Time-symmetric fluctuations in nonequilibrium systems

For nonequilibrium steady states, we identify observables whose fluctuations satisfy a general symmetry and for which a new reciprocity relation can be shown. Unlike the situation in recently discussed fluctuation theorems, these observables are time-reversal symmetric. That is essential for exploiting the fluctuation symmetry beyond linear response theory. Besides time-reversal, a crucial role is played by the reversal of the driving fields, that further resolves the space-time action. In particular, the time-symmetric part in the space-time action determines second order effects of the nonequilibrium driving.Comment: 4 page

Thermoelectric phenomena via an interacting particle system

We present a mesoscopic model for thermoelectric phenomena in terms of an interacting particle system, a lattice electron gas dynamics that is a suitable extension of the standard simple exclusion process. We concentrate on electronic heat and charge transport in different but connected metallic substances. The electrons hop between energy-cells located alongside the spatial extension of the metal wire. When changing energy level, the system exchanges energy with the environment. At equilibrium the distribution satisfies the Fermi-Dirac occupation-law. Installing different temperatures at two connections induces an electromotive force (Seebeck effect) and upon forcing an electric current, an additional heat flow is produced at the junctions (Peltier heat). We derive the linear response behavior relating the Seebeck and Peltier coefficients as an application of Onsager reciprocity. We also indicate the higher order corrections. The entropy production is characterized as the anti-symmetric part under time-reversal of the space-time Lagrangian.Comment: 19 pages, 2 figures, submitted to Journal of Physics

Math saves the forest

Wireless sensor networks are decentralised networks consisting of sensors that can detect events and transmit data to neighbouring sensors. Ideally, this data is eventually gathered in a central base station. Wireless sensor networks have many possible applications. For example, they can be used to detect gas leaks in houses or fires in a forest.\ud In this report, we study data gathering in wireless sensor networks with the objective of minimising the time to send event data to the base station. We focus on sensors with a limited cache and take into account both node and transmission failures. We present two cache strategies and analyse the performance of these strategies for specific networks. For the case without node failures we give the expected arrival time of event data at the base station for both a line and a 2D grid network. For the case with node failures we study the expected arrival time on two-dimensional networks through simulation, as well as the influence of the broadcast range

Building bridges between physics & biology, a play of nature in three parts.

Some results of non-equilibrium statistical mechanics are presented,both in the context of biological systems as well as in a classicalphysics context. In the biological context we seek the microscopicperspective as well as the macroscopic perspective. The physics contextis sought mainly as a test case and reference for development ofgeneralized perturbation or expansion techniques.Kinesin Concerningthe microscopic perspective we present a model for kinesin, a molecularmotor responsible for many important cellular processes that requirework. Kinesin is capable of transforming chemically stored energy intowork through a series of chemical and conformational changes, steppingalong microtubules (a biochemical polymer that structures cells) as its`rails'. Our approach to model this motor enzyme is to consider thespatial-chemical states as states of a Markov process, modelling therates as exchanges of mass and entropy with thermal and chemical (orparticle) reservoirs of the environment. Due to translationalinvariance of the process we need only describe a single steppingcycle. Under some additional assumptions (based on experiments) we mayfurther reduce the state space until we arrive at a model consisting ofsix states that are well defined. The model describes theexperimentally observed behavior of kinesin well.The thermoelectric effect Wepresent a interacting particle model for the thermoelectric effect.This leads to some insight in the working of temperature gradients asthermodynamic forces. On the other hand it provides us with apossibility to investigate perturbations beyond the linear regime.Perturbation and generalized fluctuation relations Nextwe argue that --in spite of its general validity-- the fluctuationtheorem is not useful to obtain higher order response coefficients. Byintroducing the notion of field-reversal we provide the(time-)symmetrical equivalent of the fluctuation theorem as acomplementary relation. We then argue that a generalized form of thefluctuation theorem (derived by making use of field-reversal only),combines these fluctuation relations in order to derive responsecoefficients up to any given order (and consequently not necessarily byperturbing around equilibrium). These arguments are strengthenedthrough a more explicit derivation of these relations in the context ofMarkov processes and further elucidated with help of some examples.Models for DEB theory Atthe end we venture into the macroscopic perspective with help of DEBtheory, a biological theory describing mass and energy flows forindividual organisms. We present two different models that investigatethe possibility of a relatively simple underlying local dynamics. Firstwe propose a simple type of chemical reaction model --a caricature of arealistic chemical reaction system-- without any kind of geometricalstructure. This model describes the dynamics for V1-morphs (organismswhose surface area grows as their volume) according to DEB theory withonly a single free parameter. Then, in order to describe the dynamicsfor isomorphs, we propose a "wire" model that takes the geometricalstructure of the organism into account, in order to obtain coincidencewith the dynamics dictated by DEB theory.Contents Abstract 1 Preface 3 Prologue 7 What are you staring at? 9 Chapter 1. Putting things in perspective 11 1.1. Breaking and Forming Circles 11 1.2. The Big, the Petite and the Ugly 12 1.3. Building Bridges 13 1.4. As the Eagle Flies, Outline 14 Who plays whom? 15 Chapter 2. The main players 19 2.1. Mathematics 19 2.2. Physics 31 2.3. Biology 36 2.4. Chemistry 38 Part 1. Bottom up view 45 The ant caries a load 47 Chapter 3. Kinesin 51 3.1. Molecular motors 51 3.2. Kinesin 52 3.3. A chemical motor model 53 3.4. The model 58 3.5. Results 63 Part 2. Lateral view 77 Building bridges 79 Chapter 4. A model for the thermoelectric effect 81 4.1. Thermoelectric effect 81 4.2. Toy model for heat conduction 83 4.3. The general model 85 4.4. Currents and dissipation 90 4.5. Entropy production 92 4.6. Linear response regime 94 5 6 CONTENTS 4.7. Beyond linear order, final remarks 97 Chapter 5. Expanding 99 5.1. Introduction 99 5.2. Fluctuation symmetry of the entropy production 100 5.3. Stochastic Action set-up 101 5.4. The time-symmetric part 102 5.5. Markov processes 106 5.6. Expansion 110 5.7. Examples 121 Part 3. Top down view 133 What lives beneath 135 Chapter 6. Below the surface of DEB 139 6.1. Introduction 139 6.2. DEB theory 140 6.3. Preliminary considerations 143 6.4. A primitive organism – a particle reaction model 145 6.5. A spherically structured model 157 Epilogue 163 Awakenings 165 Discussion and prospects 167 Building bridges 167 Towards a statistical mechanics of biology 168 Where does it end? 169 Summary 171 Overview 171 Kinesin 172 The thermo-electric effect 175 Expansions 177 DEB theory 178 Samenvatting 181 Overzicht 181 Kinesine 182 Het thermo-elektrisch effect 185 Expansies 187 DEB theorie 189 Bibliography 193status: publishe

Math saves the forest : Analysis and optimization of message delivery in wireless sensor networks

Wireless sensor networks are decentralised networks consisting of sensors that can detect events and transmit data to neighbouring sensors. Ideally, this data is eventually gathered in a central base station. Wireless sensor networks have many possible applications. For example, they can be used to detect gas leaks in houses or fires in a forest. In this report, we study data gathering in wireless sensor networks with the objective of minimising the time to send event data to the base station. We focus on sensors with a limited cache and take into account both node and transmission failures. We present two cache strategies and analyse the performance of these strategies for specific networks. For the case without node failures we give the expected arrival time of event data at the base station for both a line and a 2D grid network. For the case with node failures we study the expected arrival time on two-dimensional networks through simulation, as well as the influence of the broadcast range. Keywords: sensor networks, data gathering, stochastic optimisation, distributed algorithms, random walks, first-passage percolation

real-model2

settings and output for migrate-N model

fstci

The FST values and their confidence intervals

real-model1

settings and output for migrate-N model

Data from: Genetic consequences of breaking migratory traditions in barnacle geese Branta leucopsis

Cultural transmission of migratory traditions enables species to deal with their environment based on experiences from earlier generations. Also, it allows a more adequate and rapid response to rapidly changing environments. When individuals break with their migratory traditions, new population structures can emerge that may affect gene flow. Recently, the migratory traditions of the Barnacle Goose Branta leucopsis changed, and new populations differing in migratory distance emerged. Here, we investigate the population genetic structure of the Barnacle Goose to evaluate the consequences of altered migratory traditions. We used a set of 358 single nucleotide polymorphism (SNP) markers to genotype 418 individuals from breeding populations in Greenland, Spitsbergen, Russia, Sweden and the Netherlands, the latter two being newly emerged populations. We used discriminant analysis of principal components, FST, linkage disequilibrium and a comparison of geneflow models using migrate-n to show that there is significant population structure, but that relatively many pairs of SNPs are in linkage disequilibrium, suggesting recent admixture between these populations. Despite the assumed traditions of migration within populations, we also show that genetic exchange occurs between all populations. The newly established nonmigratory population in the Netherlands is characterized by high emigration into other populations, which suggests more exploratory behaviour, possibly as a result of shortened parental care. These results suggest that migratory traditions in populations are subject to change in geese and that such changes have population genetic consequences. We argue that the emergence of nonmigration probably resulted from developmental plasticity