Our vacuum-dominated universe can be successively approximated as an aggregation of stars, star clusters, galaxies, or superclusters. If these large scale structures are self-similar in that each level of structure is, on average, comprised of the same number of next smaller structures, the number and characteristic masses of large scale structures in the universe can be estimated from the average stellar mass. Since the main levels of large scale structure are self-similar gravitationally-bound systems of the next lower level of structures, the virial theorem and the holographic principle indicate self-similarity (scale invariance) of large scale structure occurs because the average gravitational potential energy per unit volume of each main structural level depends only on the gravitational constant and is the same for all four levels of large scale structure. The existence of four levels of large scale structure results from self-similarity, the Jeans' length at each level of structure, and the holographic principle. Estimating structure masses on that basis predicts an average stellar mass near the solar mass.

In this Letter we present resonance properties in terahertz metamaterials consisting of a split-ring resonator array made from high temperature superconducting films. By varying the temperature, we observed efficient metamaterial resonance switching and frequency tuning with some features not revealed before. The results were well reproduced by numerical simulations of metamaterial resonance using the experimentally measured complex conductivity of the superconducting film. We developed a theoretical model that explains the tuning features, which takes into account the resistive resonance damping and additional split-ring inductance contributed from both the real and imaginary parts of the temperature-dependent complex conductivity. The theoretical model further predicted more efficient resonance switching and frequency shifting in metamaterials consisting of a thinner superconducting split-ring resonator array, which were also verified in experiments.

This work employs Hall magnetohydrodynamic (MHD) simulations to study the X-lines formed during the reconnection of magnetic fields with differing strengths and orientations embedded in plasmas of differing densities. Although random initial perturbations trigger the growth of X-lines with many orientations, at late time a few robust X-lines sharing an orientation reasonably consistent with the direction that maximizes the outflow speed, as predicted by Swisdak and Drake [Geophys. Res. Lett., 34, L11106, (2007)], dominate the system. The existence of reconnection in the geometry examined here contradicts the suggestion of Sonnerup [J. Geophys. Res., 79, 1546 (1974)] that reconnection occurs in a plane normal to the equilibrium current. At late time the growth of the X-lines stagnates, leaving them shorter than the simulation domain.

Raman signals from molecules adsorbed on a noble metal surface are enhanced by many orders of magnitude due to the plasmon resonances of the substrate. Additionally, the enhanced spectra are modified compared to the spectra of neat molecules: many vibrational frequencies are shifted and relative intensities undergo significant changes upon attachment to the metal. With the goal of devising an effective scheme for separating the electromagnetic and chemical effects, we explore the origin of the Raman spectra modification of benzenethiol adsorbed on nanostructured gold surfaces. The spectral modifications are attributed to the frequency dependence of the electromagnetic enhancement and to the effect of chemical binding. The latter contribution can be reproduced computationally using molecule-metal cluster models. We present evidence that the effect of chemical binding is mostly due to changes in the electronic structure of the molecule rather than to the fixed orientation of molecules relative to the substrate.

The Feynman integral is one of the most accurate methods for calculating density operator dynamics in open quantum systems. However, the number of time steps that can realistically be used is always limited, therefore one often obtains an approximation of the density operator at a sparse grid of points in time. Instead of relying only on \textit{ad hoc} interpolation methods such as splines to estimate the system density operator in between these points, I propose a method that uses physical information to assist with this interpolation. This method is tested on a physically significant system, on which its use allows important qualitative features of the density operator dynamics to be captured with as little as 2 time steps in the Feynman integral. This method allows for an enormous reduction in the amount of memory and CPU time required for approximating density operator dynamics within a desired accuracy. Since this method does not change the way the Feynman integral itself is calculated, the value of the density operator approximation at the points in time used to discretize the Feynamn integral will be the same whether or not this method is used, but its approximation in between these points in time is considerably improved by this method.

The light speed anisotropy, i.e., the variation of the light speed with respect to direction in an "absolute" reference frame, is a profound issue in physics. The one-way experiment, performed at the GRAAL facility of the European Synchrotron Radiation Facility (ESRF) in Grenoble, reported results on the light speed anisotropy by Compton scattering of laser photons on high-energy electrons. We show in this paper that the azimuthal distribution of the GRAAL experiment data can be elegantly reproduced by a new theory of Lorentz invariance violation or space-time anisotropy, based on a general principle of physical independence of the mathematical background manifold.

Degree distribution of nodes, especially a power law degree distribution, has been regarded as one of the most significant structural characteristics of social and information networks. Node degree, however, only discloses the first-order structure of a network. Higher-order structures such as the edge embeddedness and the size of communities may play more important roles in many online social networks. In this paper, we provide empirical evidence on the existence of rich higherorder structural characteristics in online social networks, develop mathematical models to interpret and model these characteristics, and discuss their various applications in practice. In particular, 1) We show that the embeddedness distribution of social links in many social networks has interesting and rich behavior that cannot be captured by well-known network models. We also provide empirical results showing a clear correlation between the embeddedness distribution and the average number of messages communicated between pairs of social network nodes. 2) We formally prove that random k-tree, a recent model for complex networks, has a power law embeddedness distribution, and show empirically that the random k-tree model can be used to capture the rich behavior of higherorder structures we observed in real-world social networks. 3) Going beyond the embeddedness, we show that a variant of the random k-tree model can be used to capture the power law distribution of the size of communities of overlapping cliques discovered recently.

We discuss averaged turbulence modeling of multi-scales of length for an incompressible Newtonian fluid, with the help of the maximum information principle. We suppose that there exists a function basis to decompose the turbulent fluctuations in a flow of our concern into the components associated with various spatial scales and that there is a probability density function $\pdf$ of these fluctuation components. The unbiased form for $\pdf$ is determined and the turbulence model is closed, with the multi-scale correlations up to the fourth order, through maximizing the information under the constraints of equality and inequality for that flow. Due to the computational difficulty to maximize the information, a closely related but simple alternative objective is sought, like the determinant or the trace of the second order correlations of the turbulent flow. Some preliminary results and implications from the application to homogeneous turbulence are presented. Some issues yet to be resolved are indicated.

This project began as a collection of handouts attempting to provide a slightly more in depth theoretical background to the first year labs performed at University College Dublin. Over time, these handouts were patched together, and this book (if it can be called a book) emerged. The book is intended to complement the University College Dublin first year laboratory manuals, but can also be read independently. The UCD labs span a wide range of subjects, and consequently so do the chapters of this book, beginning with experimental techniques, moving onto classical mechanics, touching on E&M, and ending with a variety of more advanced topics.

Theoretical cross sections for the pressure broadening by hydrogen of rotational transitions of water are compared to the latest available measurements in the temperature range 65-220 K. A high accuracy interaction potential is employed in a full close coupling calculation. A good agreement with experiment is observed above ~80 K while the sharp drop observed experimentally at lower temperatures is not predicted by our calculations. Possible explanations for this discrepancy include the failure of the impact approximation and the possible role of ortho-to-para conversion of H2.

The results of a theoretical investigation on the low-velocity stopping power of the ions moving in a magnetized collisional plasma are presented. The stopping power for an ion is calculated employing linear response theory using the dielectric function approach. The collisions, which leads to a damping of the excitations in the plasma, is taken into account through a number-conserving relaxation time approximation in the linear response function. In order to highlight the effects of collisions and magnetic field we present a comparison of our analytical and numerical results obtained for a nonzero damping or magnetic field with those for a vanishing damping or magnetic field. It is shown that the collisions remove the anomalous friction obtained previously [Nersisyan et al., Phys. Rev. E 61, 7022 (2000)] for the collisionless magnetized plasmas at low ion velocities. One of major objectives of this study is to compare and contrast our theoretical results with those obtained through a novel diffusion formulation based on Dufty-Berkovsky relation evaluated in magnetized one-component plasma models framed on target ions and electrons.

We present a novel canonical description of the incompressible fluid dynamics. This description uses the dynamical constraints, in our case reflecting "incompressibility" assumption, and leads to replacement of usual hydrodynamical Poisson brackets for density and velocity fields with Dirac brackets. The resulting equations are then known nonlinear, and non-local in space, equations for incompressible fluid velocity.

We comment on past and more recent efforts to derive a formula yielding the fine structure constant in terms of integers and transcendent numbers. We analyse these "exoteric" attitudes and describe the myths regarding {\alpha}, which seems to have very ancient roots, tracing back to Cabbala and to medieval alchemic conceptions. We discuss the obsession for this constant developed by Pauli and the cultural "environment" in which such an "obsession" grew. We also derive a simple formula for {\alpha} in terms of two numbers {\pi} and 137 only. The formula we propose reproduces the experimental values up to the last significant digit, it has not any physical motivation and is the result of an alchemic combination of numbers. We make a comparison with other existing formulae, discuss the relevant limits of validity by comparison with the experimental values and discuss a criterion to recover a physical meaning, if existing, from their mathematical properties.

We show the presence of both a minimum and clear oscillations in the frequency dependence of the translocation time of a polymer described as a unidimensional Rouse chain driven by a spatially localized oscillating linear potential. The observed oscillations of the mean translocation time arise from the synchronization between the very mean translocation time and the period of the external force. We have checked the robustness of the frequency value for the minimum translocation time by changing the damping parameter, finding a very simple relationship between this frequency and the correspondent translocation time. The translocation time as a function of the polymer length has been also evaluated, finding a precise $L^2$ scaling. Furthermore, the role played by the thermal fluctuations described as a Gaussian uncorrelated noise has been also investigated, and the analogies with the resonant activation phenomenon are commented.

We study the community structure of the multi-network of commodity-specific trade relations among world countries over the 1992-2003 period. We compare structures across commodities and time by means of the normalized mutual information index (NMI). We also compare them with exogenous community structures induced by geographical distances and regional trade agreements. We find that commodity-specific community structures are very heterogeneous and much more fragmented than that characterizing the aggregate ITN. This shows that the aggregate properties of the ITN may result (and be very different) from the aggregation of very diverse commodity-specific layers of the multi network. We also show that commodity-specific community structures, especially those related to the chemical sector, are becoming more and more similar to the aggregate one. Finally, our findings suggest that geographical distance is much more correlated with the observed community structure than RTAs. This result strengthens previous findings from the empirical literature on trade.

Exact time-dependent solutions of Maxwell's equations in Maxwell's fish eye show that perfect imaging is not an artifact of a drain at the image, although a drain is required for subwavelength resolution.

We probe for statistical and Coulomb induced spin textures among the low-lying states of repulsively-interacting particles confined to potentials that are both rotationally and time-reversal invariant. In particular, we focus on two-dimensional quantum dots and employ configuration-interaction techniques to directly compute the correlated many-body eigenstates of the system. We produce spatial maps of the single-particle charge and spin density and verify the annular structure of the charge density and the rotational invariance of the spin field. We further compute two-point spin correlations to determine the correlated structure of a single component of the spin vector field. In addition, we compute three-point spin correlation functions to uncover chiral structures. We present evidence for both chiral and quasi-topological spin textures within energetically degenerate subspaces in the three- and four-particle system. These correlation functions are obtained directly from the correlated many-body eigenstates of the system, containing thousands of Slater determinant states.

Ions in water are the liquid of life. Life occurs almost entirely in 'salt water'. Water itself (without ions) is lethal to animal cells and damaging for most proteins. Water must contain the right ions in the right amounts if it is to sustain life. Physical chemistry is the language of electrolyte solutions. Physical chemistry and biology are intertwined. Physical chemists and biologists come from different traditions that separated for several decades as biologists described the molecules of life. Communication is not easy between a fundamentally descriptive tradition and a fundamentally analytical one. Biologists have now learned to study well defined systems with physical techniques, of considerable interest to physical chemists. Physical chemists are increasingly interested in spatially inhomogeneous systems with structures on the atomic scale so common in biology. Physical chemists will find it productive to work on well defined systems built by evolution to be reasonably robust, with input output relations insensitive to environmental insults. This article deals with properties of ion channels that in my view can be dealt with by 'physics as usual', with much the same tools that physical chemists apply to other systems. Indeed, I introduce and use a tool of physicists-a field theory (and boundary conditions) based on an energy variational approach developed by Chun Liu-not too widely used among physical chemists. My goal is to provide the knowledge base, and identify the assumptions, that biologists use in studying ion channels, avoiding jargon. Rather simple models of selectivity and permeation in ion channels work quite well in important cases. Those physical models and cases are the main focus of this review because they demonstrate the strong essential link between the traditional treatments of ions in chemical physics, and the biological function of ion channels.

Using multi-dimensional PIC simulations we show that the magnetic undulator-type field of the plasma magnetostatic mode is indeed produced by the interaction of a laser pulse with a relativistic ionization front, as predicted by linear theory for a cold plasma. When the front with this magnetostatic mode is followed by a relativistic electron beam, the interaction of the beam with this magnetic field, produces FEL-type synchrotron radiation, providing a direct signature of the magnetostatic mode. The possibility of generating readily detectable ultrashort wavelength radiation using this mode, by employing state-of-the-art laser systems, is demonstrated, thus opening the way towards experimental observation of the hitherto unseen magnetostatic mode and the use of this plasma FEL mechanism to provide a source of high-brilliance ultrashort wavelength radiation.

An experimental study of liquid drop impacts on a granular medium is proposed. Four fluids were used to vary physical properties: pure distilled water, water with glycerol at 2 concentrations 1:1 and 1:2 v/v and water with Tween 20 at the concentration of 0.1g/l. The drop free fall height was varied to obtain a Weber number (We) between 10 and 2000. Results showed that obtained crater morphologies highly depend on the impacting drop kinetic energy E_{K}. Different behaviours during the drop spreading, receding and absorption are highlighted as function of the fluids viscosity and surface tension. Experimental absorption times are also commented and compared with a simplified theoretical model. Drops maximal extensions and craters diameters were found to scale as $We^{1/5}$ and $E_K^{1/5}$ respectively. In both cases, found dependencies are smaller than those reported in literature: $We^{1/4}$ for drop impacts on solid or granular surfaces and $E_K^{1/4}$ for spherical solid impacts on granular media.

A fast multichannel Stokes/Mueller polarimeter with no mechanically moving parts has been designed to have close to optimal performance from 430-2000 nm by applying a genetic algorithm. Stokes (Mueller) polarimeters are characterized by their ability to analyze the full Stokes (Mueller) vector (matrix) of the incident light. This ability is characterized by the condition number, $\kappa$, which directly influences the measurement noise in polarimetric measurements. Due to the spectral dependence of the retardance in birefringent materials, it is not trivial to design a polarimeter using dispersive components. We present here both a method to do this optimization using a genetic algorithm, as well as simulation results. Our results include fast, broad-band polarimeter designs for spectrographic use, based on 2 and 3 Ferroelectric Liquid Crystals, whose material properties are taken from measured values. The results promise to reduce the measurement noise significantly over previous designs, up to a factor of 4.5 for a Mueller polarimeter, in addition to extending the spectral range.

Double beta $\beta\beta$ decay experiments are one of the most active research topics in Neutrino Physics. The measurement of the neutrinoless mode $0\nu\beta\beta$ could give unique information on the neutrino mass scale and nature. The current generation of experiments aims at detector target masses at the 100 kg scale, while the next generation will need to go to the ton scale in order to completely explore the inverse hierarchy models of neutrino mass. Very good energy resolutions and ultra-low background levels are the two main experimental requirements for a successful experiment. The topological information of the $\beta\beta$ events offered by gaseous detectors like gas Time Projection Chambers (TPC) could provide a very powerful tool of signal identification and background rejection. However only recent advances in TPC readouts may assure the competitiveness of a high pressure gas TPCs for $\beta\beta$ searches, especially regarding the required energy resolution. In this paper we present first results on energy resolution with state-of-the-art microbulk Micromesh Gas Amplification Structure (Micromegas) using a 5.5 MeV alpha source in high pressure pure xenon. Resolutions down to 2 % FWHM have been achieved for pressures up to 5 bar. These results, together with their recently measured radiopurity , prove that Micromegas readouts are not only a viable option but a very competitive one for $\beta\beta$ searches.

This report proposes to discuss the Fourier domain analysis performances of a RESPER probe. A uniform ADC, which is characterized by a sensible phase inaccuracy depending on frequency, is connected to a Fast Fourier Transform (FFT) processor, that is especially affected by a round-off amplitude noise linked to both the FFT register length and samples number. If the register length is equal to 32 bits, then the round-off noise is entirely negligible, else, once bits are reduced to 16, a technique of compensation must occur. In fact, oversampling can be employed within a short time window, reaching a compromise between the needs of limiting the phase inaccuracy due to ADC and not raising too much the number of averaged FFT values sufficient to bound the round-off. Finally, the appendix presents an outline of somewhat lengthy demonstrations needed to calculate the amplitude and especially phase inaccuracies due to the round-off noise of FFT processors.

The application package "IONORT" for the calculation of ray-tracing can be used by customers using the Windows operating system. It is a program whose interface with the user is created in MATLAB. In fact, the program launches an executable that integrates the system of differential equations written in Fortran and imports the output in the MATLAB program, which generates graphics and other information on the ray. This work is inspired mainly by the program of Jones and Stephenson, widespread in the scientific community that is interested in radio propagation via the ionosphere. The program is written in FORTRAN 77, a mainframe CDC-3800. The code itself, as well as being very elegant, is highly efficient and provides the basis for many programs now in use mainly in the Coordinate Registration (CR) of Over The Horizon (OTH) radar. The input and output of this program require devices no longer in use for several decades and there are no compilers that accept instructions written for that type of mainframe. For this reason, the core of the program to perform numerical integration, after the necessary amendments, was passed to a modern compiler under the Windows operating system and the executable has been imported into a MATLAB program. Thus, all input and output operations are handled by modern MATLAB program that implements the Fortran program and imports the output. This provides great versatility to the entire application package with presentations in two dimensions (2D) and three-dimensional (3D) geo-referenced on real maps.

We stand by our result [H. Mueller et al., Nature 463, 926-929 (2010)]. The comment [P. Wolf et al., Nature 467, E1 (2010)] revisits an interesting issue that has been known for decades, the relationship between test of the universality of free fall and redshift experiments. However, it arrives at its conclusions by applying the laws of physics that are questioned by redshift experiments; this precludes the existence of measurable signals. Since this issue applies to all classical redshift tests as well as atom interferometry redshift tests, these experiments are equivalent in all aspects in question.

In order to produce muon beam of high enough quality to be used for a Muon Collider, its large phase space must be cooled several orders of magnitude. This task can be accomplished by ionization cooling. Ionization cooling consists of passing a high-emittance muon beam alternately through regions of low Z material, such as liquid hydrogen, and very high accelerating RF cavities within a multi-Tesla solenoidal focusing channel. But first high power tests of RF cavity with beryllium windows in solenoidal magnetic field showed a dramatic drop in accelerating gradient due to RF breakdowns. It has been concluded that external magnetic fields parallel to RF electric field significantly modifies the performance of RF cavities. However, magnetic field in Helical Cooling Channel has a strong dipole component in addition to solenoidal one. The dipole component essentially changes electron motion in a cavity compare to pure solenoidal case, making dark current less focused at field emission sites. The simulation of dark current dynamic in HCC performed with CST Studio Suit is presented in this paper.

A nonlinear time dependent fluid simulation model is developed that describes the evolution of magnetohydrodynamic waves in the presence of collisional and charge exchange interactions of a partially ionized plasma. The partially ionized plasma consists of electrons, ions and a significant number of neutral atoms. In our model, the electrons and ions are described by a single fluid compressible magnetohydrodynamic (MHD) model and are coupled self-consistently to the neutral gas, described by the compressible hydrodynamic equations. Both the plasma and neutral fluids are treated with different energy equations that describe thermal energy exchange processes between them. Based on our self-consistent model, we find that propagating Alfv\'enic and fast/slow modes grow and damp alternately through a nonlinear modulation process. The modulation appears to be robust and survives strong damping by the neutral component.