Spatial Compactification and Decay-Rate Behavior

The pahse transition from instanton-dominated quantum tunneling regime to sphaleron-dominated classical crossover regime is explored in (1+1)-dimensional scalar field theory when spatial coordinate is compactified. It is shown that the type of sphaleron transition is critically dependent on the circumference of the spatial coordinate.Comment: 12 pages, 6 postscript figures included, accepted version in PL

Winding Number Transitions in the Mottola-Wipf Model on a Circle

Winding number transitions from quantum to classical behavior are studied in the case of the {1+1} dimensional Mottola-Wipf model with the space coordinate on a circle for exploring the possibility of obtaining transitions of second order. The model is also studied as a prototype theory which demonstrates the procedure of such investigations. In the model at hand we find that even on a circle the transitions remain those of first order.Comment: 17pages + 5 ps figures, final version to appear in Nucl. Phys.

Nucleation at finite temperature beyond the superminispace model

The transition from the quantum to the classical regime of the nucleation of the closed Robertson-Walker Universe with spacially homogeneous matter fields is investigated with a perturbation expansion around the sphaleron configuration. A criterion is derived for the occurrence of a first-order type transition, and the related phase diagram for scalar and vector fields is obtained. For scalar fields both the first and second order transitions can occur depending on the shape of the potential barrier. For a vector field, here that of an O(3) nonlinear $\sigma$-model, the transition is seen to be only of the first order.Comment: 15 pages, 3 figure

Hidden functional relation in Large-N Quark-Monopole system at finite temperature

The quark-monopole potential is computed at finite temperature in the context of $AdS/CFT$ correspondence. It is found that the potential is invariant under $g \to 1/g$ and $U_T \to U_T / g$. As in the quark-quark case there exists a maximum separation between quark and monopole, and $L$-dependence of the potential exhibits a bifurcation behavior. We find a functional relation $dE_{QM}^{Reg} / dL = [(1/E_{(1,0)}^{Reg}(U_0))^2 + (1/E_{(0,1)}^{Reg}(U_0))^2]^{-1/2}$ which is responsible for the bifurcation. The remarkable property of this relation is that it makes a relation between physical quantities defined at the $AdS$ boundary through a quantity defined at the bulk. The physical implication of this relation for the existence of the extra dimension is speculated.Comment: 22 pages, 3 figures, v1 one more reference added v2 version to appear in NP

Fermi Edge Singularities and Backscattering in a Weakly Interacting 1D Electron Gas

The photon-absorption edge in a weakly interacting one-dimensional electron gas is studied, treating backscattering of conduction electrons from the core hole exactly. Close to threshold, there is a power-law singularity in the absorption, $I(\epsilon) \propto \epsilon^{-\alpha}$, with $\alpha = 3/8 + \delta_+/\pi - \delta_+^2/2\pi^2$ where $\delta_+$ is the forward scattering phase shift of the core hole. In contrast to previous theories, $\alpha$ is finite (and universal) in the limit of weak core hole potential. In the case of weak backscattering $U(2k_F)$, the exponent in the power-law dependence of absorption on energy crosses over to a value $\alpha = \delta_+/\pi - \delta_+^2/2\pi^2$ above an energy scale $\epsilon^* \sim [U(2k_F)]^{1/\gamma}$, where $\gamma$ is a dimensionless measure of the electron-electron interactions.Comment: 8 pages + 1 postscript figure, preprint TPI-MINN-93/40-

3D chemical characterization of frozen hydrated hydrogels using ToF-SIMS with argon cluster sputter depth profiling

Hydrogels have been used extensively in bioengineering as artificial cell culture supports. Investigation of the interrelationship between cellular response to the hydrogel and its chemistry ideally requires methods that allow characterization without labels and can map species in three dimensional to follow biomolecules adsorbed to, and absorbed into, the open structure before and during culture. Time-of-flight secondary ion mass spectrometry (ToF-SIMS) has the potential to be utilized for through thickness characterization of hydrogels. The authors have established a simple sample preparation procedure to successfully achieve analysis of frozen hydrated hydrogels using ToF-SIMS without the need for dry glove box entry equipment. They demonstrate this on a poly(2-hydroxyethyl methacrylate) (pHEMA) film where a model protein (lysozyme) is incorporated using two methods to demonstrate how protein distribution can be determined. A comparison of lysozyme incorporation is made between the situation where the protein is present in a polymer dip coating solution and where lysozyme is in an aqueous medium in which the film is incubated. It is shown that protonated water clusters H(H2O)nþ where n ¼ 5–11 that are indicative of ice are detected through the entire thickness of the pHEMA. The lysozyme distribution through the pHEMA hydrogel films can be determined using the intensity of a characteristic amino acid secondary ion fragment

MRI size assessment of cerebral microvasculature using diffusion-time-dependent stimulated-echo acquisition: A feasibility study in rodent

In this study, a stimulated-echo (STE) method was employed to robustify the cerebral vessel size estimation nearair-tissue, bone-tissue interfaces, and large vessels. The proposed solution is to replace the relaxation rate changefrom gradient-echo (GRE) with that from STE with long diffusion time after the injection of an intravascularcontrast agent, superparamagnetic iron oxide nanoparticles. The corresponding diffusion length of STE is shorterthan the length over which the unwanted macroscopicfield inhomogeneities but is still longer than the corre-lation length of thefields induced by small vessels. Therefore, the unwantedfield inhomogeneities are refocused,while preserving microscopic susceptibility contrast from cerebral vessels. The mean vessel diameter (dimen-sionless) derived from the diffusion-time-varying STE method was compared to the mean vessel diameter ob-tained by a conventional spin-echo (SE) and GRE combination based on Monte-Carlo proton diffusion simulationsand in vivo rat experiments at 7 T. The in vivo mean vessel diameter from the MRI experiments was directlycompared to available reference mouse brain vasculature obtained by a knife-edge scanning microscope (KESM),which is considered to be the gold standard. Monte-Carlo simulation revealed that SE and GRE-based MRrelaxation rate changes (??R2and??R2*, respectively) can be enhanced using single STE-based MR relaxation ratechange (??RSTE) by regulating diffusion time, especially for small vessels. The in vivo mean vessel diameter fromthe STE method demonstrated a closer agreement with that from the KESM compared to the combined SE andGRE method, especially in the olfactory bulb and cortex. This study demonstrates that STE relaxation rate changescan be used as consistent measures for assessing small cerebral microvasculature, where macroscopicfield in-homogeneity is severe and signal contamination from adjacent large vessels is significant

Conductance Fluctuations in PbTe Wide Parabolic Quantum Wells

We report on conductance fluctuations which are observed in local and non-local magnetotransport experiments. Although the Hall bar samples are of macroscopic size, the amplitude of the fluctuations from the local measurements is close to e^2/h. It is shown that the fluctuations have to be attributed to edge channel effects.Comment: postscript file including 3 figs, 3 pages, Paper presented at 3rd Int. Symposium on "New Phenomena in Mesoscopic Structures" in Maui, Hawaii 199

Control Theory Forecasts of Optimal Training Dosage to Facilitate Children’s Arithmetic Learning in a Digital Educational Application

Education can be viewed as a control theory problem in which students seek ongoing exogenous input—either through traditional classroom teaching or other alternative training resources—to minimize the discrepancies between their actual and target (reference) performance levels. Using illustrative data from n= 784 Dutch elementary school students as measured using the Math Garden, a web-based computer adaptive practice and monitoring system, we simulate and evaluate the outcomes of using off-line and finite memory linear quadratic controllers with constraints to forecast students’ optimal training durations. By integrating population standards with each student’s own latent change information, we demonstrate that adoption of the control theory-guided, person- and time-specific training dosages could yield increased training benefits at reduced costs compared to students’ actual observed training durations, and a fixed-duration training scheme. The control theory approach also outperforms a linear scheme that provides training recommendations based on observed scores under noisy and the presence of missing data. Design-related issues such as ways to determine the penalty cost of input administration and the size of the control horizon window are addressed through a series of illustrative and empirically (Math Garden) motivated simulations