structure and {P}eierls stress of dissociated dislocations in nickel},
  Journal = {Mod. Simul. Mater. Sci. Eng.},
  Pages = {1},
  Volume = {11},
  Year = {2003}}
  We study the core structure and determine the Peierls stress (PS) of dissociated ½ <110> dislocations in FCC nickel by atomistic molecular dynamics simulations, using an EAM potential. Different pictures for the behaviour of edge and screw dislocations of this type emerge from the results of the simulations. On the one hand, the edge dislocation is observed to dissociate along a path that corresponds to the crystallographic Burgers vector of partials. The separation distance between partials is found to be a multiple of the lattice constant. Under the action of an external stress, the partials move in phase and behave globally as a rigid complex. Correspondingly, the PS for a single partial is close to the effective PS for the extended dislocation. On the other hand, in the screw dislocation, the separation distance is smaller and close to a half- integer of the lattice constant. The strong core overlap produces a significant reduction of the lateral Burgers vector in the dissociation process. Under a stress, the partials move out of phase and the separation distance undergoes some modulations. In this case, the effective PS is found to be smaller than the PS for partials.


• M. Patra, M. Patriarca and M. Karttunen
  Stability of charge inversion, Thomson problem and application to electrophoresis
  Phys. Rev. E 67 (2003) 031402
  [arxiv.org:physics/0211006]   BibTex   [abstract]
  
  @article{Patra2003a,
  Author = {Patra, M. and Patriarca, M. and Karttunen, M.},
  Title = {Stability of charge inversion, {T}homson problem and application to electrophoresis},
  Journal = {Phys. Rev. E},
  Pages = {031402},
  Volume = {67},
  Year = {2003}}
  We analyze charge inversion in colloidal systems at zero temperature using stability concepts and connect this to the classical Thomson problem of arranging electrons on sphere. We show that for a finite microion charge, the globally stable, lowest-energy state of the complex formed by the colloid and the oppositely charged microions is always overcharged. This effect disappears in the continuous limit. Additionally, a layer of at least twice as many microions as required for charge neutrality is always locally stable. In an applied external electric field the stability of the microion cloud is reduced. Finally, this approach is applied to a system of two colloids at low but finite temperature.


• P. Szelestey, M. Patriarca, L. F. Perondi and K. Kaski
  Modified EAM potentials for modelling stacking fault behavior in Cu, Al, Au and Ni
  Int. J. Mod. Phys. B 16(19) (2002) 2823
  BibTex   [abstract]
  
  @article{Szelestey2002a,
  Author = {Szelestey, P. and Patriarca, M. and Perondi, L. F. and Kaski, K.},
  Title = {Modified {EAM} potentials for modelling stacking-fault behavior in {C}u, {A}l, {A}u and {N}i},
  Journal = {Int. J. Mod. Phys. B},
  Pages = {2823},
  Volume = {16},
  Year = {2002}}
  In this paper we have developed Embedded Atom Model potentials, following the fitting scheme proposed by Chantasiriwan and Milstein, in order to describe the stacking fault behaviour of copper, gold, nickel, and aluminium. We show that the potentials based on this scheme can be modified to provide reasonable stacking-fault energy values and consequently a better description of the plastic properties. Modifications were done by changing the cut-off distance in case of aluminium and nickel and in case of gold and copper by also modifying the functional form of the pair potential. In order to validate these modified potentials we have tested them by studying various properties, such as structural, defect and surface energies and phonon spectra and comparing results with those from experiments and other model potentials.


• M. Patriarca, A. Kuronen and K. Kaski
  Nucleation and dynamics of dislocations in mismatched heterostructures
  in 2001 MRS Fall Meeting Proceedings Vol. 696 Symposium N 4.4, MRS
  BibTex   [abstract]
  
  @inbook{Patriarca2001a,
  Author = {Patriarca, M. and Kuronen, A. and Kaski, K.},
  Title = {Nucleation and dynamics of dislocations in mismatched heterostructures},
  Booktitle = {2001 MRS Fall Meeting Proceedings},
  Publisher = {Material Research Society},
  Volume = {696, Symposium N 4.4},
  Year = {2001}}
  In this paper we have investigated, through computer simulations, dislocation nucleation and dislocation dynamics in a heterostructure system with the lattice-mismatch interface, i.e. a system with internal strain. In particular, we have studied the dependence of the nucleation thresholds on the basic parameters of the crystals, such as the amount of mismatch and the system temperature. These studies have been carried out by using the simulation code with a graphical user interface developed at our laboratory. This on-line simulation system produces a real time interactive visualization of the 3-D Molecular Dynamics model. Furthermore, it detects the presence of dislocations and tracks them by an algorithm based on potential energy mapping.


• B.L. Altschuler, C. Biagini and M. Patriarca
  Quantum chaos and transport in mesoscopic systems
  in: Field Theories for low-dimensional systems
  G. Morandi, P. Sodano, A. Tagliacozzo and V. Tognetti Editors,
  Springer-Verlag, Berlin (2000), Chap.7
  BibTex  
  
  @inbook{Altschuler2000a,
  Author = {B.L. Altschuler and C. Biagini and M. Patriarca},
  Title = {Quantum chaos and transport in mesoscopic systems},
  Booktitle = {Field Theories for low-dimensional systems},
  Publisher = {Springer-Verlag},
  Address = {Berlin},
  Chapter = {7},
  Year = {2000}}


• M. Patriarca
  Quantum mechanical versus stochastic processes in path integration
  Path Integrals from peV to TeV: 50 years after Feynman's Paper, R. Casalbuoni, R. Giachetti, V. Tognetti, R. Vaia and P. Verrucchi Eds., World Scientific, Singapore, 1999, p.589
  BibTex   [abstract]
  
  @inproceedings{Patriarca1999a,
  Author = {Patriarca, M.},
  Title = {Quantum mechanical versus stochastic processes in path integration},
  Booktitle = {Path Integrals from peV to TeV: 50 years from Feynman's Paper},
  Editor = {Casalbuoni, R. and Giachetti, R. and Tognetti, V. and Vaia, R. and Verrucchi, P.},
  Publisher = {World Scientific},
  Address = {Singapore},
  Pages = {589},
  Year = {1999}}
  By using path integrals, the stochastic process associated to the time evolution of the quantum probability density |ψ( x, t )|² is rewritten as a classical stochastic process. It is found that the motion of a quantum particle is formally determined by a stochastic differential equation with an external mulitplicative noise, defined however by a non positive probability functional. This provides a clear example of the negative (or "extended") probabilities characteristic of quantum mechanics.


• C. Presilla, R. Onofrio and M. Patriarca
  Classical and quantum measurements of position
  J. Phys. A 30(21) (1997) 7385
  [arxiv.org:hep-th/9406024]   BibTex   [abstract]
  
  @article{Presilla1997a,
  Author = {Presilla, C. and Onofrio, R. and Patriarca, M.},
  Journal = {J. Phys. A},
  Pages = {7385},
  Title = {Classical and quantum measurements of position},
  Volume = {30},
  Year = {1997}}
  We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the measured system. Selective and non-selective measurement processes are then introduced according to a selection of or an average over all possible initial configurations of the measurement apparatus. At quantum level, the selective processes are described by a nonlinear stochastic Schrödinger equation whose solutions evolve into properly defined coherent states in the case of linear systems. For arbitrary measured systems, classical behaviour is always recovered in the macroscopic limit.


• M. Patriarca
  Statistical correlations in the oscillator model of quantum Brownian motion
  Il Nuovo Cimento B 111 (1996) 61
  BibTex   [abstract]  
  
  @article{Patriarca1996a,
  Author = {Patriarca, M.},
  Journal = {Il Nuovo Cimento B},
  Pages = {61},
  Title = {Statistical correlations in the oscillator model of quantum {B}rownian motion},
  Volume = {111},
  Year = {1996}}
  We study the problem of the initial conditions for the oscillator model of quantum dissipative systems. It is argued that, even in the classical case, the hypothesis that the environment is in thermal equilibrium implies a statistical correlation between the environment and the central system. Analogously to the classical model, we obtain a simple form of initial conditions for the quantum problem, that takes into account such a correlation. As a check on the new form of correlated initial conditions, we study the forced Brownian particle with arbitrary colored noise. On the one hand, starting from the correlated initial conditions, we show that the average position of a wave packet is equal to that of the corresponding classical Brownian particle. On the other hand, starting from the initial conditions based on the factorization hypothesis, that implies absence of correlation, nonphysical results are obtained.


• F. Illuminati, M. Patriarca and P. Sodano
  Quantum dissipation in non-homogeneous environments
  Fluctuation Phenomena: Disorder and Nonlinearity
  A.R. Bishop, S. Jimenez and L. Vazquez Editors
  World Scientific, Singapore (1995), p.53.
  BibTex   [abstract]
  @inproceedings{Illuminati1995a,
  Address = {Singapore},
  Author = {Illuminati, F. and Patriarca, M. and Sodano, P.},
  Booktitle = {Fluctuation Phenomena: Disorder and Nonlinearity},
  Editor = {Bishop, A. R. and Jimenez, S. and Vazquez, L.},
  Keywords = {QBM},
  Pages = {53},
  Publisher = {World Scientific},
  Title = {Quantum dissipation in non homogeneous environments},
  Year = {1995}}
  See the article below:
  - F. Illuminati, M. Patriarca and P. Sodano,
  Classical and quantum dissipation in nonhomogeneous environments,
  Physica A 211 (1994) 449 [arxiv.org:hep-th/9406024].


• F. Illuminati, M. Patriarca and P. Sodano
  Classical and quantum dissipation in nonhomogeneous environments
  Physica A 211 (1994) 449
  [arxiv.org:hep-th/9406024]   BibTex   [abstract]
  
  @article{Illuminati1994a,
  Author = {Illuminati, F. and Patriarca, M. and Sodano, P.},
  Journal = {Physica A},
  Pages = {449},
  Title = {Classical and quantum dissipation in nonhomogeneous environments},
  Volume = {211},
  Year = {1994}}
  We generalize the oscillator model of a particle interacting with a thermal reservoir by introducing arbitrary nonlinear couplings in the particle coordinates. The equilibrium positions of the heat bath oscillators are promoted to space-time functions, which are shown to represent a modulation of the internal noise by the external forces. The model thus provides a description of classical and quantum dissipation in non homogeneous environments. In the classical case we derive a generalized Langevin equation with nonlinear multiplicative noise and a position-dependent fluctuation-dissipation theorem associated to non homogeneous dissipative forces. When time-modulation of the noise is present, a new force term is predicted besides the dissipative and random ones. The model is quantized to obtain the non homogenous influence functional and master equation for the reduced density matrix of the Brownian particle. The quantum evolution equations reproduce the correct Langevin dynamics in the semiclassical limit. The consequences for the issues of decoherence and localization are discussed.


• F. Marchesoni and M. Patriarca
  Self-organized criticality in dislocation networks
  Phys. Rev. Lett. 72 (1994) 4101
  BibTex   [abstract]
  
  @article{Marchesoni1994a,
  Author = {Marchesoni, F. and Patriarca, M.},
  Title = {Self-organized criticality in dislocation networks},
  Journal = {Phys. Rev. Lett.},
  Pages = {4101},
  Volume = {72},
  Year = {1994}}
  The response of a dislocation network subject to a periodic external stress is simulated in the kink representation. Kink-kink and kink-pinning point interactions lead to a local, random reduction in the breakaway stress, so that a certain fraction of the total dislocation line is critically pinned according to a self-organized pattern. Mechanical dissipation caused by critically pinned dislocation segments is suggested to be responsible for the finite values of the decrement function measured experimentally at low frequencies.


• M. Patriarca
  Boundary conditions for the Schrödinger equation in the simulation of quantum systems
  Phys. Rev. E 50 (1994) 1616
  BibTex   [abstract]
  
  @article{Patriarca1994a,
  Author = {Patriarca, M.},
  Title = {Boundary conditions for the Schr{\"o}dinger equation in the simulation of quantum systems},
  Journal = {Phys. Rev. E},
  Pages = {1616},
  Volume = {50},
  Year = {1994}}
  We study the problem of the boundary conditions in the numerical simulation of closed and open quantum systems, described by a Schrödinger equation. On one hand, we show that a closed quantum system is defined by local boundary conditions. On the other hand, we argue that, because of the uncertainty principle, no local boundary conditions can be defined for open quantum systems. For this reason plane waves or wave packet trains cannot be simulated on a finite numerical lattice with the usual procedures. We suggest a method which avoids these difficulties by using only a small numerical lattice and maintains the correspondence with the physical picture, in which the incident and scattered waves may be infinitely extended.


• M. Patriarca
  Sistemi quantistici in ambienti dissipativi (Quantum systems in dissipative environments)
  Tesi di Dottorato (PhD Thesis)
  BibTex   [abstract]
  
  @phdthesis{Patriarca1993a,
  Author = {Patriarca, M.},
  Keywords = {QBM QM FV model},
  School = {University of Perugia},
  Title = {{S}istemi {Q}uantistici in {A}mbienti {D}issipativi},
  Year = {1993}}
  See the article above:
  Statistical correlations in the oscillator model of quantum Brownian motion, Il Nuovo Cimento B 111 (1996) 61


• F.A. Gianturco, M. Patriarca and O. Roncero
  Resonant states and photodissociation cross sections in protonated rare gases: the Ne-H⁺ and Ar-H⁺ systems
  Molecular Physics 67 (1989) 281
  BibTex   [abstract]
  
  @article{Gianturco1989a,
  Author = {Gianturco, F. A. and Patriarca, M. and Roncero, O.},
  Title = {Resonant states and photodissociation cross sections in the protonated rare gases: {T}he $\mathrm{{N}e{H}}^{+}$ and $\mathrm{{A}r{H}}^{+}$ systems},
  Journal = {Mol. Phys.},
  Pages = {281},
  Volume = {67},
  Year = {1989}}
  The ground state interaction potentials for the Ne(¹S) and Ar(¹S) systems with H⁺ as a partner have been obtained in a rather simple analytic form and with a parameter optimization that took into consideration a broad range of experimental data, thus extending and verifying earlier work which considered only scattering experiments. It is clearly shown by the present work that the available spectroscopic data on the location of the diatomic bound states and on the transitions between them, the measured differential cross sections at various collision energies and the mobility coefficients at various E/N values are all well reproduced by our final potential forms, as opposed to the poorer performances of earlier analytic potentials that had been suggested for the same systems. As a consequence of the present analysis very accurate, multiproperty potential functions are thus obtained and provided for the two systems under study.


• F.A. Gianturco and M. Patriarca
  Accurate Ne-H⁺ and Ar-H⁺ interactions from spectroscopic and scattering states: a comparison of theory with experiments
  Il Nuovo Cimento 11 D (1989) 1287
  BibTex   [abstract]
  
  @article{Gianturco1989b,
  Author = {Gianturco, F. A. and Patriarca, M.},
  Title = {Accurate $\mathrm{{N}e{H}}^{+}$ and $\mathrm{{A}r{H}}^{+}$ interactions from spectroscopic and scattering states: A comparison of theory with experiments},
  Journal = {Il Nuovo Cimento D},
  Pages = {1287},
  Volume = {11},
  Year = {1989}}
  Highly accurate potential functions obtained earlier by us for Ne-H⁺ and Ar-H⁺ have been used to compute the entire manifold of quasi-bound states within a given range of possible widths. Semiclassical and quantal methods were employed and compared for both diatomics, showing very good accord with each other. General dipole function are then extracted from a combined use of ab initio and model calculations and employed to evaluate transition moments and then used to compute theoretical photodissociation cross sections and asymmetry parameters β(E). Resonant dissociation widths and positions are finally compared with the same quantities from the direct predissociative process and results are discussed vis à vis possible experiments on the present systems.


• M. Patriarca
  Trattamento quantistico di ioni molecolari semplici (Quantum treatment of simple molecular ions)
  Tesi di Laurea (Master Thesis)
  University of Rome La Sapienza
  BibTex   [abstract]
  
  @MastersThesis{Patriarca1987a,
  author = {Marco Patriarca},
  title = {Trattamento quantistico di ioni molecolari semplici},
  school = {University of Rome {\it La Sapienza}},
  year = {1987},
  address = {Rome, Italy},
  month = {November 26th}}
  See the two articles above:
  - F.A. Gianturco and M. Patriarca, Accurate Ne-H⁺ and Ar-H⁺ interactions from spectroscopic and scattering states: a comparison of theory with experiments, Il Nuovo Cimento 11 D (1989) 1287,
  - F.A. Gianturco and M. Patriarca and O. Roncero, Resonant states and photodissociation cross sections in protonated rare gases: the Ne-H⁺ and Ar-H⁺ systems, Molecular Physics 67 (1989) 281.