Solute transport in a heterogeneous aquifer: a search for nonlinear deterministic dynamics

International audienceThe potential use of a nonlinear deterministic framework for understanding the dynamic nature of solute transport processes in subsurface formations is investigated. Time series of solute particle transport in a heterogeneous aquifer medium, simulated using an integrated probability/Markov chain (TP/MC) model, groundwater flow model, and particle transport model, are studied. The correlation dimension method, a popular nonlinear time series analysis technique, is used to identify nonlinear determinism. Sensitivity of the solute transport dynamics to the four hydrostratigraphic parameters involved in the TP/MC model: (1) number of facies; (2) volume proportions of facies; (3) mean lengths (and thereby anisotropy ratio of mean length) of facies; and (4) juxtapositional tendencies (i.e. degree of entropy) among the facies is also studied. The western San Joaquin Valley aquifer system in California is considered as a reference system. The results indicate, in general, the nonlinear deterministic nature of solute transport dynamics (dominantly governed by only a very few variables, on the order of 3), even though more complex behavior is possible under certain (extreme) hydrostratigraphic conditions. The sensitivity analysis reveals: (1) the importance of the hydrostratigraphic parameters (in particular, volume proportions of facies and mean lengths) in representing aquifer heterogeneity; and (2) the ability of the correlation dimension method in capturing the (extent of) complexity of the underlying dynamics. Verification and confirmation of the present results through use of other nonlinear deterministic techniques and assessment of their reliability for a wide range of solute transport scenarios are recommended

Topologically Massive Non-Abelian Gauge Theories: Constraints and Deformations

We study the relationship between three non-Abelian topologically massive gauge theories, viz. the naive non-Abelian generalization of the Abelian model, Freedman-Townsend model and the dynamical 2-form theory, in the canonical framework. Hamiltonian formulation of the naive non-Abelian theory is presented first. The other two non-Abelian models are obtained by deforming the constraints of this model. We study the role of the auxiliary vector field in the dynamical 2-form theory in the canonical framework and show that the dynamical 2-form theory cannot be considered as the embedded version of naive non-Abelian model. The reducibility aspect and gauge algebra of the latter models are also discussed.Comment: ReVTeX, 17 pp; one reference added, version published in Phys. Rev.

Multilayered feed forward Artificial Neural Network model to predict the average summer-monsoon rainfall in India

In the present research, possibility of predicting average summer-monsoon rainfall over India has been analyzed through Artificial Neural Network models. In formulating the Artificial Neural Network based predictive model, three layered networks have been constructed with sigmoid non-linearity. The models under study are different in the number of hidden neurons. After a thorough training and test procedure, neural net with three nodes in the hidden layer is found to be the best predictive model.Comment: 19 pages, 1 table, 3 figure

On the equivalence between topologically and non-topologically massive abelian gauge theories

We analyse the equivalence between topologically massive gauge theory (TMGT) and different formulations of non-topologically massive gauge theories (NTMGTs) in the canonical approach. The different NTMGTs studied are St\"uckelberg formulation of (A) a first order formulation involving one and two form fields, (B) Proca theory, and (C) massive Kalb-Ramond theory. We first quantise these reducible gauge systems by using the phase space extension procedure and using it, identify the phase space variables of NTMGTs which are equivalent to the canonical variables of TMGT and show that under this the Hamiltonian also get mapped. Interestingly it is found that the different NTMGTs are equivalent to different formulations of TMGTs which differ only by a total divergence term. We also provide covariant mappings between the fields in TMGT to NTMGTs at the level of correlation function.Comment: One reference added and a typos corrected. 15 pages, To appear in Mod. Phys. Lett.

Nonlinear Jaynes-Cummings model of atom-field interaction

Interaction of a two-level atom with a single mode of electromagnetic field including Kerr nonlinearity for the field and intensity-dependent atom-field coupling is discussed. The Hamiltonian for the atom-field system is written in terms of the elements of a closed algebra, which has SU(1,1) and Heisenberg-Weyl algebras as limiting cases. Eigenstates and eigenvalues of the Hamiltonian are constructed. With the field being in a coherent state initially, the dynamical behaviour of atomic-inversion, field-statistics and uncertainties in the field quadratures are studied. The appearance of nonclassical features during the evolution of the field is shown. Further, we explore the overlap of initial and time-evolved field states.Comment: 14 pages, 6 figures is PS forma

Predicting blunt cerebrovascular injury in pediatric trauma: Validation of the Utah Score

Risk factors for blunt cerebrovascular injury (BCVI) may differ between children and adults, suggesting that children at low risk for BCVI after trauma receive unnecessary computed tomography angiography (CTA) and high-dose radiation. We previously developed a score for predicting pediatric BCVI based on retrospective cohort analysis. Our objective is to externally validate this prediction score with a retrospective multi-institutional cohort. We included patients who underwent CTA for traumatic cranial injury at four pediatric Level I trauma centers. Each patient in the validation cohort was scored using the “Utah Score” and classified as high or low risk. Before analysis, we defined a misclassification rate <25% as validating the Utah Score. Six hundred forty-five patients (mean age 8.6 ± 5.4 years; 63.4% males) underwent screening for BCVI via CTA. The validation cohort was 411 patients from three sites compared with the training cohort of 234 patients. Twenty-two BCVIs (5.4%) were identified in the validation cohort. The Utah Score was significantly associated with BCVIs in the validation cohort (odds ratio 8.1 [3.3, 19.8], p < 0.001) and discriminated well in the validation cohort (area under the curve 72%). When the Utah Score was applied to the validation cohort, the sensitivity was 59%, specificity was 85%, positive predictive value was 18%, and negative predictive value was 97%. The Utah Score misclassified 16.6% of patients in the validation cohort. The Utah Score for predicting BCVI in pediatric trauma patients was validated with a low misclassification rate using a large, independent, multicenter cohort. Its implementation in the clinical setting may reduce the use of CTA in low-risk patients

Laughlin Wave Function and One-Dimensional Free Fermions

Making use of the well-known phase space reduction in the lowest Landau level(LLL), we show that the Laughlin wave function for the $\nu = {1\over m}$ case can be obtained exactly as a coherent state representation of an one dimensional $(1D)$ wave function. The $1D$ system consists of $m$ copies of free fermions associated with each of the $N$ electrons, confined in a common harmonic well potential. Interestingly, the condition for this exact correspondence is found to incorporate Jain's parton picture. We argue that, this correspondence between the free fermions and quantum Hall effect is due to the mapping of the $1D$ system under consideration, to the Gaussian unitary ensemble in the random matrix theory.Comment: 7 pages, Latex , no figure

Supersymmetry, Shape Invariance and Solvability of AN−1A_{N-1} and BCNBC_{N} Calogero-Sutherland Model

Using the ideas of supersymmetry and shape invariance we re-derive the spectrum of the $A_{N-1}$ and $BC_N$ Calogero-Sutherland model. We briefly discuss as to how to obtain the corresponding eigenfunctions. We also discuss the difficulties involved in extending this approach to the trigonometric models.Comment: 15 pages, REVTeX,No figure

A micromechanism study of thermosonic gold wire bonding on aluminum pad

A micromechanism of thermosonic gold wire bonding was elaborated by examining its interfacial characteristics as a result of the bonding process, including the fragmentation of the native aluminum oxide layer on Al pads, and formation of initial intermetallic compounds IMCs. It is found that the existence of an approximately 5 nm thick native oxide layer on original Al pads has a significant effect on the bonding, and the nucleation of IMCs during the bonding process must overcome this relatively inert thin film. Bonding strength was fundamentally determined by the degree of fragmentation of the oxide films, through which the formation of IMCs can be initiated due to the direct contact of the metal surfaces to be bonded. The extent of fracture the oxide layer was strongly influenced by the level of ultrasonic power, as at its high level alumina fragmentation becomes pervasive resulting in contiguous alloy interfaces and robust bonds. The IMCs formed at the interfaces were identified as Al₄Al and AuAl₂ with a thickness of 150–300 nm. The formation mechanism of such IMCs was explained by the effective heat of formation theory.This research was funded as a PMI2 Project Grant No. RC 41 through the UK Department for Innovation, Universities and Skills DIUS