Molecular dynamics (MD) simulations are used to compute the equilibrium dynamics of a single component fluid with Yukawa interaction potential v(r) = (Ze)^2 exp(−r/λs )/4π eps_0 r. This system, which is known as the Yukawa one-component plasma (YOCP), represents a simplified description of a non-ideal plasma consisting of ions, charge Ze, and electrons. For finite screening lengths λs, the MD results are used to investigate the domain of validity of the hydrodynamic description, i.e., the description given by the Navier-Stokes equations. The way in which this domain depends on the thermodynamic conditions of the YOCP, as well as the strength and range of the interactions, is determined. Remarkably, it is found that the domain of validity is completely determined by the range of the interactions (i.e., λs); this alone determines the maximum wave number k_max at which the hydrodynamic description is applicable. The dynamics of the YOCP at wavevectors beyond k_max are then investigated; these are shown to be in striking agreement with a simple and well known generalisation of the Navier-Stokes equations. In the extreme case of the Coulomb interaction potential (λs = ∞), the very existence of a hydrodynamic description is a known but unsolved problem [Baus & Hansen, 1980]. For this important special case, known as the one-component plasma (OCP), it is shown that the ordinary hydrodynamic description is never valid. Since the OCP is the prototypical system representing a non-ideal plasma, a number of different approaches for modelling its dynamics have been formulated previously. By computing the relevant quantities with MD, the applicability of a number of models proposed in the literature is examined for the first time.

In this work, we wish to determine the free energy landscape and the nucleation rate associated with the process of homogeneous ice nucleation. To do this, we simulate the homogeneous nucleation of ice with the mW monatomic model of water and with all-atom models of water using primarily the umbrella sampling rare event method. We find that the use of the mW model of water, which has simpler dynamics compared to all-atom models of water, but is nevertheless surprisingly good at reproducing experimental data, results in very reasonable agreement with classical nucleation theory, in contrast to some previous simulations of homogeneous ice nucleation. We suggest that previous simulations did not observe the lowest free energy pathway in order parameter space because of their use of global order parameters, leading to a deviation from classical nucleation theory predictions. Whilst monatomic water can nucleate reasonably quickly, all-atom models of water are considerably more difficult to simulate, primarily because of their slow dynamics of ice growth and the fact that standard order parameters do not work well in driving nucleation when such models are being used. In this thesis, we describe a local, rotationally invariant order parameter that is capable of growing ice homogeneously in a biassed simulation without the unnatural effects introduced by global order parameters, and without leading to non-physical chain-like growth of 'ice' clusters that results from a naïve implementation of the standard Steinhardt-Ten Wolde order parameter. We have successfully used this order parameter to force the growth of ice clusters in simulations of all-atom models of water. However, although ice growth can be achieved, equilibrating simulations with all-atom models of water is extremely difficult. We describe several approaches to speeding up the equilibration in all-atom models of water to enable the computation of free energy profiles for homogeneous ice nucleation.

This thesis considers two areas of research in non-equilibrium soft matter at the mesoscale. In the first part we introduce active colloids in the context of active matter and focus on the particular case of phoretic colloids. The general theory of phoresis is presented along with an expression for the phoretic velocity of a colloid and its rotational diffusion in two and three dimensions. We introduce a model for thermally active colloids that absorb light and emit heat and propel through thermophoresis. Using this model we develop the equations of motion for their collective dynamics and consider excluded volume through a lattice gas formalism. Solutions to the thermoattractive collective dynamics are studied in one dimension analytically and numerically. A few numerical results are presented for the collective dynamics in two dimensions. We simulate an unconfined system of thermally active colloids under directed illumination with simple projection based geometric optics. This system self-organises into a comet-like swarm and exhibits a wide range of non- equilibrium phenomena. In the second part we review the background of polymer translocation, including key experiments, theoretical progress and simulation studies. We present, discuss and use a common model to investigate the potential of patterned nanopores for stochastic sensing and identification of polynucleotides and other heteropolymers. Three pore patterns are characterised in terms of the response of a homopolymer with varying attractive affinity. This is extended to simple periodic block co-polymer heterostructures and a model device is proposed and demonstrated with two stochastic sensing algorithms. We find that mul- tiple sequential measurements of the translocation time is sufficient for identification with high accuracy. Motivated by fluctuating biological channels and the prospect of frequency based selectivity we investigate the response of a homopolymer through a pore that has a time dependent geometry. We show that a time dependent mobility can capture many features of the frequency response.

This thesis addresses the isotropic diffuse gamma-ray background, as measured by the Fermi gamma ray space telescope, and its implications for indirect detection of dark matter. We describe the measurement of the isotropic background, including also an alternative analysis method besides the one published by the Fermi-LAT collaboration. The measured isotropic diffuse background is compatible with a power law differential energy spectrum with a spectral index of  -2.41 ± 0.05 and -2.39 ± 0.08, for the two analysis methods respectively. This is a softer spectrum than previously reported by the EGRET experiment. This rules out any dominant contribution with a significantly different shape, e.g. from dark matter, in the energy range 20 MeV to 102.4 GeV. Instead we present upper limits on a signal originating from annihilating dark matter of extragalactic origin. The uncertainty in the dark matter signal is primarily dependent on the cosmological evolution of the dark matter distribution. We use recent N-body simulations of structure formation, as well as a semi-analytical calculation, to assess this uncertainty. We investigate three main annihilation channels and find that in some, but not in all, of our scenarios we can start to probe, and sometimes rule out, interesting parameter spaces of particle physics models beyond the standard model.We also investigate the possibility to use the angular anisotropies of the annihilation signal to separate it from a background originating from conventional sources, e.g. from active galactic nuclei. By carefully modelling the performance of the Fermi gamma-ray space telescope and galactic foregrounds we find that this method could be as sensitive as using information from the energy spectrum only. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 4: Manuscript.</p>

This thesis consists of research work in the broad area of soft condensed matter theory with a focus on active matter. The study of long wavelength, low frequency collective behavior of active particles (bacterial suspensions, fish schools, motor-microtubule extracts, active gels) forms an interesting modification to liquid-crystal hydrodynamics, in which the constituent particles carry permanent stresses that stir the fluid. Activity introduces novel instabilities and many novel aspects emerge. Our works focus on the dynamics, order, fluctuations and instabilities in these systems. In particular, we investigated the dynamics, order and fluctuation properties emerging from effective hydrodynamic descriptions of translationally ordered active matter and also studied those in microwave-driven quantum Hall nematics. We also investigated the rheological properties of active suspensions subjected to an applied orienting field. A summary of the works carried out is as follows. Translationally ordered active phases – active smectics and active cholesterics: Active or self-propelled particles consume and dissipate energy generating permanent stresses that stir the fluid around them. The collective behavior of systems of active particles, in systems with translational order, pose interesting questions and possibilities of new physics that differ strikingly from those in systems at thermal equilibrium with the same spatial symmetry. We developed the hydrodynamic equations of motion for (a) an active system with spontaneously broken translational symmetry in one direction, i.e., smectic and (b) the simplest uniaxially ordered phase of active chiral objects, namely, an active cholesteric. We analyze the fluctuation properties as well as the nature of characteristic instabilities that these systems can display and make a number of predictions. For example, in the case of an active smectic, we show that active stresses generate an effective active layer tension which, if positive, sup-presses the Landau-Peierls effect, leading to long-range smectic order in dimension d =3 and quasi-long-range in d =2, in sharp contrast with thermal equilibrium systems. Negative active layer tension in bulk systems, however, lead to a spontaneous Helfrich-Hurault undulation instability of the layers, accompanied by spontaneous flow. Also, active smectics, unlike orientationally ordered active systems, normally have finite concentration fluctuations. Similarly, for the case of cholesterics we show that cholesteric elasticity intervenes to suppress some of the instabilities present in active nematics. xi Numerical simulation of active smectics: We present results from a Brownian Dynamics simulation, with no hydrodynamic interaction, of a system of apolar active particles form-ing translational liquid-crystalline order in a suspension. The particles interact through a prolate-ellipsoidal Gay-Berne potential. We model activity minimally through different noise temperatures for movement along and normal to the orientation axis of each particle. We present preliminary results on the disruptive effect of activity on smectic order for the parameter values investigated. Future work will test the predictions of our theory [1] on active smectics. Rheology of active suspensions near field-induced critical points : Shear induces orientation of active stresses in a suspension, through flow alignment. Depending on the sign, activity then either enhances or reduces the viscosity. The change in viscosity, in the zero frequency limit, is proportional to the product of the magnitude of active stress and the system relaxation time. A strong enough orienting field can make the system approach a critical point and the relaxation time diverges. We show that, this results in the divergence of viscosity at zero frequency making the system strongly viscoelastic. Depending on the sign, activity strengthens or reduces the effect of the field. We also investigate the rheological property of an active suspension with mixed polar and nematic oreder. Active quantum Hall systems: We construct the hydrodynamic theory for a 2d charged active nematic with 3d electrostatics. We have investigated the interplay of the Coulomb interaction and activity in these systems. We show that activity competes to enhance the charge density fluctuations normally suppressed by long-ranged Coulomb interactions. The charge structure factor Sq of the corresponding passive charged nematic goes to zero as q, whereas in charged active nematics, activity leads to a nonvanishing charge structure factor at small wavenumber. We also show how the effect of an applied magnetic field can be incorporated into the dynamics of the system and leave scope for further studies on these effects.

Aux XVIIIe et XIXe siècles, les historiens des sciences associaient généralement Francis Bacon et Galilée pour leur rôle dans l’émergence de la science moderne, mais, à la fin du XIXe et au début du XXe siècle, la Révolution scientifique fut identifiée de manière stricte à la construction de la physique mathématique, ce qui eut souvent pour conséquence de rejeter Bacon hors de l’histoire des sciences. Nous reprenons l’étude conjointe de ces deux auteurs pour mesurer quelle est exactement la nature de leur divergence. Dans la première partie de notre travail, nous abordons les questions cosmologiques. Sur quels arguments Galilée fonde-t-il sa défense publique du copernicianisme entre 1610 et 1616, jusqu’à la première condamnation de l’opinion copernicienne par l’Eglise Catholique ? Pour quelles raisons Bacon, qui suit cette campagne copernicienne, rejette-t-il la plupart des découvertes astronomiques de Galilée ? Pourquoi Bacon, tout en réussissant à percevoir le caractère (trop peu) systématique du géocentrisme, refuse-t-il l’héliocentrisme ? Dans la deuxième partie de notre travail, nous abordons les questions relatives à la méthode, ainsi que les théories de la matière et du mouvement. Quel est le rôle de la perception sensible et la fonction des mathématiques dans les théories de Bacon ? Quelle est la signification de sa théorie du mouvement, qui multiplie les objets d’étude en proposant une typologie des différents mouvements concrets, alors que la physique mathématique tend à réduire tout déplacement au seul mouvement linéaire inertiel ? Quelle est la fonction de l’atomisme mathématique de Galilée ? Dans quelle mesure sa science du mouvement se distingue-t-elle de l’approche baconienne ? La différence fondamentale entre la science galiléenne et la démarche de Bacon consiste, selon nous, dans la nature des expériences et des observations qui sont convoquées, ainsi que dans le type d’abstraction que ces deux auteurs veulent conférer à la philosophie naturelle. / During the eighteenth and nineteenth centuries, historians of science usually considered that Francis Bacon and Galileo had respectively played their role in the merging of modern science, but, at the end of the nineteenth and the beginning of the twentieth century, Scientific Revolution has been strictly reduced to the elaboration of mathematical physics, which had for consequence to exclude Bacon from the history of science. Our aim is to underline the exact nature of the difference between those two authors. In the first part, we deal with the cosmological problems. What arguments did Galileo produce to sustain his public commitment for the Copernican system, from 1610 to 1616, until the first condemnation of copernicanism by the Roman Church ? For what reasons did Bacon reject most of Galileo’s astronomical discoveries ? Why Bacon, who clearly perceived the fact that the geocentric theory lacked systematic character, refused heliocentrism ? In the second part, we deal with the methodological questions, we analyse matter theories and the science of motion. What is the role of sense perception and what is the fonction of mathematics in Bacon’s theories ? What is the significance of his theory of motion, which multiplies the objects of study, proposing a typology of concrete movements, while mathematical physics aims at reducing any motion to the rectilinear inertial movement ? What is the fonction of the mathematical atomism proposed by Galileo ? In what measure does his science of motion distinguish from the baconian approach ? We think that the fondamental difference between the science of Galileo and the theories of Bacon consists in the nature of the experiments and observations used, and in the type of abstraction they are looking for in natural philosophy.

No description available.

<p>The pi-striped, <em>d</em>-wave superconducting (SC) state, which is a type of pair density wave wherein the SC order is spatially modulated, has recently been shown to generate the key ingredients for quantum oscillations consistent with experimental observations (Zelli <em>et al.</em>, 2011, 2012). This was accomplished with a phenomenological approach using non-self-consistent Bogoliubov-de Gennes (BdG) theory. The objective of this thesis is to explore two aspects of this approach: the addition of a charge density wave (CDW) order to the previous non-self-consistent calculations, and an attempt at stabilizing the pi-striped state in fully self-consistent BdG theory. It was found that the CDW order had a minimal effect on the Fermi surface characteristics of the pi-striped state, but that a sufficiently strong CDW degrades the Landau levels which are essential for the formation of quantum oscillations. The self-consistent mean-field calculations were unable to stabilize the pi-striped state under a range of modifications to the Hamiltonian. Free energy calculations with the modulated SC order treated as a parameter demonstrate that the pi-striped state is always less energetically favourable than the normal state for the scenarios which were considered. The results of this study constitute a basis for future, more comprehensive studies, using the BdG approach, of the stability of possible pi-striped SC phases.</p> / Master of Science (MSc)

In this thesis I discuss the nature of ‘measurement’ in quantum theory. ‘Measurement’ is associated with several different processes: the gradual imprinting of information about one system onto another, which is well understood; the collapse of the wavefunction, which is ill-defined and troublesome; and finally, the means by which inferences about unknown experimental parameters are made. I present a theoretical extension to an experimental proposal from Leggett and Garg, who suggested that the quantum-or-classical reality of a macroscopic system may be probed with successive measurements arrayed in time. The extension allows for a finite level of imperfection in the protocol, and makes use of Leggett’s ‘null result’ measurement scheme. I present the results of an experiment conducted in Oxford that, up to certain loopholes, defies a non-quantum interpretation of the dynamics of phosphorous nuclei embedded in silicon. I also present the theory of statistical parameter estimation, and discover that a recent trend to employ time symmetric ‘postselected’ measurements offers no true advantage over standard methods. The technique, known as weak-value amplification, combines a weak transfer of quantum information from system to meter with conditional data rejection, to surprising effect. The Fisher information is a powerful tool for evaluating the performance of any parameter estimation model, and it reveals the technique to be worse than ordinary, preselected only measurements. That this is true despite the presence of noise (including magnetic field fluctuations causing deco- herence, poor resolution detection, and random displacements), casts serious doubt on the utility of the method.

We study correlated two-level quantum impurity models coupled to a metallic conduction band in the hope of gaining insight into the physics of nanoscale quantum dot systems. We focus on the possibility of formation of a spin-1 impurity local moment which, on coupling to the band, generates an underscreened (USC) singular Fermi liquid state. By employing physical arguments and the numerical renormalization group (NRG) technique, we analyse such systems in detail examining in particular both the thermodynamic and dynamic properties, including the differential conductance. The quantum phase transitions occurring between the USC phase and a more ordinary Fermi liquid (FL) phase are analysed in detail. They are generically found to be of Kosterlitz-Thouless type; exceptions occur along lines of high symmetry where first-order transitions are found. A `Friedel-Luttinger sum rule' is derived and, together with a generalization of Luttinger's theorem to the USC phase, is used to obtain general results for the $T=0$ zero-bias conductance --- it is expressed solely in terms of the number of electrons present on the impurity and applicable in both the USC and FL phases. Relatedly, dynamical signatures of the quantum phase transition show two broad classes of behaviour corresponding to the collapse of either a resonance or antiresonance in the single-particle density of states. Evidence of both of these behaviours is seen in experimental devices. We study also the effect of a local magnetic field on both single- and two-level quantum impurities. In the former case we attempt to resolve some points of contention that remain in the literature. Specifically we show that the position of the maximum in the spin resolved density of states (and related peaks in the differential conductance) is not linear in the applied field, showing a more complicated form than a simple `Zeeman splitting'. The analytic result for the low-field asymptote is recovered. For two-level impurities we illustrate the manner in which the USC state is destroyed: due to two cancelling effects an abrupt change in the zero-bias conductance does not occur as one might expect. Comparison with experiment is made in both cases and used to interpret experimental findings in a manner contrary to previous suggestions. We find that experiments are very rarely in the limit of strong impurity-host coupling. Further, features in the differential conductance as a function of bias voltage should not be simply interpreted in terms of isolated quantum dot states. The many-body nature of such systems is crucially important to their observed properties.