Kevin O'Neill

The physics of mathematical frost heave models: A review

Abstract This paper is concerned with the physical and thermodynamical bases of frost heave modeling. An attempt is made to isolate and illuminate issues which all such models must address, at least by implication. Although numerous relevant publications are surveyed, emphasis is less on an enumeration of items in the literature, and more on the concepts themselves, and on their alternative mathematical expressions, approximations, and manners of applications. Ultimately a selection of specific mathematical models is discussed, in light of the points raised in the general discussion.

Finite element simulation of planar instabilities during solidification of an undercooled melt

Abstract Two-dimensional finite element solutions for planar solidification from an undercooled melt are presented. These simulations are based on the transient heat equation in both solid and liquid and show the onset and propagation of both stable and unstable numerical waveforms which reproduce those predicted in the continuum analysis with fidelity. The inherent instabilities associated with the freezing process dictate a more comprehensive treatment of the interfacial temperature than that specified in stable Stefan-type problems. Herein, we apply radiation-type boundary conditions on the interface that incorporate temperature effects associated with curvature and interfacial kinetics. The interfacial temperature depression due to curvature is the primary restraining factor during dendritic growth. Its numerical representation requires special care to avoid fatal discretization error; additionally, curvature must be treated implicitly within the thermal iteration and within the time step to overcome otherwise severe time-step constraints. The numeric simulations of anisotropic ice show similar waveform patterns at the onset of the instability to those of isotropic cases. However, as the amplitude of the waveform increases significant lengths of interface become orientated along the C axis where interfacial kinetics inhibit growth. This alters the interface shape by elongating the dendrite finger.

Application of a spheroidal-mode approach and a differential evolution algorithm for inversion of magneto-quasistatic data in UXO discrimination

We construct a spheroidal-mode approach for unexploded ordnance (UXO) inversion under time harmonic excitations in the magneto-quasistatic regime. Use of spheroidal modes gives us the ability to deal with a variety of objects from elongated needles to flat plates, with better accuracy than the simple dipole models commonly used. The method can also be used for complex objects whose shape cannot be well approximated by spheroidal surfaces. In this case, we define a spheroidal surface surrounding the objects as a computational device for obtaining the objects scattered field in the spheroidal coordinate system. The coefficients obtained in the spheroidal coordinate system are shown to be the characteristics of the object. Stored in a library, they can produce fast and complete forward models for use in pattern matching inversion. For a single spheroidal object reconstruction, a differential evolution optimization algorithm, combined with the spheroidal mode formulation, inverts success- fully for the objects size, location, orientation, magnetic permeability and conductivity. For more general objects, the system determines the fitness of a candidate relative to a UXO being sought by comparing measured data with its signature.

A derivation of the equations for transport of liquid and heat in three dimensions in a fractured porous medium

Abstract Governing equations can be derived for transient, three-dimensional transport of heat and mass in compressible, liquid saturated fractured porous media. Recently developed mathematical techniques can be used which relate local space averages of derivatives of medium properties to the derivatives of those averages. Using these techniques, well established thermomechanical transport equations which apply at microscopic points may be transformed into equations in macroscopic variables; i.e. in variables which pertain to the scale of observation. In the absence of chemical reactions, transfer between source entities and the medium may be taken care of in a consistent, physically realistic way, such that macroscopic source terms arise naturally in the course of the macroscopization procedures.

Realistic subsurface anomaly discrimination using electromagnetic induction and an SVM classifier

The environmental research program of the United States military has set up blind tests for detection and discrimination of unexploded ordnance. One such test consists of measurements taken with the EM-63 sensor at Camp Sibert, AL. We review the performance on the test of a procedure that combines a field-potential (HAP) method to locate targets, the normalized surface magnetic source (NSMS) model to characterize them, and a support vector machine (SVM) to classify them. The HAP method infers location from the scattered magnetic field and its associated scalar potential, the latter reconstructed using equivalent sources. NSMS replaces the target with an enclosing spheroid of equivalent radial magnetization whose integral it uses as a discriminator. SVM generalizes from empirical evidence and can be adapted for multiclass discrimination using a voting system. Our method identifies all potentially dangerous targets correctly and has a false-alarm rate of about 5%.

Analyzing the effects of conductive and permeable soil on the EMI response for UXO discrimination

Unexploded ordinances (UXO) are buried typically in the top 1 m of soil. Low frequency (from tens of Hertz up to several hundreds of kHertz) electromagnetic induction (EMI) sensing has been identified as one of most promising technology for UXO detection as well for discrimination. They use the principle of EM1 in which unseen object are detected by sensing eddy current induced in metal by a primary magnetic field. It is known that the EMI sensors are sensitive to the scatters electromagnetic parameters (conductivity and permeability). Therefore, in this paper, low frequency scattering from a highly conducting and permeable metallic objects buried in geological soil are exposed and analyzed from the unexploded ordnances (UXO) detection and discrimination point of new. The method of auxiliary sources (MAS) in conjunction with thin skin approximation (TSA) is used for understanding physics of electromagnetic induction (EMI) scattering phenomena. Several numerical examples are designed to show how the geological soils electromagnetic parameters (conductivity and permeability) affect objects EMI response.

AN EXPERT-FREE TECHNIQUE FOR LIVE SITE UXO TARGET CLASSIFICATION

In this paper we examine methods of automatic classification applied to Unexploded Ordnance (UXO) across data sets from a live site. All sensors used are time-domain Electromagnetic Induction (EMI) sensors. We solve for target extrinsic and intrinsic parameters using the Differential Evolution (DE) and Ortho-Normalized Volume Magnetic Source (ONVMS) algorithm. This inversion provides target locations and intrinsic time-series total ONVMS principal eigenvalues. We fit these to an empirical power decay model, the Pasion-Oldenburg model, providing dimensionality reduction for a Machine Learning (ML) approach. We group anomalies by the unsupervised Weighted-Pair Group Method with Averaging (WPGMA) algorithm. After requesting Ground Truths (GT) for the central element of each cluster, we train a supervised Gaussian Mixture Model (GMM), in which each class of UXO is represented by a multivariate Gaussian probability density. We request Ground Truths in rounds until we are confident there are no remaining Targets of Interest (TOI) in our survey of the site. Our system for UXO cleanup is fully automatic and expert free, and uses a priori knowledge combined with a learned algorithm.

One-dimensional transport from a highly concentrated, transfer type source

Abstract In both heat and mass transfer, situations arise in which an entity considered as a source/sink has strength which can only be expressed in terms of an unknown rate of source—flow field transfer. This occurs when transfer between the source and medium is driven by a dependent variable difference which is unknown, because the responding medium value is unknown. Manifold mathematical complexities arise when in addition the source is highly concentrated spatially, relative to the size of the overall domain. A 1-dim. convective-diffusive transport equation suitable for this case may be solved by simultaneous use of the Fourier transform and its inverse in the same equation, together with other transformation and manipulation. From the solution obtained for the case of constant source intensity, one may construct a general expression for the solution when source intensity varies arbitrarily in time. Explicit expressions are obtained for solution of the fundamental case of temporally sinusoidal source intensity.