Non-critical Regions Research Articles

Off-diagonal Geometric Phase of Two-Qubit System

This paper focuses on the off-diagonal geometric phase of the thermal state of a two-qubit system under the external magnetic field. The properties of geometric phases of the state in critical and non-critical regions are discussed respectively. The sudden change of structure of degeneracy at the critical point do not affect the geometric phase of the model. Increasing temperature tends to suppress the off-diagonal geometric phase. The relationship between the geometric phase and external magnetic field is also discussed.

Finite-temperature entanglement for low-dimensional quantum spin chains

Based on transfer-matrix density matrix renormalization group (TMRG) method, a general procedure to calculate the finite-temperature pairwise entanglement of low-dimensional quantum chains is proposed. The reduced pairwise density matrix is reconstructed with TMRG, and measures of quantum entanglement can be calculated from the pairwise density matrix. The finite-temperature entanglement of the diamond chain model and the spin trimerized model, which are two typical models revealing $1∕3$ plateaus in the magnetization curves, is calculated. For the diamond chain model, the anisotropy coefficient $\ensuremath{\Delta}$ is found to have a great effect on the appearance of the magnetization plateau, and the plateau disappears when $\ensuremath{\Delta}=0.5$. Moreover, our results show that the pairwise entanglement can provide information complementary to that obtained from bulk properties. For the trimerized model, the temperature dependence of the pairwise entanglement is calculated, and the threshold temperature ${T}_{c}$, above which the thermal entanglement vanishes, is found to be independent of the external magnetic field $B$. In addition, the scaling behavior of the thermal entanglement is calculated in the Trotter space. With the augmentation of the system in the Trotter direction, we find that the low-temperature entanglement shows obvious variation in the vicinity of quantum phase transition (QPT) point ${B}_{c}$ and converges fast in noncritical regions, which provides another way to identify QPT of one-dimensional quantum systems.

Block-block entanglement and quantum phase transitions in the one-dimensional extended Hubbard model

In this paper, we study block-block entanglement in the ground state of a one-dimensional extended Hubbard model. Our results show that the phase diagram derived from the block-block entanglement manifests a richer structure than that of the local (single-site) entanglement because it comprises nonlocal correlation. Besides phases characterized by the charge-density wave, the spin-density wave, and phase separation, which can be sketched out by the local entanglement, singlet superconductivity phase could be identified on the contour map of the block-block entanglement if the block size is larger than 1. Scaling analysis shows that ${\mathrm{log}}_{2}(l)$ behavior of the block-block entanglement may exist in both the noncritical and critical regions, while some local extremum are induced by the finite-size effect. We also study the block-block entanglement defined in the momentum space and discuss its relation to the phase transition from singlet superconducting state to the charge-density-wave state.

Self-paced reading and sentence comprehension in Parkinson's disease

Parkinson's disease (PD) is associated with disturbances in sentence processing, particularly for noncanonical sentences. The present study aimed to analyse sentence processing in PD patients and healthy control participants, using a word-by-word self-paced reading task and an auditory comprehension task. Both tasks consisted of subject relative (SR) and object relative (OR) sentences, with comprehension accuracy measured for each sentence type. For the self-paced reading task, reading times (RTs) were also recorded for the non-critical and critical processing regions of each sentence. Analysis of RTs using mixed linear model statistics revealed a delayed sensitivity to the critical processing region of OR sentences in the PD group. In addition, only the PD group demonstrated significantly poorer comprehension of OR sentences compared to SR sentences during an auditory comprehension task. These results may be consistent with slower lexical retrieval in PD, and its influence on the processing of noncanonical sentences.

A Methodology for the Simultaneous Design of Supply and Signal Networks

We present an early-stage global wire-design methodology that simultaneously considers the performance needs for both signal lines and power grids under congestion considerations. An iterative procedure is employed in which the global routing is performed according to a congestion map that includes the resource utilization of the power grid, followed by a step in which the power grid is adjusted to relax the congestion in crowded regions. This adjustment is in the form of wire removal in noncritical regions, followed by a wire-sizing step that overcomes the voltage noise after wire removal and a wire-width resizing that meets the maximum current-density constraint. Experimental results show that the overall routability can be significantly improved while the power-grid noise is maintained within both the voltage-drop and current-density constraints.

Image-guided craniotomy for cerebral metastases: techniques and outcomes.

The purpose of the present study was to analyze the outcomes after craniotomies for brain metastases in a modern series using image-guided technologies either in the regular operating room or in the intraoperative magnetic resonance imaging unit. Neurosurgical outcomes were analyzed for 49 patients who underwent 55 image-guided craniotomies for excision of brain metastases during a 5-year period. Tumors were located in critical and noncritical function regions of the brain. A total of 23 craniotomies for tumors in critical brain were performed using intravenous sedation anesthesia; craniotomies for noncritical function brain regions were completed under general anesthesia. The patients were also divided into Radiation Therapy Oncology Group recursive partitioning analysis (RPA) classes on the basis of age, Karnofsky Performance Scale scores, state of primary disease, and presence or absence of extracranial metastases. There was no perioperative mortality. Gross total resection, as verified by postoperative contrast-enhanced computed tomography or magnetic resonance imaging, was achieved in 96% of patients. The median anesthesia time was 4.25 hours, and the median length of hospital stay was 3 days. In 51 symptomatic cases, there was complete resolution of symptoms in 70% (n = 36), improvement in 14% (n = 7), and no change in 12% (n = 6) postoperatively. No patient who was neurologically intact preoperatively deteriorated after surgery, and 93% of patients maintained or improved their functional status. Only two patients (3.6%) with significant preoperative deficits had increased long-term deficits postoperatively. The mean follow-up was 1 year, and the local recurrence rate was 16%. The median survival of the entire group was 16.23 months (17.5 mo in RPA Class I, 22.9 mo in RPA Class II, and 9.8 mo in RPA Class III). Gross total resection of brain metastases, including those involving critical function areas, can be safely achieved with a low morbidity rate using contemporary image-guided systems. RPA Class I and II patients with controlled primary disease benefit from aggressive treatment by surgery and radiation.

Revisiting the composite laminate problem with an adaptive multi-level computational model

The series of free-edge boundary-value problems treated by Pagano and Rybicki (Pagano NJ, Rybicki EF. On the significance of effective modulus solutions for fibrous composite. J Comp Mat 1974;8: 214–28; Rybicki EF, Pagano NJ. A study of the influence of microstructure on the modified effective modulus approach for composite laminates. Proceedings of the 1975 Int. Conf. Compos. Mater 1976;2:198–207) demonstrates the breakdown of homogenization in the region of macroscopic gradients. Their study shows the need for an appropriate level of resolution in determining reasonably accurate stresses in the region of macro gradients. Problems of this type can be readily handled by using an adaptive multi-level computational model with varying resolutions for critical and non-critical regions. The model introduces three levels, a pure macroscopic problem with homogenized coefficients modeled through a conventional displacement based FE code, macro-micro coupling through asymptotic homogenization where periodicity of microstructure is assumed, and microscopic analysis using a Voronoi cell finite-element model. The effect of increasing number of rows on the results is studied by the multiscale model and the homogenized model. Fiber/matrix interfacial stresses are also provided as these are expected to initiate the failure process in these fiber-reinforced composite laminates.

A multi-level computational model for multi-scale damage analysis in composite and porous materials

An adaptive multi-level methodology is developed in this paper to create a hierarchy of computational sub-domains with varying resolution for multiple scale problems. It is intended to concurrently predict evolution of variables at the structural and microstructural scales, as well as to track the incidence and propagation of microstructural damage in composite and porous materials. The microstructural analysis is conducted with the Voronoi cell finite element model (VCFEM), while a conventional displacement based FEM code executes the macroscopic analysis. The model introduces three levels in the computational domain which include macro, macro–micro and microscopic analysis. It differentiates between non-critical and critical regions and ranges from macroscopic computations using continuum constitutive relations to zooming in at `hotspots' for pure microscopic simulations. Coupling between the scales in regions of periodic microstructure is accomplished through asymptotic homogenization. An adaptive process significantly increases the efficiency while retaining appropriate level of accuracy for each region. Numerical examples are conducted for composite and porous materials with a variety of microscopic architectures to demonstrate the potential of the model.

Multiple scale computational model for damage in composite materials

In this paper, a hierarchical multiple scale computational model is proposed to concurrently predict evolution of variables at the structural and microstructural scales, as well as to track the incidence and propagation of microstructural damage. The microscopic analysis is conducted with the Voronoi cell finite element model (VCFEM) while a conventional displacement based FEM code executes the macroscopic analysis. Adaptive schemes and mesh refinement strategies are developed to create a hierarchy of computational sub-domains with varying resolution. Such hierarchy allow for differentiation between non-critical and critical regions, and help in increasing the efficiency of computations through preferential ‘zoom in’ regions. Coupling between the scales for regions with periodic microstructure is accomplished through asymptotic homogenization, whereas regions of nonuniformity and non-periodicity are modeled by true microstructural analysis with VCFEM. Various numerical examples are executed for validating the effectiveness of the model for different microstructural configurations.

Correlation length and the scaling parameter in the renormalization group

The basic procedure of renormalization group theory is used to split the free energy into a Kadanoff block formation part, and a renormalized block-block interaction part. The study of this redistribution as a function of the scaling parameter $s$ shows that there is a stationarity value ${s}^{*}$ of $s$, which turns out to have the same critical behavior as the correlation length. It is suggested that ${s}^{*}$ can be used as an appropriate measure and definition of the correlation length, even for noncritical regions. The calculation of ${s}^{*}$ is thereby performed explicitly for the Gaussian, and numerically for the ${S}^{4}$ model. A sharp separation between noncorrelated and correlated regimes is also found for the Gaussian model, well above the critical temperature. For the ${S}^{4}$ model, the results suggest that $\ensuremath{\xi}$ is characterized by a high-temperature Gaussian branch and by a genuine ${S}^{4}$ branch at low temperatures, connected by a ``plateau'' in the intermediate region.

Eyeblink Classical Conditioning in Alzheimer's Disease and Cerebrovascular Dementia

Eyeblink classical conditioning (EBCC) is severely and consistently impaired in probable Alzheimer's disease (AD), presumably due to normal age related changes in the cerebellum and AD-related hippocampal cholinergic disruption. Less consistent impairment and more variable EBCC performance was predicted in patients with cerebrovascular dementia (CVD) because some CVD patients should have impairment in EBCC when their lesions affect the EBCC circuitry, whereas others with lesions in noncritical regions should have normal EBCC. As predicted, variability in EBCC performance was greater in patients with CVD than in probable AD patients. Acquisition of conditioned responses in the group of CVD patients was better than in the probable AD group. These data show in another sample of normal control subjects and probable AD patients that EBCC has a high sensitivity for probable AD.

Optimal and Near‐optimal Global Register Allocation Using 0-1 Integer Programming

This paper presents a fundamentally new approach to global register allocation that optimally allocates registers and optimally places spill code, significantly decreasing spill code overhead compared with the traditional graph-coloring approach. The Optimal Register Allocation (ORA) approach formulates global register allocation as a 0–1 integer programming problem, incorporating all aspects of register allocation within a unified framework, including copy elimination, live range splitting, rematerialization, callee and caller register spilling, special instruction-operand requirements, and paired registers. A prototype ORA allocator is built into the Gnu C Compiler (GCC). For the SPEC92 integer benchmarks, the ORA allocator actually produces a net decrease of more than 100 million cycles across the entire benchmark set, because the dynamic copies the ORA allocator removes exceed the dynamic loads and stores that are inserted. In contrast, the GCC allocator and a Chaitin-style graph-coloring allocator each cause a net increase of more than 1 billion cycles. Because global register allocation is NP-complete, optimal register allocation has been considered intractable. However, the run-time complexity of the ORA approach is shown experimentally to be O(n3). A profile-guided hybrid allocation approach is proposed that uses the ORA allocator for the performance critical regions in the performance critical functions, while using a graph-coloring allocator for the non-critical functions and regions. An ORA-GCC hybrid allocator takes an average of 4.6 seconds per function to produce an allocation that is within 1% of optimal for 97% of the SPEC92 integer benchmark functions, showing that the hybrid allocator is practical as an advanced optimization for performance-critical codes.

Optimal and Near-optimal Global Register Allocation Using 0-1 Integer Programming

This paper presents a fundamentally new approach to global register allocation that optimally allocates registers and optimally places spill code, significantly decreasing spill code overhead compared with the traditional graph-coloring approach. The Optimal Register Allocation (ORA) approach formulates global register allocation as a 0–1 integer programming problem, incorporating all aspects of register allocation within a unified framework, including copy elimination, live range splitting, rematerialization, callee and caller register spilling, special instruction-operand requirements, and paired registers. A prototype ORA allocator is built into the Gnu C Compiler (GCC). For the SPEC92 integer benchmarks, the ORA allocator actually produces a net decrease of more than 100 million cycles across the entire benchmark set, because the dynamic copies the ORA allocator removes exceed the dynamic loads and stores that are inserted. In contrast, the GCC allocator and a Chaitin-style graph-coloring allocator each cause a net increase of more than 1 billion cycles. Because global register allocation is NP-complete, optimal register allocation has been considered intractable. However, the run-time complexity of the ORA approach is shown experimentally to be O(n3). A profile-guided hybrid allocation approach is proposed that uses the ORA allocator for the performance critical regions in the performance critical functions, while using a graph-coloring allocator for the non-critical functions and regions. An ORA-GCC hybrid allocator takes an average of 4.6 seconds per function to produce an allocation that is within 1% of optimal for 97% of the SPEC92 integer benchmark functions, showing that the hybrid allocator is practical as an advanced optimization for performance-critical codes.

Eyeblink classical conditioning in Alzheimer's disease and cerebrovascular dementia

Eyeblink classical conditioning (EBCC) is severely and consistently impaired in probable Alzheimer's disease (AD), presumably due to normal age related changes in the cerebellum and AD-related hippocampal cholinergic disruption. Less consistent impairment and more variable EBCC performance was predicted in patients with cerebrovascular dementia (CVD) because some CVD patients should have impairment in EBCC when their lesions affect the EBCC circuitry, whereas others with lesions in noncritical regions should have normal EBCC. As predicted, variability in EBCC performance was greater in patients with CVD than in probable AD patients. Acquisition of conditioned responses in the group of CVD patients was better than in the probable AD group. These data show in another sample of normal control subjects and probable AD patients that EBCC has a high sensitivity for probable AD.

Semiempirical determination of solution structure in polymer solution based on the clustering theory. 2. Noncritical and critical regions

Semiempirical determination of solution structure in polymer solution based on the clustering theory. 2. Noncritical and critical regions

Directed-site percolation clusters: The scaling function in dimensions two to six

Exact series for lattices of dimension between 2 and 6 are used to report on the asymptotic features of the scaling function for the average number of clusters in directed percolation, close to, and away from, the most recent estimated intervals forp c . Scanning of the noncritical regions yields exponent ranges compatible with the undirected percolation equivalents. Close top c the scaling function varies fairly linearly in terms of the variablez=(p−p c )s σ and this result is rather stable particularly bearing in mind the modestly available precision forp c in higher dimensionalities.

Semi-empirical equation of state for polymers and simple liquids in non-critical and critical regions

The semi-empirical equation of state for the polymers polystyrene (PS), polyisobutylene (PIB) and polydimethyl siloxane (PDMS) and the simple liquids benzene, n-heptane, carbon tetrachloride and argon at a negligible external pressure has been determined using the experimental data of thermal pressure coefficient γ v , molar volume V and thermal expansion coefficient α p . The equation of state obtained in this work is expressed by P = ( X β o V )c 1 exp(α −1 oI o)T − c o exp(a −1 oI o) , where X = (V c − V) V and I o = ∫ V V c X β o V dV , V c is the critical volume and α 0, β 0, a 0, c1 and c 0 are constants determined experimentally. We have obtained good agreement between the values of α p and γ v calculated and observed, within 1–2% over a wide temperature range. The semi-empirical equation of state in the critical region is expressed by V c − V∝( T c − T) 0.33, P − P c∝( V c − V) 5.0, β −1 T ∝( T c − T) 1.33 and α −1 p∝( T c − T) 0.67 for β 0 = 2.0, which agrees semi-quantitatively with the experimental critical indices.

Determining Multiphase Pressure Drops and Flow Capacities in Down-Hole Safety Valves

A new relationship describing dynamic multiphase orifice pressure drops and fluid flow capacities has been derived and tested with field data. The mathematical model relates dynamic orifice behavior in both critical and noncritical flow regions. Correlations are presented for predicting the ultimate (critical) capacity of an presented for predicting the ultimate (critical) capacity of an orifice for any given set of dynamic conditions. Introduction A new relationship describing dynamic, multiphase orifice pressure drops and fluid flow capacities has been derived and tested with actual field data. The mathematical model relates dynamic orifice behavior in both critical and noncritical flow regimes. Orifice pressure drops and capacities are related to pertinent fluid properties and choke dimensions. Graphical pertinent fluid properties and choke dimensions. Graphical correlations are also presented to predict the ultimate (critical) capacity of an orifice for any given set of dynamic conditions. To verify the model, a field test was designed and carried out in a flowing oil well. Both orifice pressure drops and fluid flow rates were measured in the well and the information was compared with analogous data predicted by the model. Comparable information was then predicted by the model. Comparable information was then used to compute an "orifice discharge coefficient" that enables calculation of actual orifice capacities from theoretical ones. The discharge coefficients are presented for 14/64-, 16/64- and 20/64-in. orifice diameters. The collected data reflect the behavior of an Otis Engineering Corp. J-type 22J037 safety valve. However, the model may be used to estimate multiphase pressure drops through restrictive beans in safety valves of other internal geometrical configurations. Discussion The increased need for more accurate settings on downhole, self-contained, flowing safety devices (storm chokes) has prompted efforts by many oil-producing companies to develop new multiphase orifice flow relationships. Interest in antipollution devices, especially in offshore oil-producing areas, has also encouraged the major oil companies to re-evaluate old, established procedures for the design of oil- and gas-well safety procedures for the design of oil- and gas-well safety valves. A review of the existing orifice flow literature and analysis of standard safety-valve design procedures yielded the following facts concerning noncritical multiphase orifice flow.Most orifice flow models do not adequately reflect the compressible nature of actual oilwell multiphase orifice flow. Consequently, models now in use do not adequately describe the dynamic behavior of orifice flow.The existing orifice flow relationships become less exact as the dynamic conditions approach the critical value; that is, at a given upstream pressure, no further flow-rate increase occurs through the orifice, regardless of the pressure drop across the orifice. Those who are involved in manufacturing down-hole, pressure-drop-operated safety valves are aware of the pressure-drop-operated safety valves are aware of the problems associated with accurate prediction of orifice problems associated with accurate prediction of orifice flow behavior. Most agree that a more rigorous mathematical model is needed to describe the mechanics of orifice flow under all oilfield conditions. The orifice relationships used by design engineers, though acceptable under certain flow conditions, are questionable for applications falling outside these specifications. A more rigorous procedure applicable to oilfield JPT P. 1145