Houghton Conference Poster Presentations May 4, 2015

Transcription

1 Houghton Conference Poster Presentations May 4, 2015 Equal- time statistics of the stochastically forced Lorenz- 63 attractor via Fokker- Planck and cumulant expansion methods Altan Turowicz Allawala, Brown University We investigate the Fokker- Planck (FP) description of the invariant measure of the three- dimensional Lorenz- 63 attractor with additional stochastic forcing. We present a sparse- matrix method to find the invariant measure by accessing the zero modes of the linear Fokker- Planck operator. A perturbative expansion in equal- time cumulants approach is also presented. Theoretical and computational issues of both approaches are discussed along with a comparison of results. Anomalous processes with general waiting times: functionals and multi- point structure Andrea Cairoli, Queen Mary University of London Many transport processes in nature exhibit anomalous diffusive properties with non- trivial scaling of the mean square displacement, e.g., diffusion of cells or of chromosomes inside the cell nucleus, where typically a crossover between different scaling regimes appears over time. Here, we investigate a class of anomalous diffusion processes that is able to capture such complex dynamics by virtue of a general waiting time distribution. We obtain a complete characterization of such generalized anomalous processes, including their functionals and multi- point structure, using a representation in terms of a normal diffusive process plus a stochastic time change. A generalized Feynman- Kac formula is derived, where the non- Markovian features are manifest in a memory kernel that is naturally related to the characteristic functional of the waiting times. In the special case of power law distributed waiting times we recover well- known results from the theory of continuous time random walks. Our results are readily applicable to joint velocity- position data of anomalous diffusive systems, for which a consistent underlying stochastic process can often not be identified among conventional models. Flow- driven Delocalization of Populations in Disordered Environments Thiparat Chotibut, Harvard University Growth in controlled laboratory environments such as a Petri dish can be used to study the spatial evolutionary dynamics of microorganisms. However, natural populations often grow up in heterogeneous environments with spatially varying growth rates, and can be subjected to fluid advection as well. Using lattice Boltzmann simulations, we study single species population dynamics subject to constant flows under heterogeneous growth conditions. We show that quenched random growth rates lead to localized growth niches even in the presence of a background fluid flow. Non- equilibrium steady states when the

2 flow velocity is weak exhibit a mixture of localized high- density growth niches and a low- density background mass distribution influenced by extended states of the linearized growth operator. At sufficiently strong advection, however, the growth niches delocalize to form elongated parallel streaks of order the system size along the flow direction. We study the localized and delocalized growth eigenfunctions of the associated non- Hermitian tight- binding model, as well as a phase transition characterized by a diverging correlation length in the flow direction. Cell List Algorithms for Nonequilibrium Molecular Dynamics Matthew Dobson, University of Massachusetts A common approach in the molecular simulation of homogeneous linear background flow is the use of boundary conditions that deform with the flow. Recent developments have been made in finding long- term compatible boundary conditions for a general class of three- dimensional flows. We present two modifications of the standard cell list algorithm for nonequilibrium molecular dynamics. The modified algorithms handle the dynamic, deforming simulation geometry reduce the computational complexity of force computations from O(N^2) to O(N) in the number of particles N. Chirality, causality, and fluctuation- dissipation theorems in non- equilibrium steady states Dima Feldman, Brown University Edges of some quantum Hall liquids and a number of other systems exhibit chiral transport: excitations can propagate in one direction only, e.g., clockwise. We derive a family of fluctuation- dissipation relations in non- equilibrium steady states of such chiral systems. The theorems connect nonlinear response with fluctuations far from thermal equilibrium and hold only in case of chiral transport. They can be used to test chiral or non- chiral character of the system. Mathematical Modeling of Oceanic Phytoplankton Blooms in Chaotic Flows Mara Freilich, Brown University Phytoplankton blooms are geochemically and ecologically important, but current understanding of the causes of phytoplankton blooms provides little power to predict the timing, extent, and distribution of blooms. In this presentation, I study the ways in which large- scale biomass and variability of phytoplankton is affected by light limitation, chaotic advection, and diffusion. I use deterministic non- linear models of plankton growth and analyze the emergence of heterogeneity in terms of non- dimensional ratios between biological and physical timescales.

3 Analytical framework for modeling of long- range transport of fungal plant epidemics Oleg Kogan, Cornell University A new framework for the study of long- range transport of fungal plant epidemics is proposed. The null nonlinear model includes advective transport through the free atmosphere, spore production on the ground, and transfer of spores between the ground and the advective atmospheric layer. We find that the speed of the downwind front does not have a strong dependence on the rate of spore transfer between the advective layer and the ground. Thus, even vanishingly small transfer rates result in a substantial epidemic wave in the direction of the wind. We also consider the effect of an additional, random- walk like mechanism of transport through the near- ground atmospheric boundary layer, and attempt to understand which route dominates the transport over long distances. This framework should be applicable to other processes that involve a region of reactions on a surface (such as a catalyst) and a separate channel of advective transport (such as a gas or blood flow). Physically feasible isothermal autonomous Maxwell's demon Aki Tapio Kutvonen, Aalto University In this work we use the recent developments in thermodynamics at small scales and information thermodynamics to study a physically feasible model of autonomous Maxwell's demon. Ising universality describes emergent synchronization of oscillating ecological populations Andrew Noble, UC Davis and UMass Amherst Understanding the synchronization of oscillations across space is fundamentally important to many scientific disciplines. In ecology, long- range synchronization of oscillations in spatial populations may elevate extinction risk and signal an impending catastrophe. The prevailing assumption is that synchronization on distances longer than the dispersal scale can only be due to environmental correlation (the Moran effect). In contrast, we show how long- range synchronization can emerge over distances much longer than the length scales of either dispersal or environmental correlation. In particular, we demonstrate that the transition from incoherence to long- range synchronization of two- cycle oscillations in noisy spatial population models is described by the Ising universality class of statistical physics. This result shows, in contrast to all previous work, how the Ising critical transition can emerge directly from the dynamics of ecological populations. The co- authors: Jonathan Machta (UMass Amherst and SFI) and Alan Hastings (UC Davis).

4 Numerical and Statistical Simulation of an Idealized Model Tachocline Abigail Plummer, Brown University A tachocline is a thin shear layer thought to play an important role in the magnetic activity of Sun- like stars. Motivated by the need to better understand this layer, as well as the need to devise smarter geophysical and astrophysical fluid modeling techniques, we analyze an idealized two- dimensional model of the solar tachocline using numerical and statistical simulation techniques. In particular, a joint instability is investigated in which the tachocline models differential rotation is stable in the absence of a magnetic field but unstable in its presence. This joint instability occurs in a physically realistic parameter regime for the Sun, and provides a challenging and complex physical system for experimenting with statistical modeling techniques. A set of parameters are identified that produce a 10- year cycle in which energy is transformed from kinetic energy to magnetic potential energy and back, mimicking observed cyclic behavior in the Sun, using a Direct Numerical Simulat. Autonomous Brownian motor driven by nonadiabatic variation of internal parameters Alexander Plyukhin, Saint Anselm College We discuss an autonomous motor based on a Brownian particle driven from thermal equilibrium by periodic in time variation of the internal potential through which the particle interacts with molecules of the surrounding thermal bath. We demonstrate for such a motor the absence of a linear response regime: The average driving force and drift velocity are shown to be quadratic in both the frequency and amplitude of the variation. The adiabatic approximation (of an infinitely slow variation) and the leading correction to it (linear in the variation's frequency) both lead to zero drift and are insufficient to describe the motor's operation. Quantum jump approach for dissipative manybody dynamics Ivan Savenko We believe that quantum correlations in many- body systems should be considered explicitly and have therefore developed an approach which keeps track of the time evolution of both state populations and the correlators between energy states. Thus, particle self- scattering and interaction with a bath are accounted for in respective appropriate ways. A system of exciton polaritons in a semiconductor microcavity is considered as an example. Spatial and temporal coherence functions are calculated.

5 The effect of finite heat capacity on the calorimetric measurement of dissipation in a quantum two- level system Samu Harri Antero Suomela, Aalto University We study the influence of the finite heat capacity of the bath on the fluctuation relations, such as the Jarzynski relation. Due to the finite heat capacity, the bath temperature fluctuates. We show that these temporal variations lead to deviations from the standard fluctuation relations. However, an entropy fluctuation theorem can be recovered by taking into account all the entropy production terms associated with the stochastic process under study. Stochastic thermodynamics of a dragged nanocolloid hydrodynamically coupled to a fluid heat bath Vaibhav Thakore, Aalto University Stochastic thermodynamics of mesoscale systems has been extensively studied using a dragged colloidal particle in a trap as a model system. The colloid is assumed to be a massive Brownian particle that undergoes stochastic motion governed by a Langevin- type equation. The Langevin description of the colloidal motion however completely ignores the hydrodynamic coupling of the colloid to the heat bath. Here, we present results for the stochastic thermodynamics of a dragged nanocolloid hydrodynamically coupled to a fluid heat bath. The motion of the colloidal nanoparticle is modeled using a hybrid fluctuating lattice Boltzmann (FLB) and molecular dynamics (MD) method that accounts for full nonlinear hydrodynamic effects. The mesoscopic FLB- MD method employed in our simulations for the dragged colloidal particle in a trap allows testing of the fluctuation theorems in the truly transient regime of system evolution.