@incollection{statphys23_1064, title = {Dwell time of a Brownian interacting molecule in a cellular microdomain}, address = {Genova, Italy}, author = {T.H. Taflia and D.D. Holcman}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi}, month = {9-13 July}, year = 2007, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=1064}, abstract = {The mechanism that regulates the number and the type of receptors at a synapse control the synaptic weight. Any fluctuations of their number results in a variation of the synaptic weight and affects the reliability of the synaptic transmission. Moreover, certain experimental protocols have lead to a Long Term Potentiation of a synapse, a mechanism which is associated with a change of the number and the type of certain receptors . The regulation of synaptic plasticity is a fundamental process underlying learning and memory. Recently, single molecule tracking has revealed that the number of postsynaptic receptors, which participate to the synaptic transmission, is not fixed but it changes due to constant traffick of receptors on the surface of neurons. Receptors move in and out from synaptic regions and following these observations, many questions have been raised: in particular, what determines the time spent by a receptor inside a synapse? How receptors can be stabilized inside a synapse? How long they stay inside synaptic microdomains? Such questions are partially answered in the present paper. In particular, our computation of the Dwell time of a receptor inside a specific microdomain,called post synaptic domain (PSD). In the present article, we propose to estimate the mean time spent by a Brownian molecule inside a microdomain which contains a small hole on the boundary and agonist molecules located inside. We found that the mean time depends on several parameters such as the backward binding rate (with the agonist molecules), the mean escape time from the microdomain and the mean time a molecule reaches the binding sites (forward binding rate). In addition, we estimate the mean and the variance of the number of bounds made by a molecule before it exits. In particular, we apply the present results to obtain an estimate of the mean time spent (Dwell time) by a Brownian receptor inside a synaptic domain, when it moves freely by lateral diffusion on the surface of a neuron and interacts locally with scaffolding molecules.}, biburl = {http://www.bibsonomy.org/bibtex/2334ea6c67262b6505773197e343a6a93/statphys23}, keywords = {boundary brownian first mean mixed motion passage problem statphys23 synaptic time topic-10 value weight} } @incollection{statphys23_0991, title = {Efficiency of encounter-controlled reactions in regular and disordered networks}, address = {Genova, Italy}, author = {A. Garcia Cantu and E. Abad}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi}, month = {9-13 July}, year = 2007, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=991}, abstract = {Using a Markov chain formulation, we study the efficiency of an encounter-controlled reaction for a pair of walkers diffusing through both regular and disordered networks. The efficiency is determined by the mean number of steps the walkers perform before meeting. Ordinarily, the efficiency is expected to increase monotonically as the effective size of the network diminishes, e.g. as a result of increasing the relative mobility between particles or introducing shortcuts by randomly rewiring connections between nodes. However, we show that the efficiency can display nontrivial nonmonotonic behavior within a proper parameter range. An explanation of this behavior is proposed in terms of a competition between the increase of the relative diffusion coefficient and the increase in the probability of escaping from the typical interaction zone.}, biburl = {http://www.bibsonomy.org/bibtex/29ebcf73e144586c769a6985c153f938f/statphys23}, keywords = {diffusion-controlled first networks on passage problems reactions statphys23 topic-3 walks} } @incollection{statphys23_0777, title = {Robustness of adiabatic passage through a quantum critical point}, address = {Genova, Italy}, author = {A. Fubini and G. Falci and A. Osterloh}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi}, month = {9-13 July}, year = 2007, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=777}, abstract = {We analyze the crossing of a quantum critical point based on exact results for the transverse XY model. In dependence of the change rate of the driving field, the evolution of the ground state is studied while the transverse magnetic field is tuned through the critical point with a linear ramping. The excitation probability is obtained exactly and is compared to previous studies and to the Landau-Zener formula, a long time solution for non-adiabatic transitions in two-level systems. The exact time dependence of the excitations density in the system allows to identify the adiabatic and diabatic regions during the sweep and to study the m esoscopic fluctuations of the excitations. The effect of white noise is investigated, where the critical point transmutes into a non-hermitian ``degenerate region''. Besides an overall increase of the excitations during and at the end of the sweep, the most destructive effect of the noise is the decay of the state purity that is enhanced by the passage through the degenerate region.}, biburl = {http://www.bibsonomy.org/bibtex/203d506efc28e5d8a5c4f1a3ecc9e0145/statphys23}, keywords = {adiabatic dynamics models noise passage phase quantum spin statphys23 topic-8 transitions} } @incollection{statphys23_0671, title = {Transport and first passage properties of a discrete version of the Ornstein-Uhlenbeck process}, address = {Genova, Italy}, author = {H. Larralde}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi}, month = {9-13 July}, year = 2007, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=671}, abstract = {A discrete version of the Ornstein-Uhlenbeck process, which arises as a simple generalization of the discrete random walk, is analyzed. The statistical properties of the free propagator for the process are evaluated for the one dimensional case. It is shown that if the jump distribution has finite variance the usual equation for the evolution of the probability distribution of the Ornstein-Uhlenbeck process is recovered in the continuum limit. However, the discrete process is well defined also for long tailed jump distributions and can be used to describe a L\`evy walk under the effect of a harmonic potential. Further, some first passage properties of the process are studied. In particular, it is shown that the universal features of Sparre-Andersen's theorem do not extend to the discrete O-U process. Finally, a brief discussion of the generalization of this process to describe random walks in general potentials is presented and briefly compared with results arising from the fractional diffusion approach.}, biburl = {http://www.bibsonomy.org/bibtex/2103d35d06c2a84f13b8f28da4cba0d16/statphys23}, keywords = {first ornstein passage process random statistics statphys23 topic-3 walks} } @incollection{statphys23_0435, title = {Two-dimensional intermittent search processes: An alternative to Levy flight strategies}, address = {Genova, Italy}, author = {C. Loverdo and O. Benichou and R. Voituriez and M. Moreau}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi}, month = {9-13 July}, year = 2007, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=435}, abstract = {Levy flights are known to be optimal search strategies in the particular case of revisitable targets. In the relevant situation of nonrevisitable targets, we propose an alternative model of two-dimensional 2D search processes, which explicitly relies on the widely observed intermittent behavior of foraging animals. We show analytically that intermittent strategies can minimize the search time, and therefore do constitute real optimal strategies. We study two representative modes of target detection and determine which features of the search time are robust and do not depend on the speci?c characteristics of detection mechanisms. In particular, both modes lead to a global minimum of the search time as a function of the typical times spent in each state, for the same optimal duration of the ballistic phase. This last quantity could be a universal feature of 2D intermittent search strategies. References : G.M. Viswanathan, S.V. Buldyrev, S.Havlin, M.G.E. Da Luz, E.P. Raposo et H.E. Stanley : Optimizing the success of random searches. Nature, 401(6756):911-914, (1999). O.Benichou, C.Loverdo, M.Moreau et R.Voituriez, A minimal model of intermittent search in dimension two, Journal of Physics : Condensed Matter 19, 065141 (2007) O.Benichou, C.Loverdo, M.Moreau et R.Voituriez, Two-dimensional intermittent search processes : An alternative to Levy flight strategies Physical Review E 74, 020102 (2006) This last article has been commented in a news and views in Nature : M.F. Shlesinger : Mathematical physics : Search research. Nature, 443:281, (2006)}, biburl = {http://www.bibsonomy.org/bibtex/2e02993157386c96fded387c4a2a526f4/statphys23}, keywords = {first intermittent passage processes random search statphys23 strategies time topic-11 walks} } @incollection{statphys23_0421, title = {Optimal Search Strategies for Hidden Targets}, address = {Genova, Italy}, author = {O. Benichou and C. Loverdo and M. Moreau and R. Voituriez}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi}, month = {9-13 July}, year = 2007, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=421}, abstract = {Many physical, chemical or biological problems can be rephrased as search processes, involving a searcher and a target of unknown position. We show that intermittent search strategies, alternating active search phases and non reactive displacement phases, are universal for a wide class of problems involving search time optimization. More precisely, we address the general question of determining in which cases a searcher should, or should not, interrupt his search activity by losing time in non reactive phases of mere displacement, and which durations of each phase optimize the search time. Using a representative analytical model, we show that intermittent strategies do optimize the search time as soon as the target is difficult to detect, and we explicitly give the optimal search strategies, which depend on the memory skills of the searcher. References:\\ 1. M. Coppey, O. Benichou, R. Voituriez, and M. Moreau, Biophys. J. 87, 1640 (2004) 2. O. Benichou, M. Coppey, M. Moreau, PH Suet, R. Voituriez, Phys. Rev. Lett. {\bf 94}, 198101 (2005) 3. O Benichou, C. Loverdo, M. Moreau, R. Voituriez, Phys. Rev. E {\bf 74}, 020102 (2006)}, biburl = {http://www.bibsonomy.org/bibtex/2779aa51e3517d98ac494795906a1b4fb/statphys23}, keywords = {first passage processes random search statistics statphys23 topic-11 walks} } @incollection{statphys23_0349, title = {Persistence effects in first-passage time characteristics of liquids}, address = {Genova, Italy}, author = {A.J. Dammers and V.J. Van Hijkoop and M.O. Coppens}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi}, month = {9-13 July}, year = 2007, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=349}, abstract = {We analyse diffusive molecular motion in several liquids, obtained from molecular dynamics simulations, by a first passage time analysis. Within the simulation box, a slab of thickness $L$, with two (virtual) parallel absorbing boundaries, normal to the $z$ axis, is defined. A particle, initially present at a position ${z=z_0}$ in the slab, is monitored until it crosses one of the boundaries, and the elapsed time is recorded. From the diffusion equation, with Smoluchowski boundary conditions ${c(0)=c(L)=0}$, one may derive [1] that the mean exit time for an ensemble of such particles is given by the parabolic equation ${T(z_0)=\frac{1}{2D}z_0(L-z_0)}$, where $D$ is the diffusion coefficient. Our simulation data, however, can only be reconciled with this equation if we assume that each boundary is shifted outwards by an amount $\lambda_M$, i.e., we replace ${z_0\rightarrow\widetilde{z}_0=z_0+\lambda_M}$ and ${L\rightarrow\widetilde{L}=L+2\lambda_m}$. % The quantity $\lambda_M$ is identified as the Milne extrapolation length [2][3]. It is related to the presence of a kinetic boundary layer near an absorbing interface, where large deviations from the Maxwellian velocity distribution occur. This phenomenon can be derived from a Fokker-Planck equation, which accounts for positions and velocities, in contrast to the diffusion equation, where only positions are present. Far away from the interface, however, the system can still be described by a diffusion equation, however with an apparently shifted absorbing boundary. The Milne length was found analytically [3] as ${\lambda_M = |\zeta(\frac{1}{2})|\,l_v}$. Here $\zeta(\frac{1}{2})=- 1.4603\dots$ is a Riemann zeta function and $l_v=D\,\sqrt{m/k_{B}T}$ is a velocity correlation length, with $m$ the molecular mass, $T$ the temperature and $k_B$ the Boltzmann constant. % Our simulations show deviations from this theoretical prediction. For simple liquids (Ar, O$_2$, CO$_2$) we obtain values approximately 1.5 times larger. For water (several models) approximately a factor 3 is found. This is interpreted in terms of memory effects in the molecular motion. It appears to be stronger in a hydrogen bonding liquid like water than in simple liquids, in accordance with current understanding of such systems.\\ 1) S. Redner, \textit{A Guide to First-Passage Processes} (Cambridge University Press, 2001).\\ 2) M. Burschka and U. Titulaer, J. Stat. Phys. \textbf{25}, 569 (1981).\\ 3) T. W. Marshall and E. J. Watson, J. Phys. A: Math. Gen. \textbf{20}, 1345 (1987).}, biburl = {http://www.bibsonomy.org/bibtex/2c3ebea496ace50cb5e286586ce7c74b7/statphys23}, keywords = {boundary diffusion extrapolation first kinetic layer length liquids milne passage statphys23 time topic-6} } @incollection{statphys23_0258, title = {Distributions of passage times and distances along critical curves}, address = {Genova, Italy}, author = {A. Zoia and Y. Kantor and M. Kardar}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi}, month = {9-13 July}, year = 2007, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=258}, abstract = {Scale invariant curves, such as coastlines and fracture fronts, abound in nature. Fractal dimension provides the scaling of the length $\ell$ along the curve between two points to their actual separation $R$ in Euclidean space. However, for stochastic shapes, the actual length will fluctuate, and knowledge of its full distribution greatly augments the information about scaling. We numerically investigate such distributions for scale invariant (critical) curves in two dimensions. While the actual quantity that we measure is the distribution of lengths along the fractal curves, an underlying motivation is to understand the distribution of first passage times for traversing such curves. To provide an example, experiments characterizing the behavior of chemical tracers point out that the flow field of a water-saturated heterogeneous porous sediment or fractured hard rock formation can possibly be regarded as a network of fractal paths. Also, we may wish to track the spread of an inject along a coastline or a crack. In such cases, finding the distribution of first passage times between points of known Euclidean distance requires knowledge of the dynamics of the process as well as the distribution of lengths. If we assume that the motion along the path is independent of its shape (as in a simple damage spreading process, or curvature independent diffusion), we can then obtain the distribution of first passage times from a simple convolution of the distribution of lengths. At the minimum, the results of such an assumption may help to rule out simple hypotheses about the dynamics and/or structures of the fractal shapes in physical models. Important examples of scale invariant curves in two dimensions are self-avoiding walks (SAWs) and percolation fronts (PFs): additional instances may be obtained from critical systems. These examples suggest that generating and studying stochastic scale-invariant curves is a computationally hard process. Indeed, the past decades have witnessed much effort and progress in efficient numerical algorithms for generating SAWs and critical systems. An important recent development concerns the Stochastic Loewner Evolution (SLE), which provides a way of generating such curves through mappings (in the complex plane) of a simple Markovian random walk. While the main interest in SLE has been as a way of extracting analytic information about critical systems, here we use it as an efficient means to generate curves with different values of the fractal dimension. One issue with SLE as a numerical tool is that (since it is strictly defined in the continuum limit) the length of the curve is not well defined. This question has also been discussed by Kennedy, and like him we introduce a specific procedure for calculating distances along curves generated by discretized SLE. The mathematical ambiguity makes it essential to verify the correctness of this procedure. We do so by comparing distributions obtained from lattice implementation of SAWs and PFs with those obtained from implementation of SLE with appropriate parameters. Having gained confidence on this procedure, we use SLE to generate different sets of scale invariant curves with fractal dimensions $1