Pseudo-differential operators with nonlinear quantizing functions

In this paper we develop the calculus of pseudo-differential operators corresponding to the quantizations of the form $$Au(x)=\int_{\mathbb{R}^n}\int_{\mathbb{R}^n}e^{i(x-y)\cdot\xi}\sigma(x+\tau(y-x),\xi)u(y)dyd\xi,$$ where $\tau:\mathbb{R}^n\to\mathbb{R}^n$ is a general function. In particular, for the linear choices $\tau(x)=0$, $\tau(x)=x$, and $\tau(x)=\frac{x}{2}$ this covers the well-known Kohn-Nirenberg, anti-Kohn-Nirenberg, and Weyl quantizations, respectively. Quantizations of such type appear naturally in the analysis on nilpotent Lie groups for polynomial functions $\tau$ and here we investigate the corresponding calculus in the model case of $\mathbb{R}^n$. We also give examples of nonlinear $\tau$ appearing on the polarised and non-polarised Heisenberg groups, inspired by the recent joint work with Marius Mantoiu.Comment: 26 page

Efficiency fluctuations in quantum thermoelectric devices

We present a method, based on characterizing efficiency fluctuations, to asses the performance of nanoscale thermoelectric junctions. This method accounts for effects typically arising in small junctions, namely, stochasticity in the junction's performance, quantum effects, and nonequilibrium features preventing a linear response analysis. It is based on a nonequilibrium Green's function (NEGF) approach, which we use to derive the full counting statistics (FCS) for heat and work, and which in turn allows us to calculate the statistical properties of efficiency fluctuations. We simulate the latter for a variety of simple models where our method is exact. By analyzing the discrepancies with the semi-classical prediction of a quantum master equation (QME) approach, we emphasize the quantum nature of efficiency fluctuations for realistic junction parameters. We finally propose an approximate Gaussian method to express efficiency fluctuations in terms of nonequilibrium currents and noises which are experimentally measurable in molecular junctions.Comment: 11 pages, 6 figures, v2: version accepted in PR

Quantum Thermodynamics: A Nonequilibrium Green's Functions Approach

We establish the foundations of a nonequilibrium theory of quantum thermodynamics for noninteracting open quantum systems strongly coupled to their reservoirs within the framework of the nonequilibrium Green functions (NEGF). The energy of the system and its coupling to the reservoirs are controlled by a slow external time-dependent force treated to first order beyond the quasistatic limit. We derive the four basic laws of thermodynamics and characterize reversible transformations. Stochastic thermodynamics is recovered in the weak coupling limit.Comment: 4 pages, 3 figures, Supplementary Material, v2: published versio

IN SITU GROUND FREEZING AND SAMPLING OF A PLEISTOCENE SAND DEPOSIT IN THE SOUTH CAROLINA COASTAL PLAIN

The procedures used to freeze and sample a Pleistocene sand deposit at the Coastal Research and Education Center near Charleston, South Carolina to preserve and study the effects of diagenesis are presented in this thesis. An initial feasibility study was conducted to target a layer of clean sand at the CREC site with little to no frost heave potential. To freeze the sand deposit, a ground freezing system with a central freezing pipe was installed to target a column of sand 1-m in radius and 2.3-m long. Liquid nitrogen was continuously supplied to the large steel freezing pipe, which was fabricated to isolate and radially freeze between depths of 1.8 m and 3.8 m below the ground surface, for 270 hours. Frozen sand cores taken from five locations 0.65 m to 0.7 m away from the central freeze pipe indicate the ground around the freeze pipe was frozen between depths of 1.8 m and 3.8 m below the ground surface at all but one location. A total length of core equal to 8 m with no indication of frost heave was retrieved from the site. Results of the ground freezing system including ground temperature measurements, growth of the frozen zone, and the amount of liquid nitrogen consumed are presented and compared with predicted values. Temperatures recorded during ground freezing indicate that the rate of freezing at CREC was influenced by the direction of groundwater flow, flow rate of liquid nitrogen, and the location and type of liquid nitrogen inlet. The frozen zone estimated with temperature measurements was shown to be tapered with the largest growth at the same elevation as the liquid nitrogen inlet. The frozen zone also appeared to extend in the direction of groundwater flow and contract in the upstream direction. To reduce the time required to freeze the soil surrounding the freeze pipe, the flow rate of liquid nitrogen was increased. While temperatures decreased as predicted when the liquid nitrogen flow rate was high, the volume of liquid nitrogen consumed was much higher than predicted. Frozen samples obtained from the CREC site were transported to Clemson University and the University of South Carolina following ground freezing. The samples will be used in high quality static and cyclic triaxial tests

Pseudo-differential operators with nonlinear quantizing functions

In this paper we develop the calculus of pseudo-differential operators corresponding to the quantizations of the form Au(x) = Rn Rn ei(x- y)center dot.s( x + t(y - x),.)u(y) dy d., where t : Rn. Rn is a general function. In particular, for the linear choices t(x) = 0, t(x) = x and t(x) = x/2 this covers the well-known Kohn-Nirenberg, anti-Kohn-Nirenberg and Weyl quantizations, respectively. Quantizations of such type appear naturally in the analysis on nilpotent Lie groups for polynomial functions t and here we investigate the corresponding calculus in the model case of Rn. We also give examples of nonlinear t appearing on the polarized and non-polarized Heisenberg groups

Modeling the Static and Dynamic Properties of Uncemented, Natural Sands

Research to quantify the the influence of aging processes (or diagenesis) on the static peak shear strength, the dilatancy, and the small strain dynamic stiffness of uncemented predominatly quartz sands is presented in this dissertation. New equations are proposed to model the dilatancy and the static shear strength due to diagenesis in natural sands as functions of either age or measured to estimated velocity ratio (MEVR). New predictive relationships between small strain dynamic stiffness and age are also recommended based on laboratory and field test results in natural sands. A laboratory investigation was performed to quantify the influence of age (or diagenesis) on the peak shear strength and the dilatancy of an uncemented Pleistocene age sand deposit at the Coastal Research and Education Center (CREC) near Charleston, South Carolina. Drained triaxial compression tests were performed on high quality intact specimens retrieved using the in situ freezing and frozen core sampling method, and on remolded specimens prepared to match the densities of the intact specimens. The stress-strain behavior of intact specimens was accompanied by dilation and a maximum or peak shear value, whereas remolded specimens generally contracted throughout shearing. The peak friction angle of intact specimens was found to be 3.0-8.6° higher than the peak friction angle of remolded specimens. A diagenesis-dilatancy term was added to the dilatancy index equation proposed by Bolton (1986) to account for the difference between intact and remolded peak friction angle. The resulting equation suggests that dilatancy caused by diagenesis and by density are both suppressed with increasing confining pressure, which has important implications for the design strength of natural deposits under heavy surcharge loads. A profile of in situ peak friction angle with depth is established from the test results and compared with values estimated from empirical relationships. The diagenesis-dilatancy term was generalized as a function of age based on a dataset of triaxial compression test results for ten different uncemented, predominantly quartz sands. Stong evidence was shown that dilatancy due to diagenesis increases with age, and that a model including age and confining pressure terms significantly improved predictions over a model with no age term. Therefore an age-dilatancy model was proposed. It was also shown that other properties such as density have little influence on dilatancy due to age. Because age of natural deposits is often difficult to accurately determine, a MEVR-dilatancy model was also proposed based on the framework of the age-dilatancy model. The age-dilatancy and MEVR-dilatancy equations were recommened to estimate intact peak friction angle from remolded peak friction angle or for predicting loss of strength during a disturbance or under large surcharges provided reliable in situ peak fricting angle estimates are available. General models for estimating peak strength are implied by the age dilatancy and MEVR dilatancy equations and can be used once the model is validated with the data presented in this study and the data compiled by Bolton (1986). Relationships for predicting the change in small strain shear modulus max() G or shear wave velocity () SV with time are reviewed. The max G -time relationship proposed by Afifi and Richart (1973) and the MEVR-time relationship proposed by Andrus et al. iv (2009) are related using a term called velocity ratio VR, which is the ratio of SV at a given time relative to its value in a deposit of similar density at a selected reference age. VR datasets were established from laboratory tests conducted on remolded sands and from laboratory tests conducted on intact sands. The VR datasets were combined to propose a VR-time relationship intended for natural sands. The proposed VR-time relationship based on laboratory results was compared with the VR-time relationship based on in situ VS and penetration resistance measurements implied by MEVR. The laboratory based relationship suggested a 3% change in VR for each ten fold change in age, while the field test based relationship suggested a 8% change with each ten fold change in age. It is found that much of the difference in the slope of the laboratory and field based VR-time relationships can be explained by the difference in fines content of the VR laboratory cases and VR field cases, which provides strong evidence for an influence of fines content on diagenesis. Much closer agreement between the VR-time relationships of field and laboratory cases with clean sands only is observed. The results indicate that field and laboratory based VR-time relationships can be used as indices for degree of diagenesis, provided the influence of fines content is accounted for. The preliminary results of a numerical study to predict the response of a Pleistocene age natural sand deposit at the CREC site during an in situ liquefaction experiment involving one of the NEES@UTexas mobile field shakers are presented. A plasticity model intended for earthquake engineering applications, was used for the Pleistocene sand deposit. Calibration of the model required considerably adjusting one of three main model inputs, called the contraction rate parameter, using the procedure recommended by Boulanger and Ziotopoulou (2015) due to the relatively low density and high predicted cyclic strength of the CREC sand. The simulation predicted concentrations of cyclic shear strain, cyclic stress ratio, and excess pore pressure that were located near the corners of the mobile shaker base plate during loading, and tended to produce a biased accumulation of shear strain toward either side of the sensor area. Below the base plate and within the zone where liquefaction sensor were installed at CREC, the excess pores pressure ratio was predicted to reach a maximum value of 12% and 18% at respective depths of 2.7 m and 3.3 m in the Pleistocene deposit. The prediction of low excess pore pressure buildup agrees with the limited field observations that were available to the author at the writing of this dissertation

Validating Accelerometry and Skinfold Measures in Youth with Down Syndrome.

Current methods for measuring quantity and intensity of physical activity based on accelerometer output have been studied and validated in youth. These methods have been applied to youth with Down syndrome (DS) with no empirical research done to validate these measures. Similarly, individuals with DS have unique body proportions not represented by current methods used to estimate body composition. The purpose of this dissertation was (a) to examine the physical activity patterns in a large sample of youth with DS, (b) to examine the validity of the Actical accelerometer for measuring physical activity and (c) to investigate the accuracy of three published skinfold and anthropometric equations (Lohman, 1987; Slaughter et al., 1988; Kelly & Rimmer, 1987) used to estimate body composition in a sample of youth with DS. A total of 53 participants (27 with DS [15 males], 26 without DS [17 males]), between the ages of 8 and18 years were included in the present study. The Actical accelerometer was validated using a graded treadmill protocol. During the protocol participants wore a portable metabolic system. Heart rate, expired gases, and data counts from the Actical were collected, analyzed, and compared against current thresholds used for determining physical activity intensity. Anthropometric and skinfold measures were compared to results from a criterion measure (Bod Pod ®). Results of this study indicate (a) youth with DS engage in disproportional amounts of sedentary activity and spend very little time in moderate-to-vigorous activity, (b) the Actical ® accelerometer is a valid device for objectively measuring physical activity. However, current cut-points associated with physical activity intensities are likely to underestimate physical activity in youth with DS, and (c) Kelly and Rimmer’s (1987) anthropometric equation demonstrated the most accuracy when compared to the criterion measure. When measuring physical activity and body composition in this sample of youth with DS, considering the unique characteristics of individuals with DS improved measurement accuracy. Based on these results, future research should be directed toward developing population specific methods of measuring and interpreting physical activity and body composition data in a practical way.Ph.D.KinesiologyUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91414/1/philespo_1.pd