Search Results (8)

Topological transitions are relevant for boundary conditions. Therefore, we investigate the bulk spectra, edge states, and topological phases of Szegedy’s quantum search on a one-dimensional (1D) cycle with self-loops, where the search operator can be formulated as an open boundary condition. By establishing an equivalence with coined quantum walks (QWs), we analytically derive and numerically illustrate the quasienergies dispersion relations of bulk spectra and edge states for Szegedy’s quantum search. Interestingly, novel gapless three-band structures are observed, featuring a flat band and three-fold degenerate points. We identify the topological phases $\pm 2$ as the Chern number. This invariant is computed by leveraging chiral symmetry in zero diagonal Hermitian Hamiltonians that satisfy our quasienergies constraints. Furthermore, we demonstrate that the edge states enhance searches on the marked vertices, while the nontrivial bulk spectra facilitate ballistic spread for Szegedy’s quantum search. Crucially, we find that gapless topological phases arise from three-fold degenerate points and are protected by chiral symmetry, distinguishing ill-defined topological transition boundaries. Full article

The integration of photovoltaic (PV) systems into tensioned membrane structures presents a significant advancement for sustainable applications in the built environment. However, a critical technical challenge remains in the substantial strains induced by external loads, which can compromise both PV efficiency and the structural integrity of the membrane. Current design methodologies prioritize stress, deflection, and ponding analysis of tensioned membranes. Strain behavior of whole structures, a key factor for ensuring long-term performance and compatibility of PV-integrated membranes, has been largely overlooked. This study addresses this gap by examining the whole membrane structure designed for PV integration, with the aim of optimizing the membrane to provide suitable conditions for efficient energy transfer while minimizing membrane strains. For this purpose, it provides a comprehensive strain analysis for full-scale hyperbolic paraboloid (hypar) membrane structures under various design parameters and external loads. Employing the Finite Element Method (FEM) via Sofistik software, the research examines the relationship between load type, geometry, material properties, and patterning direction of membranes to understand their performance under operational conditions. The findings reveal that strain behavior in tensioned membrane structures is strictly influenced by these parameters. Wind loads generate significantly higher strain values compared to snow loads, with positive strains nearly doubling and negative strains tripling in some configurations. Larger structure sizes and increased curvature amplify strain magnitudes, particularly in parallel patterning, whereas diagonal patterning consistently reduces strain levels. High tensile-strength materials and optimized prestress further reduce strains, although edge type has minimal influence. By systematically analyzing these aspects, this study provides practical design guidelines for enhancing the structural and operational efficiency of PV-integrated tensioned membrane structures in the built environment. Full article

This study investigates the mixed-mode I/II fracture behavior of O-notched diagonally loaded square plate (DLSP) samples containing an edge crack within the O-notch. This investigation aims to explore the combined effects of loading rate and mode mixity on the fracture properties of steel 304L, utilizing DLSP samples. The DLSP samples, made from strain-hardening steel 304L, were tested at three different loading rates: 1, 50, and 400 mm/min, covering five mode mixities from pure mode I to pure mode II. Additionally, tensile tests were performed on dumbbell-shaped specimens at the same loading rates to examine their influence on the material’s mechanical properties. The findings revealed that stress and strain diagrams derived from the dumbbell-shaped samples were largely independent of the tested loading rates (i.e., 1–400 mm/min). Furthermore, experimental results from DLSP samples showed no significant impact of the loading rates on the maximum load values, but did indicate an increase in the ultimate displacement. In contrast to the loading rate, mode mixity exhibited a notable effect on the fracture behavior of DLSP samples. Ultimately, it was observed that the loading rate had an insignificant effect on the fracture path or trajectory of the tested DLSP samples. Full article

Frequency hopping spread spectrum (FHSS) applies widely to communication and radar systems to ensure communication information and channel signal quality by tuning frequency within a wide frequency range in a random sequence. An efficient signal processing scheme to resolve the timing and duration signature from an FHSS signal provides crucial information for signal detection and radio band management purposes. In this research, hopping time was first identified by a two-dimensional temporal correlation function (TCF). The timing information was shown at TCF phase discontinuities. To enhance and resolve the timing signature of TCF in a noisy environment, three stages of signature enhancement and morphological matching processes were applied: first, computing the TCF of the FHSS signal and enhancing discontinuities via wavelet transform; second, a dual-diagonal edge finding scheme to extract the timing pattern signature and eliminate mismatching distortion morphologically; finally, Hough transform resolved the agile frequency timing from purified line segments. A grand-scale Monte Carlo simulation of the FHSS signals with additive white Gaussian noise was carried out in the research. The results demonstrated reliable hopping time estimation obtained in SNR at 0 dB and above, with a minimal false detection rate of 1.79%, while the prior related research had an unattended false detection rate of up to 35.29% in such a noisy environment. Full article

Poly(lactic acid) is not only one of the most often used materials for 3D printing via fused deposition modeling (FDM), but also a shape-memory polymer. This means that objects printed from PLA can, to a certain extent, be deformed and regenerate their original shape automatically when they are heated to a moderate temperature of about 60–100 °C. It is important to note that pure PLA cannot restore broken bonds, so that it is necessary to find structures which can take up large forces by deformation without full breaks. Here we report on the continuation of previous tests on 3D-printed cubes with different infill patterns and degrees, now investigating the influence of the orientation of the applied pressure on the recovery properties. We find that for the applied gyroid pattern, indentation on the front parallel to the layers gives the worst recovery due to nearly full layer separation, while indentation on the front perpendicular to the layers or diagonal gives significantly better results. Pressing from the top, either diagonal or parallel to an edge, interestingly leads to a different residual strain than pressing from front, with indentation on top always firstly leading to an expansion towards the indenter after the first few quasi-static load tests. To quantitatively evaluate these results, new measures are suggested which could be adopted by other groups working on shape-memory polymers. Full article

Divisibility networks of natural numbers present a scale-free distribution as many other process in real life due to human interventions. This was quite unexpected since it is hard to find patterns concerning anything related with prime numbers. However, it is by now unclear if this behavior can also be found in other networks of mathematical nature. Even more, it was yet unknown if such patterns are present in other divisibility networks. We study networks of rational numbers in the unit interval where the edges are defined via the divisibility relation. Since we are dealing with infinite sets, we need to define an increasing covering of subnetworks. This requires an order of the numbers different from the canonical one. Therefore, we propose the construction of four different orders of the rational numbers in the unit interval inspired in Cantor’s diagonal argument. We motivate why these orders are chosen and we compare the topologies of the corresponding divisibility networks showing that all of them have a free-scale distribution. We also discuss which of the four networks should be more suitable for these analyses. Full article

Great progress has been made in recent years towards understanding the properties of disordered electronic systems. In part, this is made possible by recent advances in quantum effective medium methods which enable the study of disorder and electron-electronic interactions on equal footing. They include dynamical mean-field theory and the Coherent Potential Approximation, and their cluster extension, the dynamical cluster approximation. Despite their successes, these methods do not enable the first-principles study of the strongly disordered regime, including the effects of electronic localization. The main focus of this review is the recently developed typical medium dynamical cluster approximation for disordered electronic systems. This method has been constructed to capture disorder-induced localization and is based on a mapping of a lattice onto a quantum cluster embedded in an effective typical medium, which is determined self-consistently. Unlike the average effective medium-based methods mentioned above, typical medium-based methods properly capture the states localized by disorder. The typical medium dynamical cluster approximation not only provides the proper order parameter for Anderson localized states, but it can also incorporate the full complexity of Density-Functional Theory (DFT)-derived potentials into the analysis, including the effect of multiple bands, non-local disorder, and electron-electron interactions. After a brief historical review of other numerical methods for disordered systems, we discuss coarse-graining as a unifying principle for the development of translationally invariant quantum cluster methods. Together, the Coherent Potential Approximation, the Dynamical Mean-Field Theory and the Dynamical Cluster Approximation may be viewed as a single class of approximations with a much-needed small parameter of the inverse cluster size which may be used to control the approximation. We then present an overview of various recent applications of the typical medium dynamical cluster approximation to a variety of models and systems, including single and multiband Anderson model, and models with local and off-diagonal disorder. We then present the application of the method to realistic systems in the framework of the DFT and demonstrate that the resulting method can provide a systematic first-principles method validated by experiment and capable of making experimentally relevant predictions. We also discuss the application of the typical medium dynamical cluster approximation to systems with disorder and electron-electron interactions. Most significantly, we show that in the limits of strong disorder and weak interactions treated perturbatively, that the phenomena of 3D localization, including a mobility edge, remains intact. However, the metal-insulator transition is pushed to larger disorder values by the local interactions. We also study the limits of strong disorder and strong interactions capable of producing moment formation and screening, with a non-perturbative local approximation. Here, we find that the Anderson localization quantum phase transition is accompanied by a quantum-critical fan in the energy-disorder phase diagram. Full article

Let R denote a connected region inside a simple polygon, P. By building barriers (typically straight-line segments) in $PR$ , we want to separate from R part(s) of P of maximum area. All edges of the boundary of P are assumed to be already constructed or natural barriers. In this paper we introduce two versions of this problem. In the budget fence version the region R is static, and there is an upper bound on the total length of barriers we may build. In the basic geometric firefighter version we assume that R represents a fire that is spreading over P at constant speed (varying speed can also be handled). Building a barrier takes time proportional to its length, and each barrier must be completed before the fire arrives. In this paper we are assuming that barriers are chosen from a given set B that satisfies certain conditions. Even for simple cases (e.g., P is a convex polygon and B the set of all diagonals), both problems are shown to be NP-hard. Our main result is an efficient ≈11.65 approximation algorithm for the firefighter problem, where the set B of allowed barriers is any set of straight-line segments with all endpoints on the boundary of P and pairwise disjoint interiors. Since this algorithm solves a much more general problem—a hybrid of scheduling and maximum coverage—it may find wider applications. We also provide a polynomial-time approximation scheme for the budget fence problem, for the case where barriers chosen from a set of straight-line cuts of the polygon must not cross. Full article