Juan Pablo Fernández

The Two-Dimensional Bose–Einstein Condensate

We study the Hartree–Fock–Bogoliubov mean-field theory as applied to a two-dimensional finite trapped Bose gas at low temperatures and find that, in the Hartree–Fock approximation, the system can be described either with or without the presence of a condensate; this is true in the thermodynamic limit as well. Of the two solutions, the one that includes a condensate has a lower free energy at all temperatures. However, the Hartree–Fock scheme neglects the presence of phonons within the system, and when we allow for the possibility of phonons we are unable to find condensed solutions; the uncondensed solutions, on the other hand, are valid also in the latter, more general scheme. Our results confirm that low-energy phonons destabilize the two-dimensional condensate.

Invariant characteristics of horizontal-plane minimum-torque-change movements with one mechanical degree of freedom

Abstract.u2002Uno et al. (1989) suggested that movements are organized such that the squared change of torque is minimized over time. Although influential, this theory has attracted much less attention from experimental researchers than the competing minimum-jerk model (Flash and Hogan 1985). One reason for this relative neglect has been the lack of general quantitative predictions, which results from the belief that minimum-torque-change trajectories have to be computed numerically for individual movements and arm-dynamical parameters. In the present paper, we show that for an important special case, that of planar horizontal movements with one mechanical degree of freedom (DOF), it is actually possible to find an analytic expression for the predicted minimum-torque-change trajectories. Based on this mathematical result, we derive a set of properties which are characteristic of these trajectories and compare them to experimental data which have not previously been related to the minimum-torque-change model. Certain discrepancies between these experimental data and minimum-torque-change model predictions are revealed.

Camp Butner Live-Site UXO Classification Using Hierarchical Clustering and Gaussian Mixture Modeling

We demonstrate in detail a semisupervised scheme to classify unexploded ordnance (UXO) by using as an example the data collected with a time-domain electromagnetic towed array detection system during a live-site blind test conducted at the former Camp Butner in North Carolina, USA. The model that we use to characterize targets and generate discrimination features relies on a solution of the inverse UXO problem using the orthonormalized volume magnetic source model. Unlike other classification techniques, which often rely on library matching or expert knowledge, our combined clustering/Gaussian-mixture-model approach first uses the inherent properties of the data in feature space to build a custom training list that is then used to score all unknown targets by assigning them a likelihood of being UXO. The ground truth for the most likely candidates is then requested and used to correct the model parameters and reassign the scores. The process is repeated several times until the desired statistical margin is reached, at which point a final dig is produced. Our method could decrease intervention by human experts and, as the results of the blind test show, identify all targets of interest correctly while minimizing false-alarm counts.

MPV-II: an enhanced vector man-portable EMI sensor for UXO identification

The Man-Portable Vector (MPV) electromagnetic induction sensor has proved its worth and flexibility as a tool for identification and discrimination of unexploded ordnance (UXO). TheMPV allows remediation work in treed and rough terrains where other instruments cannot be deployed; it can work in survey mode and in a static mode for close interrogation of anomalies. By measuring the three components of the secondary field at five different locations, the MPV provides diverse time-domain data of high quality. TheMPV is currently being upgraded, streamlined, and enhanced to make it more practical and serviceable. The new sensor, dubbedMPV-II, has a smaller head and lighter components for better portability. The original laser positioning system has been replaced with one that uses the transmitter coil as a beacon. The receivers have been placed in a configuration that permits experimental computation of field gradients. In this work, after introducing the new sensor, we present the results of several identification/discrimination experiments using data provided by the MPV-II and digested using a fast and accurate new implementation of the dipole model. The model performs a nonlinear search for the location of a responding target, at each step carrying out a simultaneous linear least-squares inversion for the principal polarizabilities at all time gates and for the orientation of the target. We find that the MPV-II can identify standard-issue UXO, even in cases where there are two targets in its field of view, and can discriminate them from clutter.

The generalized SEA and a statistical signal processing approach applied to UXO discrimination

The prohibitive costs of excavating all geophysical anomalies are well known and are one of the greatest impediments to efficient clean-up of unexploded ordnance (UXO)-contaminated lands at Department of Defense (DoD) and Department of Energy (DOE) sites. Innovative discrimination techniques that can reliably distinguish between hazardous UXO and non-hazardous metallic items are required. The key element to overcoming these difficulties lies in the development of advanced processing techniques that can treat complex data sets to maximize the probability of accurate classification and minimize the false alarm rate. To address these issues, this paper uses a new approach that combines a physically complete EMI forward model called the Generalized Standardized Excitation Approach (GSEA) with a statistical signal processing approach named Mixed Modeling (MM). UXO discrimination requires the inversion of digital geophysical data, which could be divided into two pars: 1) linear - estimating model parameters such as the amplitudes of the responding GSEA sources and 2) non-linear - inverting an objects location and orientation. Usually the data inversion is an ill-posed problem that requires regularization. Determining the regularization parameter is not straightforward, and in many cases depends on personal experience. To overcome this issue, in this paper we employ the statistical approach to estimate regularization parameters from actual data using the un-surprised mixed model approach. In addition, once the non-linear inverse scattering parameters are estimated then for UXO discrimination a covariance matrix and confidence interval are derived. The theoretical basis and practical realization of the combined GSEA-Mixed Model algorithm are demonstrated. Discrimination studies are done for ATC-UXO sets of time-domain EMI data collected at the ERDC UXO test stand site in Vicksburg, Mississippi.

Near and far EMI field analyses in a conducting environment to enhance underwater UXO detection

The underlying physics of low frequency EMI scattering phenomena in underwater environments from highly conducting and permeable metallic objects is analyzed using an approach that combines the method of auxiliary sources and a surface impedance boundary condition. The combined algorithm solves EMI boundary-value problems by representing the electromagnetic fields in each domain of the structure under investigation by a finite linear combination of analytical solutions of the relevant field equations, corresponding to elementary sources situated a small distance away from the boundaries of each domain. Numerical experiments are conducted for homogeneous and multilayer targets of canonical (spheroidal) shapes subject to frequency- or time-domain illumination, as well as for heterogeneous UXO like targets, to demonstrate: (a) how marine environments change EMI sensor performance and associated processing approaches for detecting highly conducting and permeable metallic objects underwater, and (b) what are the EMI sensors detectability limits. Near and far EMI field and induced eddy-current distributions are presented to help gain insight into underwater EMI scattering phenomena. Particularly, the results illustrate coupling effects between the object and its surrounding conductive medium, especially at high frequencies (early times for time-domain sensors). The results also suggest that this coupling depends on the objects material properties, the conductivity of the medium, and the distance between the sensor and the objects center.

Optimizing EMI transmitter and receiver configurations to enhance detection and identification of small and deep metallic targets

Current electromagnetic induction (EMI) sensors of the kind used to discriminate buried unexploded orndance (UXO) can detect targets down to a depth limited by the geometric size of the transmitter (Tx) coils, the amplitudes of the transmitting currents, and the noise floor of the receivers (Rx). The last two factors are not independent: for example, one cannot detect a deeply buried target simply by increasing the amplitude of the Tx current, since this also increases the noise and thus does not improve the SNR. The problem could in principle be overcome by increasing the size of the Tx coils and thus their moment. Current multi-transmitter instruments such as the TEMTADS sensor array can be electronically tweaked to provide a big Tx moment: they can be modified to transmit signals from two, three or more Tx coils simultaneously. We investigate the possibility of enhancing the deep-target detection capability of TEMTADS by exploring different combinations of Tx coils. We model different multi-Tx combinations within TEMTADS using a full-3D EMI solver based on the method of auxiliary sources (MAS).We determine the feasibility of honing these combinations for enhanced detection and discrimination of deep targets. We investigate how to improve the spatial resolution and focusing properties of the primary magnetic field by electronically adjusting the currents of the transmitters. We apply our findings to data taken at different UXO live sites.

Path‐Integral Monte Carlo and the Squeezed Trapped Bose‐Einstein Gas

Bose‐Einstein condensation has been experimentally found to take place in finite trapped systems when one of the confining frequencies is increased until the gas becomes effectively two‐dimensional (2D). We confirm the plausibility of this result by performing path‐integral Monte Carlo (PIMC) simulations of trapped Bose gases of increasing anisotropy and comparing them to the predictions of finite‐temperature many‐body theory. PIMC simulations provide an essentially exact description of these systems; they yield the density profile directly and provide two different estimates for the condensate fraction. For the ideal gas, we find that the PIMC column density of the squeezed gas corresponds quite accurately to that of the exact analytic solution and, moreover, is well mimicked by the density of a 2D gas at the same temperature; the two estimates for the condensate fraction bracket the exact result. For the interacting case, we find 2D Hartree‐Fock solutions whose density profiles coincide quite well with ...

Absence of Fragmentation in Two-Dimensional Bose-Einstein Condensation

No HeadingWe investigate the possibility that the BEC-like phenomena recently detected on two-dimensional finite trapped systems consist of fragmented condensates. We derive and diagonalize the one-body density matrix of a two-dimensional isotropically trapped Bose gas at finite temperature. For the ideal gas, the procedure reproduces the exact harmonic-oscillator eigenfunctions and the Bose distribution. We use a new collocation-minimization method to study the interacting gas in the Hartree-Fock approximation and obtain a ground-state wavefunction and condensate fraction consistent with those obtained by other methods. The populations of the next few eigenstates increase at the expense of the ground state but continue to be negligible; this supports the conclusion that two-dimensional BEC is into a single state.

The condensate number in PIMC treatments of trapped bosons

Abstract In path integral Monte Carlo (PIMC) treatments of harmonically trapped bosons, one cannot use the usual long-range constant limit of the one-body reduced density matrix ρ 1 to determine the condensate number n 0 because ρ 1 always approaches zero in a trap. W. Krauth found that the longest permutation cycle arising in the simulation gives a consistent value of n 0 . Our analytical studies of the ideal gas suggest other ways of using permutation cycles to determine n 0 . We test these approaches on simulations involving finite-size ideal and interacting gases and find that the methods are consistent.