The Ising model describes a many-body interacting spin (or particle) system, which can be utilized to imitate the fundamental forces of nature. Although it is the simplest many-body interacting ...system of spins (or particles) with Z2 symmetry, the phenomena revealed in Ising systems may afford us lessons for other types of interactions in nature. In this work, we first focus on the mathematical structure of the three-dimensional (3D) Ising model. In the Clifford algebraic representation, many internal factors exist in the transfer matrices of the 3D Ising model, which are ascribed to the topology of the 3D space and the many-body interactions of spins. They result in the nonlocality, the nontrivial topological structure, as well as the long-range entanglement between spins in the 3D Ising model. We review briefly the exact solution of the ferromagnetic 3D Ising model at the zero magnetic field, which was derived in our previous work. Then, the framework of topological quantum statistical mechanics is established, with respect to the mathematical aspects (topology, algebra, and geometry) and physical features (the contribution of topology to physics, Jordan–von Neumann–Wigner framework, time average, ensemble average, and quantum mechanical average). This is accomplished by generalizations of our findings and observations in the 3D Ising models. Finally, the results are generalized to topological quantum field theories, in consideration of relationships between quantum statistical mechanics and quantum field theories. It is found that these theories must be set up within the Jordan–von Neumann–Wigner framework, and the ergodic hypothesis is violated at the finite temperature. It is necessary to account the time average of the ensemble average and the quantum mechanical average in the topological quantum statistical mechanics and to introduce the parameter space of complex time (and complex temperature) in the topological quantum field theories. We find that a topological phase transition occurs near the infinite temperature (or the zero temperature) in models in the topological quantum statistical mechanics and the topological quantum field theories, which visualizes a symmetrical breaking of time inverse symmetry.
The common feature for a nontrivial hard problem is the existence of nontrivial topological structures, non-planarity graphs, nonlocalities, or long-range spin entanglements in a model system with ...randomness. For instance, the Boolean satisfiability (K-SAT) problems for K ≥ 3 MSATK≥3 are nontrivial, due to the existence of non-planarity graphs, nonlocalities, and the randomness. In this work, the relation between a spin-glass three-dimensional (3D) Ising model MSGI3D with the lattice size N = mnl and the K-SAT problems is investigated in detail. With the Clifford algebra representation, it is easy to reveal the existence of the long-range entanglements between Ising spins in the spin-glass 3D Ising lattice. The internal factors in the transfer matrices of the spin-glass 3D Ising model lead to the nontrivial topological structures and the nonlocalities. At first, we prove that the absolute minimum core (AMC) model MAMC3D exists in the spin-glass 3D Ising model, which is defined as a spin-glass 2D Ising model interacting with its nearest neighboring plane. Any algorithms, which use any approximations and/or break the long-range spin entanglements of the AMC model, cannot result in the exact solution of the spin-glass 3D Ising model. Second, we prove that the dual transformation between the spin-glass 3D Ising model and the spin-glass 3D Z2 lattice gauge model shows that it can be mapped to a K-SAT problem for K ≥ 4 also in the consideration of random interactions and frustrations. Third, we prove that the AMC model is equivalent to the K-SAT problem for K = 3. Because the lower bound of the computational complexity of the spin-glass 3D Ising model CLMSGI3D is the computational complexity by brute force search of the AMC model CUMAMC3D, the lower bound of the computational complexity of the K-SAT problem for K ≥ 4 CLMSATK≥4 is the computational complexity by brute force search of the K-SAT problem for K = 3 CUMSATK=3. Namely, CLMSATK≥4=CLMSGI3D≥CUMAMC3D=CUMSATK=3. All of them are in subexponential and superpolynomial. Therefore, the computational complexity of the K-SAT problem for K ≥ 4 cannot be reduced to that of the K-SAT problem for K < 3.
Soil erosion is a widespread environmental problem that threatens environmental sustainability. The Loess Plateau (LP) in China is one of the most severely eroded areas in the world. In this study, ...the soil erosion dynamics were assessed by applying the Revised Universal Soil Loss Equation and the Revised Wind Erosion Equation; further, the underlying drivers for soil erosion processes were investigated. In addition, implications of constraint effects in soil erosion control were discussed. The results showed that there was a substantial reduction in both wind and water erosion between 2000 and 2015; it is considered that vegetation restoration (mainly in relation to government-aided ecological restoration programs), increased precipitation, and a decrease in wind speed may have contributed to these trends. Land cover and soil properties contribute to spatial patterns of soil erosion. Thus, ecological restoration programs have promoted improvements in soil properties, leading to an eventual reduction. Constraint line analysis indicates that vegetation cover has a nonlinear and threshold effect on soil erosion through constraining the water condition (i.e., rainfall). With respect to water erosion, when rainfall is below the threshold (approximately 450–500 mm), it is not sufficient to maintain a good vegetation cover (about 30–40%), and vegetation cannot efficiently prevent soil erosion; however, once rainfall exceeds the threshold, the soil retention function of the vegetation is enhanced and soil loss is substantially reduced. In addition, there is a lower (10%) and an upper (40%) threshold at which vegetation can control wind erosion, which implies that plant cover lower than 10% has a minimal effect on reducing the wind velocity at the soil surface, and the effect of vegetation on reducing wind erosion is at its maximum when plant cover is 40% or above. However, if human intervention is removed, the limited amount of rainfall on the LP would be insufficient to support large areas of trees in the long-term; therefore, the constraint effects of the water condition on vegetation cover need to be considered to improve the efficiency of afforestation and reforestation efforts aimed at mitigating and preventing soil loss.
•We quantified the soil erosion change in a spatially explicit manner.•We investigated the driving forces of soil erosion change.•The constraint effect between wind erosion and vegetation cover was quantified.•The implications of constraint effect in soil erosion control were discussed.
When cementitious materials are subjected to drying, the microstructure is significantly altered by high capillary forces established in the fine pores. To avoid drying stresses when preparing ...samples for microstructural characterization, our previous studies developed the supercritical drying method (SCD) (Zhang and Scherer, 2017) which showed rather good preservation for the microstructure of hydration products compared with the other conventional methods (Zhang et al., 2018). In this study, various drying methods, including SCD, are evaluated by using the nitrogen adsorption (NAD) technique in terms of BET surface area, sorption isotherms, pore size distribution and pore volume. Results show that the isopropanol (IPA) replacement method can better preserve the microstructure than the other methods with a slight chemical effect of IPA on the calcium silicate hydrate (C-S-H). Contrary to the previous studies, IPA was not found to have a greater influence on calcium hydroxide (CH) than the other drying methods. SCD shows slightly lower microstructural preservation than IPA replacement due to pore blockage. The fluid used for SCD (trifluoromethane) also chemically interacts with both CH and C-S-H, which may result from the pressurization during drying. Freeze-drying is suggested if one wants to avoid chemical effects on the hydration products, at the expense of damage to the microstructure.
In this article, we consider the reconstruction of ρ(t) in the (time-fractional) diffusion equation (∂tα−△)u(x,t)=ρ(t)g(x) (0<α⩽1) by observation at a single point x0. We are mainly concerned with ...the situation of x0∉suppg, which is practically important but has not been well investigated in literature. Assuming finite sign changes of ρ and an extra observation interval, we establish the multiple logarithmic stability for the problem based on a reverse convolution inequality and a lower estimate for positive solutions. Meanwhile, we develop a fixed-point iteration for the numerical reconstruction and prove its convergence. The performance of the proposed method is illustrated by several numerical examples.
A plasmonic waveguide coupled system that uses a metal-insulator-metal (MIM) waveguide with two silver baffles and a coupled ring cavity is proposed in this study. The transmission properties of the ...plasmonic system were investigated using the finite element method. The simulation results show a Fano profile in the transmission spectrum, which was caused by the interaction of the broadband resonance of the Fabry-Perot (F-P) cavity and the narrow band resonance of the ring cavity. The Fabry-Perot (F-P) cavity in this case was formed by two silver baffles dividing the MIM waveguide. The maximum sensitivity of 718 nm/RIU and the maximum figure of merit of 4354 were achieved. Furthermore, the effects of the structural parameters of the F-P cavity and the ring cavity on the transmission properties of the plasmonic system were analyzed. The results can provide a guide for designing highly sensitive on-chip sensors based on surface plasmon polaritons.
Anomalous moisture transport in cement-based materials is often reported in the literature, but the conventional single-porosity moisture transport models generally fail to provide accurate ...simulation results. Previous studies suggested that the anomalous moisture transport could be caused by different moisture transport velocity in large and small pores. Based on this concept, the present study proposes a continuous dual-permeability model for cement-based material. The proposed model includes the transport contribution of both liquid water and water vapor, which are governed by liquid advection and vapor diffusion, respectively. We explicitly consider that moisture transport in the large pore region is faster than the small pore region. The volumetric fraction of each region is determined when fitting the measured sorption isotherms by using a bimodal equation. The validation with experimental data shows that the dual-permeability model can well simulate both the “normal” and the anomalous moisture transport. The applicability of the proposed model implies that the “dual-porosity property” could be one of reasons that cause anomalous moisture transport in cementitious materials. In addition, results show that vapor diffusion can be neglected for moisture transport in both porosities at high relative humidity (RH), while at low RH, vapor diffusion must be considered.
A refractive index sensor based on metal-insulator-metal (MIM) waveguides coupled double rectangular cavities is proposed and investigated numerically using the finite element method (FEM). The ...transmission properties and refractive index sensitivity of various configurations of the sensor are systematically investigated. An asymmetric Fano resonance lineshape is observed in the transmission spectra of the sensor, which is induced by the interference between a broad resonance mode in one rectangular and a narrow one in the other. The effect of various structural parameters on the Fano resonance and the refractive index sensitivity of the system based on Fano resonance is investigated. The proposed plasmonic refractive index sensor shows a maximum sensitivity of 596 nm/RIU.
In this article, for a two dimensional fractional diffusion equation, we study an inverse problem for simultaneous restoration of the fractional order and the source term from the sparse boundary ...measurements. By using a sequence of harmonic functions, we construct useful quantitative relation between the unknowns and measurements. From Laplace transform and the knowledge in complex analysis, the uniqueness theorem is proved.
Manipulating a quantum state via electrostatic gating has been of great importance for many model systems in nanoelectronics. Until now, however, controlling the electron spins or, more specifically, ...the magnetism of a system by electric-field tuning has proven challenging
. Recently, atomically thin magnetic semiconductors have attracted significant attention due to their emerging new physical phenomena
. However, many issues are yet to be resolved to convincingly demonstrate gate-controllable magnetism in these two-dimensional materials. Here, we show that, via electrostatic gating, a strong field effect can be observed in devices based on few-layered ferromagnetic semiconducting Cr
Ge
Te
. At different gate doping, micro-area Kerr measurements in the studied devices demonstrate bipolar tunable magnetization loops below the Curie temperature, which is tentatively attributed to the moment rebalance in the spin-polarized band structure. Our findings of electric-field-controlled magnetism in van der Waals magnets show possibilities for potential applications in new-generation magnetic memory storage, sensors and spintronics.
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