Initial Slice Research Articles

Effect of starch retrogradation on texture of potato chips produced by low-pressure superheated steam drying

The effects of the degree of starch retrogradation, initial slice thickness and final moisture content on the texture of potato chips dried by low-pressure superheated steam drying (LPSSD) were investigated in this study. Potato slices of different initial thicknesses (1.5, 2.5 and 3.5 mm) were pretreated with three different methods (blanching and then freezing for 24 h, blanching and then repeated freezing/thawing either for 3 or 5 cycles) to study the effects of these pretreatment methods on the degree of starch retrogradation. The potato slices were then dried by LPSSD at 90 °C and absolute pressure of 7 kPa to three levels of final moisture content (1.5%, 2.5% and 3.5% (d.b.)) to investigate the drying kinetics and the quality of dried potato chips in terms of hardness, toughness and crispness as well as degree of crystallinity by X-ray diffraction technique. The various pretreatment methods were found to have an obvious effect on the rates of moisture reduction of the samples. Higher degrees of starch retrogradation led to an increase in the hardness and toughness of dried chips, but did not show any significant effect on the crispness of the chips. An increase in the degree of starch retrogradation led to higher degree of crystallinity of dried potato chips.

On isoperimetric surfaces in general relativity

We obtain the isoperimetric profile for the standard initial slices in the Reissner‐Nordstrom and Schwarzschild anti-de Sitter spacetimes, following recent work of Bray and Morgan on isoperimetric comparison. We then discuss these results in the context of Bray’s isoperimetric approach to the Penrose inequality.

Dirac quantization of parametrized field theory

Parametrized field theory (PFT) is free field theory on flat spacetime in a diffeomorphism invariant disguise. It describes field evolution on arbitrary (and in general, curved) foliations of the flat spacetime instead of only the usual flat foliations, by treating the ``embedding variables'' which describe the foliation as dynamical variables to be varied in the action in addition to the scalar field. A formal Dirac quantization turns the constraints of PFT into functional Schr\"odinger equations which describe evolution of quantum states from an arbitrary Cauchy slice to an infinitesimally nearby one. This formal Schr\"odinger picture-based quantization is unitarily equivalent to the standard Heisenberg picture-based Fock quantization of the free scalar field if scalar field evolution along arbitrary foliations is unitarily implemented on the Fock space. Torre and Varadarajan (TV) showed that for generic foliations emanating from a flat initial slice in spacetimes of dimension greater than 2, evolution is not unitarily implemented, thus implying an obstruction to Dirac quantization. We construct a Dirac quantization of PFT, unitarily equivalent to the standard Fock quantization, using techniques from loop quantum gravity (LQG) which are powerful enough to supercede the no-go implications of the TV results. The key features of our quantization include an LQG type representation for the embedding variables, embedding-dependent Fock spaces for the scalar field, an anomaly free representation of (a generalization of) the finite transformations generated by the constraints, and group averaging techniques. The difference between the $1+1$-dimensional case and the case of higher spacetime dimensions is that for the latter, only finite gauge transformations are defined in quantum theory, not the infinitesimal ones.

Spherically symmetric gravitational collapse of general fluids

We express Einstein's field equations for a spherically symmetric ball of general fluid such that they are conducive to an initial value problem. We show how the equations reduce to the Vaidya spacetime in a non-null coordinate frame, simply by designating specific equations of state. Furthermore, this reduces to the Schwarzschild spacetime when all matter variables vanish. We then describe the formulation of an initial value problem, whereby a general fluid ball with vacuum exterior is established on an initial spacelike slice. As the system evolves, the fluid ball collapses and emanates null radiation such that a region of Vaidya spacetime develops. Therefore, on any subsequent spacelike slice there exists three regions; general fluid, Vaidya and Schwarzschild, all expressed in a single coordinate patch with two free-boundaries determined by the equations. This implies complicated matching schemes are not required at the interfaces between the regions, instead, one simply requires the matter variables tend to the appropriate equations of state. We also show the reduction of the system of equations to the static cases, and show staticity necessarily implies zero 'heat flux.' Furthermore, the static equations include a generalization of the Tolman-Oppenheimer-Volkoff equations for hydrostatic equilibrium to include anisotropic stresses inmore » general coordinates.« less

Functional evolution of quantum cylindrical waves

Kuchař showed that the quantum dynamics of (one polarization) cylindrical wave solutions to vacuum general relativity is determined by those of a free axially symmetric scalar field along arbitrary axially symmetric foliations of a fixed flat (2 + 1)-dimensional spacetime. We investigate if such a dynamics can be defined unitarily within the standard Fock space quantization of the scalar field. Evolution between two arbitrary slices of an arbitrary foliation of the flat spacetime can be built out of a restricted class of evolutions (and their inverses). The restricted evolution is from an initial flat slice to an arbitrary (in general, curved) slice of the flat spacetime and can be decomposed into (i) ‘time’ evolution in which the spatial Minkowskian coordinates serve as spatial coordinates on the initial and the final slice, followed by (ii) the action of a spatial diffeomorphism of the final slice on the data obtained from (i). We show that although the functional evolution of (i) is unitarily implemented in the quantum theory, generic spatial diffeomorphisms of (ii) are not. Our results imply that a Tomanaga–Schwinger type functional evolution of quantum cylindrical waves is not a viable concept even though, remarkably, the more limited notion of functional evolution in Kuchař's ‘half-parametrized formalism’ is well defined.

Segmentation method for three-dimensional visualization of microscopic objects imaged with a confocal laser scanning microscope

This paper is a revision of a paper presented at the SPIE conference on Medical Imaging 2005: Physiology, Function, and Structure from Medical Images, Feb. 2005, San Diego, California. The paper presented there appears (unrefereed) in SPIE Proceedings Vol. 5746. Segmentation, or separating an image into distinct objects, is the key to creating 3-D renderings from serial slice images. This is typically a manual process requiring trained persons to tediously outline and isolate the objects in each image. We describe a template-based semiautomatic segmentation method to aid in the segmentation process and 3-D reconstruction of microscopic objects recorded with a confocal laser scanning microscope (CLSM). The simple and robust algorithm is based on the creation of a user-defined object template, followed by automatic segmentation of the object in each of the remaining image slices. The user guides the process by selecting the initial image slice for the object template, and labeling the object of interest. The algorithm is applied to mathematically defined shapes to verify the performance of the software. The algorithm is then applied to biological samples, including neurons in the common housefly. It is the quest to further understand the visual system of the housefly that provides the opportunity to develop this segmentation algorithm. Further application of this algorithm may extend to other registered and aligned serial section datasets with high contrast objects.

Semantic Category Fluency Versus Initial Letter Fluency Over 60 Seconds as a Measure of Automatic and Controlled Processing in Healthy School-aged Children

Verbal fluency was operationalized as the number of words produced in a restricted category (i.e., semantic category [SCF] and words beginning with a given letter [ILF]) in 60 seconds. Word production in the first 15 seconds of either type of fluency task was defined as a measure of automatic information processing, whereas word production in the remaining 45 seconds (in 15-second periods) was taken as a measure of controlled information processing. Data revealed that over 60 seconds healthy children aged 8.4–9.7 years (n = 91) produced significantly more words and less incorrect responses on the SCF task than on the ILF task. Although word production was a function of both type of task and time, it was highest in the initial time slice of either type of fluency and decreased as time on task increased. Finally, no sex differences were found for any measure of performance on either type of fluency task. In contrast, the level of occupational achievement of the caregiver (LOA) appeared to be a determinant of the child’s performance on either type of fluency task, indicating that LOA affects higher-order processes, such as the automation of newly learned verbal skills and effortful processing.

Functional evolution of quantum cylindrical waves

Kuchar showed that the quantum dynamics of (1 polarization) cylindrical wave solutions to vacuum general relativity is determined by that of a free axially symmetric scalar field along arbitrary axially symmetric foliations of a fixed flat 2 + 1 dimensional spacetime. We investigate if such a dynamics can be defined unitarily within the standard Fock space quantization of the scalar field. Classical scalar field evolution from an initial flat slice to an arbitrary (in general, curved) slice of the flat spacetime can be decomposed into (i) ‘time’ evolution in which the spatial Minkowskian coordinates of the initial slice serve as spatial coordinates of the final slice, followed by (ii) the action of a spatial Diffeomorphism of the final slice on the data obtained from (i). We show that although the functional evolution of (i) is unitarily implemented in the quantum theory, generic spatial Diffeomorphisms of (ii) are not. Our results imply that a Tomanaga-Schwinger type functional evolution of quantum cylindrical waves is not a viable concept even though, remarkably, the more limited notion of functional evolution in Kuchar's ‘half parametrized formalism’ is well-defined.

Can superhorizon cosmological perturbations explain the acceleration of the universe?

We investigate the recent suggestions by Barausse et al. and Kolb et al. that the acceleration of the universe could be explained by large superhorizon fluctuations generated by inflation. We show that acceleration can be produced by this mechanism. We begin by showing how the application of Raychaudhuri equation to inhomogeneous cosmologies results in several no go theorems for accelerated expansion. Next we derive an exact solution for a specific case of initial perturbations, for which application of the Kolb et al. expressions leads to an acceleration, while the exact solution reveals that acceleration is present. We show that the discrepancy can be traced to higher-order terms that were dropped in the Kolb et al. analysis. We proceed with the analysis of initial value formulation of general relativity to argue that causality severely limits what observable effects can be derived from superhorizon perturbations. By constructing a Riemann normal coordinate system on initial slice we show that infrared divergence terms arise in this coordinate system. Thus any divergences found previously can be eliminated by a local rescaling of coordinates and are unobservable. We perform an explicit analysis of the variance of the deceleration parameter for the case of single-field inflation using usual coordinates and show that the infrared-divergent terms found by Barausse et al. and Kolb et al. cancel against several additional terms not considered in their analysis. Finally, we argue that introducing isocurvature perturbations does not alter our conclusion that the accelerating expansion of the universe cannot be explained by superhorizon modes.

TU‐EE‐A4‐06: Accuracy and Precision of Implantable Radiofrequency Transponder Localization Measurements Conducted Using Multislice CT

Purpose: Accurate localization and monitoring of prostate position during radiation therapy is critical for the precise and safe delivery of dose‐escalated treatments, but is challenging due to substantial internal‐organ motion. A novel method for tracking prostate position using implantable radiofrequency markers has been developed by Calypso® Medical. An important consideration for these transponders is localization accuracy using computed‐tomography (CT) imaging. We evaluated the accuracy and precision of transponder localization using multislice CT scanning. Method and Materials: A tissue‐equivalent pelvis phantom with three implanted transponders and external alignment markers was used. The relative transponder positional accuracy was 0.1mm, while the positional accuracy of the transponders relative to the phantom surface was 0.5mm. The phantom was placed on a computer‐controlled linear stage and multiple scans were acquired using a Philips Brilliance 16‐slice CT scanner, varying the detector size, slice thickness, and pitch. Scans were repeated with the phantom moved 0.5mm longitudinally between scan acquisitions to assess position‐measurement accuracy at different locations within a reconstructed CT slice thickness. The transponders were identified and localized on the reconstructed CT images automatically using in‐house image processing software. Results: The mean error of the transponder localization was less than 0.4 mm in anterior‐posterior and lateral‐medial directions, and increased to 0.8mm in longitudinal direction primarily due to the uncertainty introduced in the initial slice identification. The predicted longitudinal shift between each consecutive scan followed the actual shift amount accurately with a mean error of 0.014mm and a standard deviation of 0.08mm. Conclusion: Our investigations have demonstrated the high accuracy of the transponder localization using a multislice CT scanner. The initial results indicate that the accuracy of such a system is sufficient for prostate localization and position monitoring in clinics. Conflict of Interest: This work is supported in part by Calypso® Medical.

On isotropic cylindrically symmetric stellar models

We attempt to match the most general cylindrically symmetric vacuum spacetime with a Robertson–Walker interior. The matching conditions show that the interior must be dust filled and that the boundary must be comoving. Further, we show that the vacuum region must be polarized. Imposing the condition that there are no trapped cylinders on an initial time slice, we can apply a result of Thorne's and show that trapped cylinders never evolve. This results in a simplified line element which we prove to be incompatible with the dust interior. This result demonstrates the impossibility of the existence of an isotropic cylindrically symmetric star (or even a star which has a cylindrically symmetric portion). We investigate the problem from a different perspective by looking at the expansion scalars of invariant null geodesic congruences and, applying to the cylindrical case, the result that the product of the signs of the expansion scalars must be continuous across the boundary. The result may also be understood in relation to recent results about the impossibility of the static axially symmetric analogue of the Einstein–Straus model.

Evolutions in 3D numerical relativity using fixed mesh refinement

We present results of 3D numerical simulations using a finite difference code featuring fixed mesh refinement (FMR), in which a subset of the computational domain is refined in space and time. We apply this code to a series of test cases including a robust stability test, a nonlinear gauge wave and an excised Schwarzschild black hole in an evolving gauge. We find that the mesh refinement results are comparable in accuracy, stability and convergence to unigrid simulations with the same effective resolution. At the same time, the use of FMR reduces the computational resources needed to obtain a given accuracy. Particular care must be taken at the interfaces between coarse and fine grids to avoid a loss of convergence at higher resolutions, and we introduce the use of ‘buffer zones’ as one resolution of this issue. We also introduce a new method for initial data generation, which enables higher order interpolation in time even from the initial time slice. This FMR system, ‘Carpet’, is a driver module in the freely available Cactus computational infrastructure, and is able to endow generic existing Cactus simulation modules (‘thorns’) with FMR with little or no extra effort.

The Taming of Closed Time-like Curves

We consider a $R^{1,d}/Z_2$ orbifold, where $Z_2$ acts by time and space reversal, also known as the embedding space of the elliptic de Sitter space. The background has two potentially dangerous problems: time-nonorientability and the existence of closed time-like curves. We first show that closed causal curves disappear after a proper definition of the time function. We then consider the one-loop vacuum expectation value of the stress tensor. A naive QFT analysis yields a divergent result. We then analyze the stress tensor in bosonic string theory, and find the same result as if the target space would be just the Minkowski space $R^{1,d}$, suggesting a zero result for the superstring. This leads us to propose a proper reformulation of QFT, and recalculate the stress tensor. We find almost the same result as in Minkowski space, except for a potential divergence at the initial time slice of the orbifold, analogous to a spacelike Big Bang singularity. Finally, we argue that it is possible to define local S-matrices, even if the spacetime is globally time-nonorientable.

The turbulence effect of the airflow on the calorific losses in foodstuff dryers

The calorific losses through the sidewalls delay drying, particularly in the higher racks of the foodstuff dryers, which provide us information on total drying time. One notes a temperature gradient of the air during its circulation upwards, between the entry and the exit of the empty dryer. This gradient is more significant with the decrease of the air velocity. The heat transfer coefficient by forced convection between the air and the interior walls is often determined by using the average Nusselt number defined in flow of boundary layer on plane plate (laminar regime). In addition, the presence of the grills, on which slices of product are spread, causes turbulence which is not taken into account by this coefficient of Nusselt number. In this paper, we determine the heat transfer coefficient between the air and the sidewalls of a dryer experimentally. The latter contains grills on which thin layer slices of a dry material (wood) of the same geometry as the initial potato slices are spread. This leads us to determine an expression of the Nusselt number of the form Nu= aRe b Pr 1/3, without mass transfer. Thereafter, this correlation of the Nusselt number is introduced into the mathematical model, already suggested in our former work, which predicts the performances, in forced convection, of the foodstuff dryers. In the end, the influence of these losses is presented by means of a comparative study between various models, those that take into account and those that ignore these losses between two beds of slices. The results thus obtained are compared with the experiment in an application on potato drying.

Geometrical optics analysis of the short-time stability properties of the Einstein evolution equations

Many alternative formulations of Einstein's evolution have lately been examined in an effort to discover one that yields slow growth of constraint-violating errors. In this paper, rather than directly search for well-behaved formulations, we instead develop analytic tools to discover which formulations are particularly ill behaved. Specifically, we examine the growth of approximate (geometric-optics) solutions, studied only in the future domain of dependence of the initial data slice (e.g., we study transients). By evaluating the amplification of transients a given formulation will produce, we may therefore eliminate from consideration the most pathological formulations (e.g., those with numerically unacceptable amplification). This technique has the potential to provide surprisingly tight constraints on the set of formulations one can safely apply. To illustrate the application of these techniques to practical examples, we apply our technique to the 2-parameter family of evolution equations proposed by Kidder, Scheel, and Teukolsky, focusing in particular on flat space (in Rindler coordinates) and Schwarzschild background (in Painlev\'e-Gullstrand coordinates).

Physics and initial data for multiple black hole spacetimes

An orbiting black hole binary will generate strong gravitational radiation signatures, making these binaries important candidates for detection in gravitational wave observatories. The gravitational radiation is characterized by the orbital parameters, including the frequency and separation at the inner-most stable circular orbit (ISCO). One approach to estimating these parameters relies on a sequence of initial data slices that attempt to capture the physics of the inspiral. Using calculations of the binding energy, several authors have estimated the ISCO parameters using initial data constructed with various algorithms. In this paper we examine this problem using conformally Kerr-Schild initial data. We present convergence results for our initial data solutions, and give data from numerical solutions of the constraint equations representing a range of physical configurations. In a first attempt to understand the physical content of the initial data, we find that the Newtonian binding energy is contained in the superposed Kerr-Schild background before the constraints are solved. We examine some deficiencies with the initial data approach to orbiting binaries, especially touching on the effects of prior motion and spin-orbital coupling of the angular momenta. Making rough estimates of these effects, we find that they are not insignificant compared to the binding energy, leaving some doubt of the utility of using initial data to predict ISCO parameters. In computations of specific initial-data configurations we find spin-specific effects that are consistent with analytical estimates.

Well Posed Constraint-Preserving Boundary Conditions for the Linearized Einstein Equations

In this paper we address the problem of specifying boundary conditions for Einstein's equations when linearized around Minkowski space using the generalized Einstein-Christoffel symmetric hyperbolic system of evolution equations. The boundary conditions we work out guarantee that the constraints are satisfied provided they are satisfied on the initial slice and ensures a well posed initial-boundary value formulation. We consider the case of a manifold with a non-smooth boundary, as is the usual case of the cubic boxes commonly used in numerical relativity. The techniques discussed should be applicable to more general cases, as linearizations around more complicated backgrounds, and may be used to establish well posedness in the full non-linear case.

Kerr–Schild-type initial data for black holes with angular momenta

Generalizing previous work we propose how to superpose spinning black holes in a Kerr–Schild initial slice. This superposition satisfies several physically meaningful limits, including the close and the far ones. Further, we consider the close limit of two black holes with opposite angular momenta and explicitly solve the constraint equations in this case. Evolving the resulting initial data with a linear code, we compute the radiated energy as a function of the masses and the angular momenta of the black holes.

Effect of 60Co irradiation on drying characteristics of apple

Few studies on the irradiation effects on dehydration characteristics and quality of dried-product ha ve been reported in the past three decades. This study focuses on drying characteristics of bio-products by hot-air after they are pretreated by gamma irradiation. Experiments were made to study the influence of different irradiation dose, air temperature, slice thickness of apple on the dehydration rate, and appearance quality ( L-values), vitamin C content, and the rehydration ratio of dried apple. A conclusion is reached that the three factors of irradiation dose, hot-air temperature, and initial slice thickness significantly affected the four indices of appearance quality ( L-values), vitamin C content, dehydration rate and rehydration ratio.

New approach to the evolution of neutron star oscillations

We present a new derivation of the perturbation equations governing the oscillations of relativistic non-rotating neutron star models using the ADM-formalism. This formulation has the advantage that it immediately yields the evolution equations in a hyperbolic form, which is not the case for the Einstein field equations in their original form. We show that the perturbation equations can always be written in terms of spacetime variables only, regardless of any particular gauge. We demonstrate how to obtain the Regge-Wheeler gauge, by choosing appropriate lapse and shift. In addition, not only the 3-metric but also the extrinsic curvature of the initial slice have to satisfy certain conditions in order to preserve the Regge-Wheeler gauge throughout the evolution. We discuss various forms of the equations and show their relation to the formulation of Allen et al. New results are presented for polytropic equations of state. An interesting phenomenon occurs in very compact stars, where the first ring-down phase in the wave signal corresponds to the first quasinormal mode of an equal mass black hole, rather than to one of the proper quasinormal modes of the stellar model. A somewhat heuristic explanation to account for this phenomenon is given. For realistic equations of state, the numerical evolutions exhibit an instability, which does not occur for polytropic equations of state. We show that this instability is related to the behavior of the sound speed at the neutron drip point. As a remedy, we devise a transformation of the radial coordinate $r$ inside the star, which removes this instability and yields stable evolutions for any chosen numerical resolution.