Lie symmetries for two-dimensional charged particle motion

We find the Lie point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries comprise a quasi-invariance transformation, a time-dependent rotation, a time-dependent spatial translation and a dilation. The associated electromagnetic fields satisfy a system of first-order linear partial differential equations. This system is solved exactly, yielding four classes of electromagnetic fields compatible with Lie point symmetries

Symmetry, singularities and integrability in complex dynamics III: approximate symmetries and invariants

The different natures of approximate symmetries and their corresponding first integrals/invariants are delineated in the contexts of both Lie symmetries of ordinary differential equations and Noether symmetries of the Action Integral. Particular note is taken of the effect of taking higher orders of the perturbation parameter. Approximate symmetries of approximate first integrals/invariants and the problems of calculating them using the Lie method are considered

Development of standardized air-blown coal gasifier/gas turbine concepts for future electric power systems

Computer models have been developed for evaluating conceptual designs of integrated coal gasification combined cycle power plants. An overall system model was developed for performing thermodynamic cycle analyses, and detailed models were developed for predicting performance characteristics of fixed bed coal gasifiers and hot gas clean up subsystem components. The overall system model performs mass and energy balances and does chemical equilibrium analyses to determine the effects of changes in operating conditions, or to evaluate proposed design changes. An existing plug flow model for fixed bed gasifiers known as the Wen II model was revised and updated. Also, a spread sheet model of zinc ferrite sulfur sorbent regeneration subsystem was developed. Parametric analyses were performed to determine how performance depends on variables in the system design. The work was done to support CRS Sirrine Incorporated in their study of standardized air blown coal gasifier gas turbine concepts

Addendum to "Superimposed Oscillations in the WMAP Data?"

We elaborate further on the possibility that the inflationary primordial power spectrum contains superimposed oscillations. We study various effects which could influence the calculation of the multipole moments in this case. We also present the theoretical predictions for two other cosmological observables, the matter power spectrum and the EE polarization channel.Comment: 4 pages, 3 figures, uses RevTex4, matches published versio

Unitary relations in time-dependent harmonic oscillators

For a harmonic oscillator with time-dependent (positive) mass and frequency, an unitary operator is shown to transform the quantum states of the system to those of a harmonic oscillator system of unit mass and time-dependent frequency, as well as operators. For a driven harmonic oscillator, it is also shown that, there are unitary transformations which give the driven system from the system of same mass and frequency without driving force. The transformation for a driven oscillator depends on the solution of classical equation of motion of the driven system. These transformations, thus, give a simple way of finding exact wave functions of a driven harmonic oscillator system, provided the quantum states of the corresponding system of unit mass are given.Comment: Submitted to J. Phys.

Biomass for thermochemical conversion: targets and challenges

Includes bibliographical references (pages 13-20).Bioenergy will be one component of a suite of alternatives to fossil fuels. Effective conversion of biomass to energy will require the careful pairing of advanced conversion technologies with biomass feedstocks optimized for the purpose. Lignocellulosic biomass can be converted to useful energy products via two distinct pathways: enzymatic or thermochemical conversion. The thermochemical pathways are reviewed and potential biotechnology or breeding targets to improve feedstocks for pyrolysis, gasification, and combustion are identified. Biomass traits influencing the effectiveness of the thermochemical process (cell wall composition, mineral and moisture content) differ from those important for enzymatic conversion and so properties are discussed in the language of biologists (biochemical analysis) as well as that of engineers (proximate and ultimate analysis). We discuss the genetic control, potential environmental influence, and consequences of modification of these traits. Improving feedstocks for thermochemical conversion can be accomplished by the optimization of lignin levels, and the reduction of ash and moisture content. We suggest that ultimate analysis and associated properties such as H:C, O:C, and heating value might be more amenable than traditional biochemical analysis to the high-throughput necessary for the phenotyping of large plant populations. Expanding our knowledge of these biomass traits will play a critical role in the utilization of biomass for energy production globally, and add to our understanding of how plants tailor their composition with their environment.Published with support from the Colorado State University Libraries Open Access Research and Scholarship Fund

An integrating factor matrix method to find first integrals

In this paper we developed an integrating factor matrix method to derive conditions for the existence of first integrals. We use this novel method to obtain first integrals, along with the conditions for their existence, for two and three dimensional Lotka-Volterra systems with constant terms. The results are compared to previous results obtained by other methods

Casimir Forces between Spherical Particles in a Critical Fluid and Conformal Invariance

Mesoscopic particles immersed in a critical fluid experience long-range Casimir forces due to critical fluctuations. Using field theoretical methods, we investigate the Casimir interaction between two spherical particles and between a single particle and a planar boundary of the fluid. We exploit the conformal symmetry at the critical point to map both cases onto a highly symmetric geometry where the fluid is bounded by two concentric spheres with radii R_- and R_+. In this geometry the singular part of the free energy F only depends upon the ratio R_-/R_+, and the stress tensor, which we use to calculate F, has a particularly simple form. Different boundary conditions (surface universality classes) are considered, which either break or preserve the order-parameter symmetry. We also consider profiles of thermodynamic densities in the presence of two spheres. Explicit results are presented for an ordinary critical point to leading order in epsilon=4-d and, in the case of preserved symmetry, for the Gaussian model in arbitrary spatial dimension d. Fundamental short-distance properties, such as profile behavior near a surface or the behavior if a sphere has a `small' radius, are discussed and verified. The relevance for colloidal solutions is pointed out.Comment: 37 pages, 2 postscript figures, REVTEX 3.0, published in Phys. Rev. B 51, 13717 (1995

Boolean analysis identifies CD38 as a biomarker of aggressive localized prostate cancer.

The introduction of serum Prostate Specific Antigen (PSA) testing nearly 30 years ago has been associated with a significant shift towards localized disease and decreased deaths due to prostate cancer. Recognition that PSA testing has caused over diagnosis and over treatment of prostate cancer has generated considerable controversy over its value, and has spurred efforts to identify prognostic biomarkers to distinguish patients who need treatment from those that can be observed. Recent studies show that cancer is heterogeneous and forms a hierarchy of tumor cell populations. We developed a method of identifying prostate cancer differentiation states related to androgen signaling using Boolean logic. Using gene expression data, we identified two markers, CD38 and ARG2, that group prostate cancer into three differentiation states. Cancers with CD38-, ARG2- expression patterns, corresponding to an undifferentiated state, had significantly lower 10-year recurrence-free survival compared to the most differentiated group (CD38+ARG2+). We carried out immunohistochemical (IHC) staining for these two markers in a single institution (Stanford; n = 234) and multi-institution (Canary; n = 1326) cohorts. IHC staining for CD38 and ARG2 in the Stanford cohort demonstrated that combined expression of CD38 and ARG2 was prognostic. In the Canary cohort, low CD38 protein expression by IHC was significantly associated with recurrence-free survival (RFS), seminal vesicle invasion (SVI), extra-capsular extension (ECE) in univariable analysis. In multivariable analysis, ARG2 and CD38 IHC staining results were not independently associated with RFS, overall survival, or disease-specific survival after adjusting for other factors including SVI, ECE, Gleason score, pre-operative PSA, and surgical margins