Highly nonlinear solitary waves in chains of ellipsoidal particles

We study the dynamic response of a one-dimensional chain of ellipsoidal particles excited by a single compressive impulse. We detail the Hertzian contact theory describing the interaction between two ellipsoidal particles under compression, and use it to model the dynamic response of the system. We observe the formation of highly nonlinear solitary waves in the chain, and we also study their propagation properties. We measure experimentally the traveling pulse amplitude (force), the solitary wave speed, and the solitary wave width. We compare these results with theoretical predictions in the long wavelength approximation, and with numerical results obtained with a discrete particle model and with finite element simulations. We also study the propagation of highly nonlinear solitary waves in the chain with particles arranged in different configurations to show the effects of the particle's geometry on the wave propagation characteristics and dissipation. We find very good agreement between experiment, theory, and simulations for all the ranges of impact velocity and particle arrangements investigated

Coopetition in a Mixed Oligopoly Market

In this study, we aim to investigate the impact of privatization on the degree of cooperation and competition in a mixed oligopoly market. We consider a duopoly market that comprises one semipublic firm and one private firm. Each firm is assumed to determine the level of two types of effort: the cooperative effort made to enlarge the total market size and the competitive effort made to increase market share. In a contest framework, our results show that the competitive effort level of the semipublic firm is smaller than that of the private firm. The more the semipublic firm is concerned for social welfare, the less it competes. On the basis of average costs, we then analyze the case in which only the semipublic firm undertakes cooperative effort. In this case, the private firm behaves as a free rider. Furthermore, we find that the semipublic firm expends more cooperative effort than does the private firm.Coopetition, Mixed oligopoly, Contests, Free rider

Coopetition in a Mixed Duopoly Market

This study aims to investigate the impact of privatization on the degree of cooperation and competition in a mixed duopoly market. In this market, one semipublic firm and one private firm determine the level of two types of effort: the cooperative effort made to enlarge the total market size and the competitive effort made to increase market share. In a contest framework, our results show that the competitive effort level of the semipublic firm is smaller than that of the private firm. The more the semipublic firm is concerned for social welfare, the less it competes. On the basis of average costs, we then identify the conditions in which only the semipublic firm undertakes cooperative effort while the private firm behaves as a free rider. Besides, contrarily to common belief, our results highlight that a bad level of privatization may favor the most the free rider. Furthermore, we find that the semipublic firm always expends more cooperative effort than does the private firm.Contests

Lorentz TEM characterisation of magnetic and physical structure of nanostructure magnetic thin films

The work presented in this thesis is an investigation which aims to quantitatively characterise the physical microstructure, magnetic structure and micromagnetic behaviour of nanostructured thin films for magnetic recording and spintronics application. The nanostructures in the present work involve continuous and patterned thin films. Chapters 1, 2, and 3 present the overview backgrounds directly relevant to the work. Chapter 4 focuses on vortex structure in magnetic nanodots. The results confirm that the behaviour of the vortex can be modified by changing the edge geometry of the dots. It is demonstrated a practical method to determine the out-of-plane component of the vortex core with high accuracy and speed. Additionally in-plane curling magnetisation of the vortex is also mapped by reconstructing the electron phase using the transport-of-intensity equation. However this method is susceptible to spurious low spatial frequency and this aspect is explored to show limitations of the method. Chapter 5 deals with the characterisation of magnetic structure in nanoconstrictions intended to trap domain walls (DWs) in the nanoconstrictions. A structure was fabricated with two micron-sized pads as the sources for creation of DWs. A DW can be driven to be pinned at the nanoconstriction resulting in a change of magnetoresistance due to the contribution of the DW to the resistance of the device. The magnetisation configuration around the constriction is studied during the reversal process. It is apparent that that understanding the magnetisation rotation around the constriction and into the pads is the key to the magnetoresistance measurements and the DW resistance is part of this process. Evidences of DW compression at the nanoconstriction were noted. In Chapter 6 the investigation of the physical structure and micromagnetism of CoIr film is described. A hexagonal crystal structure with a [0001] texture normal to the film plane was characterised. Weak anisotropy is observed in the film denoted by a complex reversal on the hard axis due to incoherent rotation of magnetic moments. The film exhibits typical soft magnetic behaviour it merits compared to other soft materials are discussed in light of the results obtained here. Chapter 7 concludes with a discussion of the outcomes of the present thesis. Additionally possible directions for future research in topics discussed in this thesis are proposed

Inflation with a class of concave inflaton potentials in Randall-Sundrum model

We investigate inflation with a class of concave inflaton potentials of the form $\sim \phi^n$ $(0<n<1)$ in the Randall-Sundrum model with an infinite extra spatial dimension. We show that this class of models is much more in good agreement with observations compared to the standard inflation. We also find the range of the five-dimensional Planck scale ($M_5$) and show that large tensor-to-scalar ratios do not eliminate small-field inflation in braneworld cosmology.Comment: 7 pages, 2 figures; matches EPJC version; comments are welcom

Unitary paradox of cosmological perturbations

If we interpret the Bekenstein-Hawking entropy of the Hubble horizon as thermodynamic entropy, then the entanglement entropy of the superhorizon modes of curvature perturbation entangled with the subhorizon modes will exceed the Bekenstein-Hawking bound at some point; we call this the unitary paradox of cosmological perturbations by analogy with black hole. In order to avoid a fine-tuned problem, the paradox must occur during the inflationary era at the critical time $t_c=\ln(3\sqrt{\pi}/\sqrt{2}\epsilon_HH_{inf})/2H_{inf}$ (in Planck units), where $\epsilon_H= -\dot{H}/H^2$ is the first Hubble slow-roll parameter and $H_{inf}$ is the Hubble rate during inflation. If we instead accept the fine-tuned problem, then the paradox will occur during the dark energy era at the critical time $t_c'=\ln(3\sqrt{\pi}H_{inf}/\sqrt{2}fe^{2N}H_\Lambda^2)/2H_\Lambda$, where $H_\Lambda$ is the Hubble rate dominated by dark energy, $N$ is the total number of e-folds of inflation, and $f$ is a purification factor that takes the range $0<f<3\sqrt{\pi}H_{inf}/\sqrt{2}e^{2N}H_\Lambda^2$.Comment: 13 pages, 3 figures; close to published versio

Insights of quantum time for quantum evolution

If time is emergent, quantum system is entangled with quantum time as it evolves. If the system contains entanglement within itself, which we can call \textit{internal entanglement} to distinguish it from the ``external" time-system entanglement, the speed of evolution is enhanced. In this paper, we explore the insights of quantum time for the evolution of a system that contains two entangled qubits. We consider two cases: (1) two initially entangled qubits that evolve under local dynamics; (2) two interacting qubits such that entanglement between them is generated over time. In both cases, the key message is that increasing internal entanglement speeds up the evolution and makes the system more entangled with time. This result could be useful to gain new insights of quantum time for black hole evaporation or cosmological perturbations in an expanding Universe, because we also have an evolving entangled bipartite system in those cases.Comment: 12 pages, 4 figure

Time-System Entanglement and Special Relativity

We know that space and time are treated almost equally in classical physics, but we also know that this is not the case for quantum mechanics. A quantum description of both space and time is important to really understand the quantum nature of reality. The Page-Wootters mechanism of quantum time is a promising starting point, according to which the evolution of the quantum system is described by the entanglement between it and quantum temporal degrees of freedom. In this paper, we use a qubit clock model to study how the time-system entanglement measures depend on the rapidity when the quantum system is Lorentz boosted. We consider the case of a spin-1/2 particle with Gaussian momentum distribution as a concrete example.Comment: 5 pages, 3 figure