Multiple scattering of classical waves: from microscopy to mesoscopy and diffusion

A tutorial discussion of the propagation of waves in random media is presented. In first approximation the transport of the multiple scattered waves is given by diffusion theory, but important corrections are present. These corrections are calculated with the radiative transfer or Schwarzschild-Milne equation, which describes intensity transport at the ``mesoscopic'' level and is derived from the ``microscopic'' wave equation. A precise treatment of the diffuse intensity is derived which automatically includes the effects of boundary layers. Effects such as the enhanced backscatter cone and imaging of objects in opaque media are also discussed within this framework. In the second part the approach is extended to mesoscopic correlations between multiple scattered intensities which arise when scattering is strong. These correlations arise from the underlying wave character. The derivation of correlation functions and intensity distribution functions is given and experimental data are discussed. Although the focus is on light scattering, the theory is also applicable to micro waves, sound waves and non-interacting electrons.Comment: Review. 86 pages Latex, 32 eps-figures included. To appear in Rev. Mod. Phy

Through-the-Wall Imaging and Multipath Exploitation

We consider the problem of using electromagnetic sensing to estimate targets in complex environments, such as when they are hidden behind walls and other opaque objects. The often unknown electromagnetic interactions between the target and the surrounding area, make the problem challenging. To improve our results, we exploit information in the multipath of the objects surrounding both the target and the sensors. First, we estimate building layouts by using the jump-diffusion algorithm and employing prior knowledge about typical building layouts. We also take advantage of a detailed physical model that captures the scattering by the inner walls and efficiently utilizes the frequency bandwidth. We then localize targets hidden behind reinforced concrete walls. The sensing signals reflected from the targets are significantly distorted and attenuated by the embedded metal bars. Using the surface formulation of the method of moments, we model the response of the reinforced walls, and incorporate their transmission coefficients into the beamforming method to achieve better estimation accuracy. In a related effort, we utilize the sparsity constraint to improve electromagnetic imaging of hidden conducting targets, assuming that a set of equivalent sources can be substituted for the targets. We derive a linear measurement model and employ l1 regularization to identify the equivalent sources in the vicinity of the target surfaces. The proposed inverse method reconstructs the target shape in one or two steps, using single-frequency data. Our results are experimentally verified. Finally, we exploit the multipath from sensor-array platforms to facilitate direction finding. This in contrast to the usual approach, which utilizes the scattering close to the targets. We analyze the effect of the multipath in a statistical signal processing framework, and compute the Cramer-Rao bound to obtain the system resolution. We conduct experiments on a simple array platform to support our theoretical approach

Rigorous Probabilistic Analysis of Equilibrium Crystal Shapes

The rigorous microscopic theory of equilibrium crystal shapes has made enormous progress during the last decade. We review here the main results which have been obtained, both in two and higher dimensions. In particular, we describe how the phenomenological Wulff and Winterbottom constructions can be derived from the microscopic description provided by the equilibrium statistical mechanics of lattice gases. We focus on the main conceptual issues and describe the central ideas of the existing approaches.Comment: To appear in the March 2000 special issue of Journal of Mathematical Physics on Probabilistic Methods in Statistical Physic

Geodynamic modelling of subduction zones : Subduction zone initiation by polarity reversal and main dynamic controls on the stability of single-sided subduction

Subduction zones are one of the most widely studied geodynamic settings, representing the primary driver for mantle convection and plate tectonics. Despite this, one question still sparks controversy to the present day: how does a subduction zone initiate? Over the past half century, multiple theories have been suggested to explain subduction zone initiation (SZI). One widely cited conceptual model for SZI is polarity reversal, resulting from the shutdown of a pre-existent subduction zone due to the arrival of a buoyant block at the trench. However, the dynamic conditions by which this process occurs remain elusive. To shed light on this complex topic and assess the geodynamic constraints behind polarity reversal SZI, two geodynamic numerical modelling studies were conducted. In both studies, it was shown that this SZI mechanism is dynamically viable, without external forcing, occurring simply as the result of the evolving force balance during an oceanic plateau collision. Additionally, the efficiency of a polarity reversal event is increased by the presence of old subducting plates, relatively young overriding plates, and/or narrow oceanic plateaus. The results were shown to be consistent with a widely studied natural polarity reversal case, the collision of the Ontong-Java Plateau and formation of the Vanuatu subduction zone. Beyond the complexity of SZI, subduction zone modelling studies have predicted the existence of double-sided subduction (i.e., the simultaneous sinking of both plates) for years. As this type of subduction zone has not been found on Earth, its inexistence has been previously tied to strong subducting plates and the constant maintenance of a weak subduction interface. Additional exploratory numerical modelling was also carried out, expanding the scope of previously tested conditions by systematically exploring the effective strength contrast between the two intervening plates. The preliminary results suggest that, under top free slip conditions, two strong plates and a weak interface are needed to ensure single-sided subduction, as opposed to a strong subducting plate and a weak interface

Viability and Performance of RF Source Localization Using Autocorrelation-Based Fingerprinting

Finding the source location of a radio-frequency (RF) transmission is a useful capability for many civilian, industrial, and military applications. This problem is particularly challenging when done “Blind,” or when the transmitter was not designed with finding its location in mind, and relatively little information is available about the signal before-hand. Typical methods for this operation utilize the time, phase, power, and frequency viewable from received signals. These features are all less predictable in indoor and urban environments, where signals undergo transformation from multiple interactions with the environment. These interactions imprint structure onto the received signal which is dependent on the transmission path, and therefore the initial location. Using a received signal, a signal characteristic known as the autocorrelation can be computed which will largely be shaped by this information. In this research, RF source localization using finger-printing (a technique involving matching to a known database) with signal autocorrelations is explored. A Gaussian-process-based method for autocorrelation based fingerprinting is proposed. Performance of this method is evaluated using a ray-tracing-based simulation of an indoor environment

Generalization of Bloch's theorem for arbitrary boundary conditions: Interfaces and topological surface band structure

We describe a method for exactly diagonalizing clean $D$-dimensional lattice systems of independent fermions subject to arbitrary boundary conditions in one direction, as well as systems composed of two bulks meeting at a planar interface. Our method builds on the generalized Bloch theorem [A. Alase et al., Phys. Rev. B 96, 195133 (2017)] and the fact that the bulk-boundary separation of the Schrodinger equation is compatible with a partial Fourier transform operation. Bulk equations may display unusual features because they are relative eigenvalue problems for non-Hermitian, bulk-projected Hamiltonians. Nonetheless, they admit a rich symmetry analysis that can simplify considerably the structure of energy eigenstates, often allowing a solution in fully analytical form. We illustrate our extension of the generalized Bloch theorem to multicomponent systems by determining the exact Andreev bound states for a simple SNS junction. We then analyze the Creutz ladder model, by way of a conceptual bridge from one to higher dimensions. Upon introducing a new Gaussian duality transformation that maps the Creutz ladder to a system of two Majorana chains, we show how the model provides a first example of a short-range chiral topological insulator hosting topological zero modes with a power-law profile. Additional applications include the complete analytical diagonalization of graphene ribbons with both zigzag-bearded and armchair boundary conditions, and the analytical determination of the edge modes in a chiral $p+ip$ two-dimensional topological superconductor. Lastly, we revisit the phenomenon of Majorana flat bands and anomalous bulk-boundary correspondence in a two-band gapless $s$-wave topological superconductor. We analyze the equilibrium Josephson response of the system, showing how the presence of Majorana flat bands implies a substantial enhancement in the $4\pi$-periodic supercurrent.Comment: 20+9 pages, 10 figure

Exergy-based Planning and Thermography-based Monitoring for energy efficient buildings - Progress Report (KIT Scientific Reports ; 7632)

Designing and monitoring energy efficiency of buildings is vital since they account for up to 40% of end-use energy. In this study, exergy analysis is investigated as a life cycle design tool to strike a balance between thermodynamic efficiency of energy conversion and economic and environmental costs of construction. Quantitative geo-referenced thermography is proposed for monitoring and quantitative assessment via continued simulation and parameter estimation during the operating phase

Methods for Optimal Output Prediction in Computational Fluid Dynamics.

In a Computational Fluid Dynamics (CFD) simulation, not all data is of equal importance. Instead, the goal of the user is often to compute certain critical "outputs" -- such as lift and drag -- accurately. While in recent years CFD simulations have become routine, ensuring accuracy in these outputs is still surprisingly difficult. Unacceptable levels of output error arise even in industry-standard simulations, such as the steady flow around commercial aircraft. This problem is only exacerbated when simulating more complex, unsteady flows. In this thesis, we present a mesh adaptation strategy for unsteady problems that can automatically reduce errors in outputs of interest. This strategy applies to problems in which the computational domain deforms in time -- such as flapping-flight simulations -- and relies on an unsteady adjoint to identify regions of the mesh contributing most to the output error. This error is then driven down via refinement of the critical regions in both space and time. Here, we demonstrate this strategy on a series of flapping-wing problems in two and three dimensions, using high-order discontinuous Galerkin (DG) methods for both spatial and temporal discretizations. Compared to other methods, results indicate that this strategy can deliver a desired level of output accuracy with significant reductions in computational cost. After concluding our work on mesh adaptation, we take a step back and investigate another idea for obtaining output accuracy: adapting the numerical method itself. In particular, we show how the test space of discontinuous finite element methods can be "optimized" to achieve accuracy in certain outputs or regions. In this work, we compute test functions that ensure accuracy specifically along domain boundaries. These regions -- which are vital to both scalar outputs (such as lift and drag) and distributions (such as pressure and skin friction) -- are often the most important from an engineering standpoint.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133418/1/kastsm_1.pd