In this thesis, we study various aspects of physics in higher-dimensional manifolds involving a single extra dimension. After giving some historical perspective on the motivation for studying higher-dimensional theories of physics, we describe classical tests for a non-compact extra dimension utilizing test particles and pointlike gyroscopes. We then turn our attention to the problem of embedding any given <i>n</i>-dimensional spacetime within an (<i>n</i>+1)-dimensional manifold, paying special attention to how any structure from the extra dimension modifies the standard <i>n</i>-dimensional Einstein equations. Using results derived from this investigation and the formalism derived for test particles and gyroscopes, we systematically introduce three specific higher-dimensional models and classify their properties; including the Space-Time-Matter and two types of braneworld models. The remainder of the thesis concentrates on specific higher-dimensional cosmological models drawn from the above mentioned scenarios; including an analysis of the embedding of Friedmann-Lemaitre-Robertson-Walker submanifolds in 5-dimensional Minkowski and topological Schwarzschild spaces, and an investigation of the dynamics of a <i>d</i>-brane that takes the form of a thin shell encircling a (<i>d</i>+2)-dimensional topological black hole in anti-deSitter space. The latter is derived from a finite-dimensional action principle, which allows us to consider the canonical quantization of the model and the solutions of the resulting Wheeler-DeWitt equation.

Ecosystems are often made up of interactions between large numbers of species. They are considered complex systems because the behaviour of the system as a whole is not always obvious from the properties of the individual parts. A complex system can be represented by a network: a set of interconnected objects. In the case of ecological networks and food webs, the objects are species and the connections are interactions between species. Many complex systems are dynamic and exhibit intricate time series. Time series analysis has been developed to understand a wide range of natural phenomena. This thesis deals with the structure, dynamics, and robustness of ecological networks, the spatial dynamics of fluctuations in a social system, and the analysis of cardiac time series. Biodiversity on Earth is decreasing largely due to human-induced causes. My work looks at the effect of anthropogenic change on ecological networks. In Chapter Two, I investigate predator adaptation on food-web robustness following species extinctions. I identify a new theoretical category of species that may buffer ecosystems against environmental change. In Chapter Three, I study changes in parasitoid-host (consumer-resource) interaction frequencies between complex and simple environments. I show that the feeding preferences of parasitoid species actively change in response to habitat modification. Ecological networks are embedded in spatially-heterogeneous landscapes. In Chapter Four, I assess the role of geography on population fluctuations in an analogous social system. I demonstrate that fluctuations in the number of venture capital firms registered in cities in the United States of America are consistent with spatial and temporal contagion. Understanding how physiological signals vary through time is of interest to medical practitioners. In Chapter Five, I present a technique for quickly quantifying disorder in high frequency event series. Applying the algorithm to patient cardiac time series provides a rapid way to detect the onset of heart arrhythmia. Increasingly, answers to scientific questions lie at the intersection of traditional disciplines. This thesis applies techniques developed in physics and mathematics to problems in ecology and medicine.

Hydrodynamics is an effective theory that is extremely successful in describing a wide range of physical phenomena in liquids, gases and plasmas. However, our understanding of the structure of the theory, its microscopic origins and its behaviour at strong coupling is far from complete. To understand how an effective theory of dissipative hydrodynamics could emerge from a closed microscopic system, we analyse the structure of effective Schwinger-Keldysh Closed-Time-Path theories. We use this structure and the action principle for open systems to derive the energy-momentum balance equation for a dissipative fluid from an effective CTP Goldstone action. Near hydrodynamical equilibrium, we construct the first-order dissipative stress-energy tensor and derive the Navier-Stokes equations. Shear viscosity is shown to vanish, while bulk viscosity and thermodynamical quantities are determined by the form of the effective action. The exploration of strongly interacting states of matter, particularly in the hydrodynamic regime, has been a major recent application of gauge/string duality. The strongly coupled theories involved are typically deformations of large-$N$ SUSY gauge theories with exotic matter that are unusual from a low-energy point of view. In order to better interpret holographic results, an understanding of the weak-coupling behaviour of such gauge theories is essential. We study the exact and SUSY-broken N=1 and N=2 super-QED with finite densities of electron number and R-charge, respectively. Despite the fact that fermionic fields couple to the chemical potentials, the strength of scalar-fermion interactions, fixed by SUSY, prevents a Fermi surface from forming. This is important for hydrodynamical excitations such as zero sound. Intriguingly, in the absence of a Fermi surface, the total charge need not be stored in the scalar condensates alone and fermions may contribute. Gauss-Bonnet gravity is a useful laboratory for non-perturbative studies of the higher derivative curvature effects on transport coefficients of conformal fluids with holographic duals. It was previously known that shear viscosity can be tuned to zero by adjusting the Gauss-Bonnet coupling, &lambda;_GB, to its maximal critical value. To understand the behaviour of the fluid in this limit, we compute the second-order transport coefficients non-perturbatively in &lambda;_GB and show that the fluid still produces entropy, while diffusion and sound attenuation are suppressed at all order in the hydrodynamic expansion. We also show that the theory violates a previously proposed universal relation between three of the second order transport coefficients. We further compute the only second-order coefficient thus far unknown, &lambda;₂, in the N=4 super Yang-Mills theory with the leading-order 't Hooft coupling correction. Intriguingly, the universal relation is not violated by these leading-order perturbative corrections. Finally, by adding higher-derivative photon field terms to the action, we study charge diffusion and non-perturbative parameter regimes in which the charge diffusion constant vanishes.

<p>Transport properties within the Boltzmann transport equation for metallic multi-layer structures as well as bulk materials, were the prime topic of this work. <i>Ab initio</i> total energy calculations for Hydrogen loaded metallic multi-layers were performed in order to shed some light onto problem of H depleted layers at the interfaces that have been experimentally observed. It was explained in connection with structural relaxation of the interface layers. </p><p>Further on conductivity behavior of Fe/V vs. Mo/V during Hydrogen load was discussed. The difference in, on first sight, rather similar multi-layer structures was explained by the magnitude of Hydrogen induced Vanadium expansion. Problem of variation of conductivity with changed c/a ratio of metals and semiconductors in general was addressed as well. The variations due to change of the Fermi surface of the corresponding materials were observed as well as some intriguing general patterns. The phenomenon could be regarded as piezoresistivity on electronic structure level. For the 3d transition metals variation of conductivity/resistivity through the period was studied.</p><p>A possible explanation for anomalous behavior of Manganese resistivity due to its much greater lattice constant in comparison to its neighbors in the period is presented. Field of disordered alloys and low dimensional magnetism was touched by discussing Mo/Ru formation energy as well as magnetic nano-wires grown on surfaces.</p><p>All total energy calculations as well as band structure calculations were performed by using Density Functional Theory based numerical computations. A short but comprehensive review of most common linear-response electron transport techniques is given.</p>

Transport properties within the Boltzmann transport equation for metallic multi-layer structures as well as bulk materials, were the prime topic of this work. Ab initio total energy calculations for Hydrogen loaded metallic multi-layers were performed in order to shed some light onto problem of H depleted layers at the interfaces that have been experimentally observed. It was explained in connection with structural relaxation of the interface layers. Further on conductivity behavior of Fe/V vs. Mo/V during Hydrogen load was discussed. The difference in, on first sight, rather similar multi-layer structures was explained by the magnitude of Hydrogen induced Vanadium expansion. Problem of variation of conductivity with changed c/a ratio of metals and semiconductors in general was addressed as well. The variations due to change of the Fermi surface of the corresponding materials were observed as well as some intriguing general patterns. The phenomenon could be regarded as piezoresistivity on electronic structure level. For the 3d transition metals variation of conductivity/resistivity through the period was studied. A possible explanation for anomalous behavior of Manganese resistivity due to its much greater lattice constant in comparison to its neighbors in the period is presented. Field of disordered alloys and low dimensional magnetism was touched by discussing Mo/Ru formation energy as well as magnetic nano-wires grown on surfaces. All total energy calculations as well as band structure calculations were performed by using Density Functional Theory based numerical computations. A short but comprehensive review of most common linear-response electron transport techniques is given.

In this thesis, we study various aspects of physics in higher-dimensional manifolds involving a single extra dimension. After giving some historical perspective on the motivation for studying higher-dimensional theories of physics, we describe classical tests for a non-compact extra dimension utilizing test particles and pointlike gyroscopes. We then turn our attention to the problem of embedding any given <i>n</i>-dimensional spacetime within an (<i>n</i>+1)-dimensional manifold, paying special attention to how any structure from the extra dimension modifies the standard <i>n</i>-dimensional Einstein equations. Using results derived from this investigation and the formalism derived for test particles and gyroscopes, we systematically introduce three specific higher-dimensional models and classify their properties; including the Space-Time-Matter and two types of braneworld models. The remainder of the thesis concentrates on specific higher-dimensional cosmological models drawn from the above mentioned scenarios; including an analysis of the embedding of Friedmann-Lemaitre-Robertson-Walker submanifolds in 5-dimensional Minkowski and topological Schwarzschild spaces, and an investigation of the dynamics of a <i>d</i>-brane that takes the form of a thin shell encircling a (<i>d</i>+2)-dimensional topological black hole in anti-deSitter space. The latter is derived from a finite-dimensional action principle, which allows us to consider the canonical quantization of the model and the solutions of the resulting Wheeler-DeWitt equation.

This dissertation splits into two distinct halves. The first half is devoted to the study of the holography of higher spin gauge theory in AdS$_3$. We present a conjecture that the holographic dual of $W_N$ minimal model in a 't Hooft-like large $N$ limit is an unusual ``semi-local" higher spin gauge theory on AdS$_3\times $S$^1$. At each point on the S$^1$ lives a copy of three-dimensional Vasiliev theory, that contains an infinite tower of higher spin gauge fields coupled to a single massive complex scalar propagating in AdS$_3$. The Vasiliev theories at different points on the S$^1$ are correlated only through the AdS$_3$ boundary conditions on the massive scalars. All but one single tower of higher spin symmetries are broken by the boundary conditions. This conjecture is checked by comparing tree-level two- and three-point functions, and also one-loop partition functions on both side of the duality. The second half focuses on the holography of higher spin gauge theory in AdS$_4$. We demonstrate that a supersymmetric and parity violating version of Vasiliev's higher spin gauge theory in AdS$_4$ admits boundary conditions that preserve ${\cal N}=0,1,2,3,4$ or $6$ supersymmetries. In particular, we argue that the Vasiliev theory with $U(M)$ Chan-Paton and ${\cal N}=6$ boundary condition is holographically dual to the 2+1 dimensional $U(N)_k\times U(M)_{-k}$ ABJ theory in the limit of large $N,k$ and finite $M$. In this system all bulk higher spin fields transform in the adjoint of the $U(M)$ gauge group, whose bulk t'Hooft coupling is $\frac{M}{N}$. Our picture suggests that the supersymmetric Vasiliev theory can be obtained as a limit of type IIA string theory in AdS$_4\times \mathbb{CP}^3$, and that the non-Abelian Vasiliev theory at strong bulk 't Hooft coupling smoothly turn into a string field theory. The fundamental string is a singlet bound state of Vasiliev's higher spin particles held together by $U(M)$ gauge interactions. / Physics

This thesis discusses the mesoscopic physics of two examples for soft condensed matter: (i) aeolian sand transport and the ensuing structure formation and (ii) solutions of stiff biopolymers. It emphasizes the impact of a heterogeneous mesoscale structure on the macroscopic phenomenology. For the aeolian sand transport, we start with a coarse-grained description of the collisions between mobile grains and the sand bed. Combining the collision geometry with basic physical principles, like momentum and energy conservation, we derive the full splash statistics as a function of impact velocity and impactor--bed grain-size ratio. This serves as a starting point for attacking the complicated transport statistics of wind-blown sand. Two approaches are proposed: first, a two-species approximation that distinguishes between high-energy rebounding grains and low-energy bed ejecta, second, a statistical description that resolves the full distribution of grain trajectories. While the former provides an ideal framework to accurately predict macroscopic averages, the latter resolves the heterogeneous mesoscale structure of the transport layer. Both approaches are shown to be in excellent agreement with various laboratory and field data. We moreover establish a new perspective on the transport's saturation transients that illustrates the crucial influence of the intermittent turbulent wind fluctuations in the field, thereby resolving a long-standing debate. Eventually, we address the formation of megaripples, an aeolian bedform that is made from strongly polydisperse sand. Combining our proposed theory with long-term field measurements, we clarify the importance of wind-driven sand sorting and, again, intermittent turbulent fluctuations. Our approach suggests to describe the megaripples as down-scaled dunes, as indeed support by various field data for their morphology and migration. In the second part of the thesis, we consider the mesoscale structure and its influence on the viscoelastic response of entangled biopolymer solutions. Their mechanics is determined by the topological entanglements of the filamentous polymers that cannot pass through each other. The tube model for semiflexible polymers represents this effect on a mean-field level, where test filament is confined to a tube-like cage formed by surrounding polymers. We employ it to investigate the solution's mesoscale packing structure and its change under finite shear deformations. Comparing our predictions with systematic computer simulations and experiments, we find the tube deformations to relax quickly after the deformation, while tube alignment and hairpin conformations are found to be long lived. In a second step, we propose a new perspective on the entangled solution's dynamics. Accounting for the nonaffine response at the level of the test filament, and assuming sticky or frictional polymer contacts, we argue that soft bending deformations of the filaments can couple to stiff axial stretching modes. This allows us to explain various experimentally observed similarities of the entangled solutions to crosslinked networks, like the increasing elastic modulus with increasing length and bending rigidity of the filaments or the softening--stiffening transition as a function of polymer concentration, polymer length, deformation rate, and various solvent properties.:I Aeolian sand transport and megaripple formation 1 Introduction 2 The splash process 3 Aeolian sand transport 4 Structure formation 5 Outlook Bibliography II Solutions of stiff biopolymers 6 Introduction 7 Entangled solutions 8 Viscoelastic response Appendix Bibliography Acknowledgments

Recent resonant inelastic x-ray scattering (RIXS) experiments have detected a significant high-energy spin-excitation anisotropy in the nematic phase of the enigmatic iron-based superconductor FeSe, whose origin remains controversial. We apply an itinerant model previously used to describe the spin-excitation anisotropy as measured by neutron scattering measurements, with magnetic fluctuations included within the RPA approximation. The calculated RIXS cross section exhibits overall agreement with the RIXS data, including the high energy spin-excitation anisotropy

We study the low-temperature physics arising in models of a strongly correlated, tunnel-coupled double quantum dot (DQD), particularly the two-impurity Anderson model (2AIM) and the two-impurity Kondo model (2IKM), employing a combination of physical arguments and the Numerical Renormalisation Group. These models exhibit a rich range of Kondo physics. In the regime with essentially one electron on each dot, there is a competition between the Kondo effect and the interdot exchange interaction. This competition gives rise to a quantum phase transition (QPT) between local singlet and Kondo singlet phases in the 2IKM, which becomes a continuous crossover in the 2AIM as a result of the interlead charge transfer present. The 2IKM is known to exhibit two-channel Kondo (2CK) physics at the QPT, and we investigate whether this is also the case for the 2AIM at the crossover. We find that while in principle 2CK physics can be observed in the 2AIM, extremely low temperatures are required, such that it is unlikely that 2CK physics will be observed in an experimental DQD system in the near future. We have studied the effect of a magnetic field on the 2AIM and the 2IKM, finding that both the zero-field QPT in the 2IKM and the zero-field crossover in the 2AIM, persist to finite field. This presents the possibility of observing 2CK physics in an experimental DQD at finite field, but we find that the temperatures required to do so are extremely low. We show that longer even-numbered chains of spins also exhibit QPTs at finite field, and argue that a 2N-spin chain should undergo N QPTs as field is increased (starting deep in the local singlet phase at zero field). We have also carried out a joint theoretical-experimental study of a carbon nanotube based DQD, in collaboration with Dr. Mark Buitelaar et al. The agreement between experimental and theoretical results is good, and the experiments are able to access the crossover present in the 2AIM at finite field. Furthermore, the experiments show the wide range of physics exhibited by DQD systems, and illustrate the utility of such systems in probing correlated electron physics.