Effect of Hilbert space truncation on Anderson localization

The 1-D Anderson model possesses a completely localized spectrum of eigenstates for all values of the disorder. We consider the effect of projecting the Hamiltonian to a truncated Hilbert space, destroying time reversal symmetry. We analyze the ensuing eigenstates using different measures such as inverse participation ratio and sample-averaged moments of the position operator. In addition, we examine amplitude fluctuations in detail to detect the possibility of multifractal behavior (characteristic of mobility edges) that may arise as a result of the truncation procedure.Comment: 20 pages, 23 figure

Many-body localization in Landau level subbands

We explore the problem of localization in topological and non-topological nearly-flat subbands derived from the lowest Landau level, in the presence of quenched disorder and short-range interactions. We consider two models: a suitably engineered periodic potential, and randomly distributed point-like impurities. We perform numerical exact diagonalization on a torus geometry and use the mean level spacing ratio $\langle r \rangle$ as a diagnostic of ergodicity. For topological subbands, we find there is no ergodicity breaking in both the one and two dimensional thermodynamic limits. For non-topological subbands, in constrast, we find evidence of an ergodicity breaking transition at finite disorder strength in the one-dimensional thermodynamic limit. Intriguingly, indications of similar behavior in the two-dimensional thermodynamic limit are found, as well. This constitutes a novel, $\textit{continuum}$ setting for the study of the many-body localization transition in one and two dimensions

Analyzing Timed Systems Using Tree Automata

Timed systems, such as timed automata, are usually analyzed using their operational semantics on timed words. The classical region abstraction for timed automata reduces them to (untimed) finite state automata with the same time-abstract properties, such as state reachability. We propose a new technique to analyze such timed systems using finite tree automata instead of finite word automata. The main idea is to consider timed behaviors as graphs with matching edges capturing timing constraints. When a family of graphs has bounded tree-width, they can be interpreted in trees and MSO-definable properties of such graphs can be checked using tree automata. The technique is quite general and applies to many timed systems. In this paper, as an example, we develop the technique on timed pushdown systems, which have recently received considerable attention. Further, we also demonstrate how we can use it on timed automata and timed multi-stack pushdown systems (with boundedness restrictions)

Localization and interactions in topological and non-topological bands in two dimensions

A two-dimensional electron gas in a high magnetic field displays macroscopically degenerate Landau levels, which can be split into Hofstadter subbands by means of a weak periodic potential. By carefully engineering such a potential, one can precisely tune the number, bandwidths, bandgaps and Chern character of these subbands. This allows a detailed study of the interplay of disorder, interaction and topology in two dimensional systems. We first explore the physics of disorder and single-particle localization in subbands derived from the lowest Landau level, that nevertheless may have a topological nature different from that of the entire lowest Landau level. By projecting the Hamiltonian onto subbands of interest, we systematically explore the localization properties of single-particle eigenstates in the presence of quenched disorder. We then introduce electron-electron interactions and investigate the fate of many-body localization in subbands of varying topological character

Revisiting Underapproximate Reachability for Multipushdown Systems

Boolean programs with multiple recursive threads can be captured as pushdown automata with multiple stacks. This model is Turing complete, and hence, one is often interested in analyzing a restricted class that still captures useful behaviors. In this paper, we propose a new class of bounded under approximations for multi-pushdown systems, which subsumes most existing classes. We develop an efficient algorithm for solving the under-approximate reachability problem, which is based on efficient fix-point computations. We implement it in our tool BHIM and illustrate its applicability by generating a set of relevant benchmarks and examining its performance. As an additional takeaway, BHIM solves the binary reachability problem in pushdown automata. To show the versatility of our approach, we then extend our algorithm to the timed setting and provide the first implementation that can handle timed multi-pushdown automata with closed guards.Comment: 52 pages, Conference TACAS 202

Beyond universal behavior in the one-dimensional chain with random nearest neighbor hopping

We study the one-dimensional nearest neighbor tight binding model of electrons with independently distributed random hopping and no on-site potential (i.e. off-diagonal disorder with particle-hole symmetry, leading to sub-lattice symmetry, for each realization). For non-singular distributions of the hopping, it is known that the model exhibits a universal, singular behavior of the density of states $\rho(E) \sim 1/|E \ln^3|E||$ and of the localization length $\xi(E) \sim |\ln|E||$, near the band center $E = 0$. (This singular behavior is also applicable to random XY and Heisenberg spin chains; it was first obtained by Dyson for a specific random harmonic oscillator chain). Simultaneously, the state at $E = 0$ shows a universal, sub-exponential decay at large distances $\sim \exp [ -\sqrt{r/r_0} ]$. In this study, we consider singular, but normalizable, distributions of hopping, whose behavior at small $t$ is of the form $\sim 1/ [t \ln^{\lambda+1}(1/t) ]$, characterized by a single, continuously tunable parameter $\lambda > 0$. We find, using a combination of analytic and numerical methods, that while the universal result applies for $\lambda > 2$, it no longer holds in the interval $0 < \lambda < 2$. In particular, we find that the form of the density of states singularity is enhanced (relative to the Dyson result) in a continuous manner depending on the non-universal parameter $\lambda$; simultaneously, the localization length shows a less divergent form at low energies, and ceases to diverge below $\lambda = 1$. For $\lambda < 2$, the fall-off of the $E = 0$ state at large distances also deviates from the universal result, and is of the form $\sim \exp [-(r/r_0)^{1/\lambda}]$, which decays faster than an exponential for $\lambda < 1$.Comment: 14 pages, 7 figure

Analyzing Timed Systems Using Tree Automata

Timed systems, such as timed automata, are usually analyzed using their operational semantics on timed words. The classical region abstraction for timed automata reduces them to (untimed) finite state automata with the same time-abstract properties, such as state reachability. We propose a new technique to analyze such timed systems using finite tree automata instead of finite word automata. The main idea is to consider timed behaviors as graphs with matching edges capturing timing constraints. Such graphs can be interpreted in trees opening the way to tree automata based techniques which are more powerful than analysis based on word automata. The technique is quite general and applies to many timed systems. In this paper, as an example, we develop the technique on timed pushdown systems, which have recently received considerable attention. Further, we also demonstrate how we can use it on timed automata and timed multi-stack pushdown systems (with boundedness restrictions)

Technoeconomic optimization and thermohydraulic characterization of superalloy supercritical CO2 microtube shell-and-tube heat exchangers

High-temperature supercritical CO2 Brayton cycles are promising candidates for future stationary power generation and hybrid electric propulsion applications. Supercritical CO2 thermal cycles potentially achieve higher energy density and thermal efficiency by operating at elevated temperatures and pressures. Heat exchangers are indispensable components of aerospace systems and improve efficiency of operation by providing necessary heat input, recovery, and dissipation. Tubular heat exchangers with unconventionally small tube sizes (tube diameters less than 5 mm) are promising components for supercritical CO2 cycles and provide excellent structural stability. Accurate and computationally efficient estimation of heat exchanger performance metrics at elevated temperatures and pressures is important for the design and optimization of sCO2 systems and thermal cycles. In this study, new Colburn and friction factor correlations are developed to quantify shell-side heat transfer and friction characteristics of flow within heat exchangers in the shell-and-tube configuration. Using experimental and CFD data sets from existing literature, multivariate regression analysis is conducted to achieve correlations that capture the effects of multiple critical geometric parameters. These correlations offer superior accuracy and versatility as compared to previous studies and predict the thermohydraulic performance of about 90% of the existing experimental and CFD data within �15%. Supplementary thermohydraulic performance data is acquired from CFD simulations with sCO2 as the working fluid to validate the developed correlations and to demonstrate application to sCO2 heat exchangers. A computationally efficient and accurate numerical model is developed to predict the performance of STHXs. The highly accurate correlations are utilized to improve the accuracy of performance pre- dictions, and the concept of volume averaging is used to abstract the geometry for reduced computation time. The numerical model is validated by comparison with CFD simulations and provides high accuracy and significantly lower computation time compared to exist- ing numerical models. A preliminary optimization study is conducted, and the advantage of using supercritical CO2 as a working fluid for energy systems is demonstrated. A microtube heat exchanger is fabricated, and essential design and fabrication guidelines of a compact shell-and-tube heat exchanger with microtubes (with inner diameters of 1.75 mm) are provided. A heat exchanger test rig is used to evaluate the thermohydraulic performance of this heat exchanger with supercritical CO2 and air as working fluids. Thermohydraulic data are reported for more than forty sets of experiments with varying Reynolds numbers for shell and tube flows. Critical performance metrics are calculated from the data and compared with predictions from the numerical model. The average deviations between the experimental and model results fall within 10% for all critical metrics. This excellent agreement validates the numerical model for supercritical CO2 heat exchanger optimization and scale-up. A generalized costing model is developed to estimate the capital costs incurred to manufacture microtube shell-and-tube heat exchangers. This model is utilized in conjunction with an accurate and efficient 2D numerical shell-and-tube heat exchanger performance prediction model to conduct optimization studies with two key objectives - minimization of cost and maximization of heat exchanger power density - on supercritical CO2 microtube heat exchangers utilizing superalloy Haynes 282 as the solid material. A methodology is then demonstrated to optimize these heat exchangers for aerospace applications, and highly compact and cost-effective optimal designs with power density around 20 kW/kg and cost per conductance less than 5 $ � K/W are obtained

Ulnar longitudinal deficiency: a rare case report and review

Ulnar hemimelia is a rare postaxial partial or complete longitudinal deficiency of ulna. It has an estimated incidence of 1/100,000-150,000 live births, with a male to female ratio of 3:2. There is usually ulnar deviation of hand and shortening of forearm. Radial head subluxation and fixed flexion deformity of the hand may be associated with it. Complex carpal, metacarpal, and digital abnormalities including absence of triquetrum, capitate and three fingered hand (tridactyly) are additional findings commonly found in association. Here, we present a case of a 17-year-old female with left sided ulnar club hand due to isolated partial ulnar aplasia

Resilience of Timed Systems

This paper addresses reliability of timed systems in the setting of resilience, that considers the behaviors of a system when unspecified timing errors such as missed deadlines occur. Given a fault model that allows transitions to fire later than allowed by their guard, a system is universally resilient (or self-resilient) if after a fault, it always returns to a timed behavior of the non-faulty system. It is existentially resilient if after a fault, there exists a way to return to a timed behavior of the non-faulty system, that is, if there exists a controller which can guide the system back to a normal behavior. We show that universal resilience of timed automata is undecidable, while existential resilience is decidable, in EXPSPACE. To obtain better complexity bounds and decidability of universal resilience, we consider untimed resilience, as well as subclasses of timed automata