Discontinuous Galerkin methods for solving the acoustic wave equation

In this work we develop a numerical simulator for the propagation of elastic waves by solving the one-dimensional acoustic wave equation with Absorbing Boundary Conditions (ABC’s) on the computational boundaries using Discontinuous Galerkin Finite Element Methods (DGFEM). The DGFEM allows us to easily simulate the presence of a fracture in the elastic medium by means of a linear-slip model. We analize the behaviour of our algorithm by comparing its results against analytic solutions. Furthermore, we show the frequency-dependent effect on the propagation produced by the fracture as appears in previous works. Finally, we present an analysis of the numerical parameters of the method.Fil: Castromán, Gabriel Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas. Departamento de Geofísica Aplicada; ArgentinaFil: Zyserman, Fabio Ivan. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas. Departamento de Geofísica Aplicada; Argentin

Multiple Avalanches Across the Metal-Insulator Transition of Vanadium Oxide Nano-scaled Junctions

The metal insulator transition of nano-scaled $VO_2$ devices is drastically different from the smooth transport curves generally reported. The temperature driven transition occurs through a series of resistance jumps ranging over 2 decades in amplitude, indicating that the transition is caused by avalanches. We find a power law distribution of the jump amplitudes, demonstrating an inherent property of the $VO_2$ films. We report a surprising relation between jump amplitude and device size. A percolation model captures the general transport behavior, but cannot account for the statistical behavior.Comment: 4 papers and 4 figures submitted to PR

On the transformations generated by the electromagnetic spin and orbital angular momentum operators

We present a study of the properties of the transversal "spin angular momentum" and "orbital angular momentum" operators. We show that the "spin angular momentum" operators are generators of spatial translations which depend on helicity and frequency and that the "orbital angular momentum" operators generate transformations which are a sequence of this kind of translations and rotations. We give some examples of the use of these operators in light matter interaction problems. Their relationship with the helicity operator allows to involve the electromagnetic duality symmetry in the analysis. We also find that simultaneous eigenstates of the three "spin" operators and parity define a type of standing modes which has been recently singled out for the interaction of light with chiral molecules. With respect to the relationship between "spin angular momentum", polarization, and total angular momentum, we show that, except for the case of a single plane wave, the total angular momentum of the field is decoupled from its vectorial degrees of freedom even in the regime where the paraxial approximation holds. Finally, we point out a relationship between the three "spin" operators and the spatial part of the Pauli-Lubanski four vector

Necessary symmetry conditions for the rotation of light

Two conditions on symmetries are identified as necessary for a linear scattering system to be able to rotate the linear polarisation of light: Lack of at least one mirror plane of symmetry and electromagnetic duality symmetry. Duality symmetry is equivalent to the conservation of the helicity of light in the same way that rotational symmetry is equivalent to the conservation of angular momentum. When the system is a solution of a single species of particles, the lack of at least one mirror plane of symmetry leads to the familiar requirement of chirality of the individual particle. With respect to helicity preservation, according to the analytical and numerical evidence presented in this paper, the solution preserves helicity if and only if the individual particle itself preserves helicity. However, only in the particular case of forward scattering the helicity preservation condition on the particle is relaxed: We show that the random orientation of the molecules endows the solution with an effective rotational symmetry; at its turn, this leads to helicity preservation in the forward scattering direction independently of any property of the particle. This is not the case for a general scattering direction. These results advance the current understanding of the phenomena of molecular optical activity and provide insight for the design of polarisation control devices at the nanoscale.Comment: 17 pages, 3 figure

Far-field measurements of vortex beams interacting with nanoholes

We measure the far-field intensity of vortex beams going through nanoholes. The process is analyzed in terms of helicity and total angular momentum. It is seen that the total angular momentum is preserved in the process, and helicity is not. We compute the ratio between the two transmitted helicity components, $\gamma_{m,p}$. We observe that this ratio is highly dependent on the helicity ($p$) and the angular momentum ($m$) of the incident vortex beam in consideration. Due to the mirror symmetry of the nanoholes, we are able to relate the transmission properties of vortex beams with a certain helicity and angular momentum, with the ones with opposite helicity and angular momentum. Interestingly, vortex beams enhance the $\gamma_{m,p}$ ratio as compared to those obtained by Gaussian beams

Efficient Environmental Regulation in the Unconventional Oil Industry

US OIL production has skyrocketed since 2007. Technological advances in oil and gas drilling (commonly referred to as ‘fracking’) have allowed producers to access vast petroleum reserves that were previously too costly to recover. The growth in oil and gas production from unconventional sources has been tremendous, so that unconventional sources now make up more than 50 percent of total US petroleum production (EIA 2015). While this represents a boost to job growth and the broader economy, growth in the oil industry comes with its fair share of problems. Academics and news agencies have documented a host of costs associated with new oil and gas production— groundwater pollution, oil spills, large “man camps” and increased crime, and even increases in traffic accidents and exploding train cars. Some of these costs were seen in Iowa with the contentious nature of right-of- Efficient Environmental Regulation in the Unconventional Oil Industry way issues associated with building out the Dakota Access pipeline across the state. Farmers and environmentalists alike are bound together in their concern for right-of-way, human rights concerns, and environmental issues

Slow sedimentation and deformability of charged lipid vesicles

The study of vesicles in suspension is important to understand the complicated dynamics exhibited by cells in vivo and in vitro. We developed a computer simulation based on the boundary-integral method to model the three dimensional gravity-driven sedimentation of charged vesicles towards a flat surface. The membrane mechanical behavior was modeled using the Helfrich Hamiltonian and near incompressibility of the membrane was enforced via a model which accounts for the thermal fluctuations of the membrane. The simulations were verified and compared to experimental data obtained using suspended vesicles labelled with a fluorescent probe, which allows visualization using fluorescence microscopy and confers the membrane with a negative surface charge. The electrostatic interaction between the vesicle and the surface was modeled using the linear Derjaguin approximation for a low ionic concentration solution. The sedimentation rate as a function of the distance of the vesicle to the surface was determined both experimentally and from the computer simulations. The gap between the vesicle and the surface, as well as the shape of the vesicle at equilibrium were also studied. It was determined that inclusion of the electrostatic interaction is fundamental to accurately predict the sedimentation rate as the vesicle approaches the surface and the size of the gap at equilibrium, we also observed that the presence of charge in the membrane increases its rigidity

Costs of Inefficient Regulation: Evidence from the Bakken

Efficient pollution regulation equalizes marginal abatement costs across sources. Here we study a new flaring regulation in North Dakota\u27s oil and gas industry and document its efficiency. Exploiting detailed well-level data, we find that the regulation reduced flaring 4 to 7 percentage points and accounts for up to half of the observed flaring reductions since 2015. We construct firm-level marginal flaring abatement cost curves and find that the observed flaring reductions could have been achieved at 20%lower cost by imposing a tax on flared gas equal to current public lands royalty rates instead of using firm-specific flaring requirements

Quantum Emulation of Gravitational Waves

Gravitational waves, as predicted by Einstein's general relativity theory, appear as ripples in the fabric of spacetime traveling at the speed of light. We prove that the propagation of small amplitude gravitational waves in a curved spacetime is equivalent to the propagation of a subspace of electromagnetic states. We use this result to propose the use of entangled photons to emulate the evolution of gravitational waves in curved spacetimes by means of experimental electromagnetic setups featuring metamaterials.Comment: 10 pages, 2 figure