Singular State Research Articles

Physical Layer Network Coding in Network MIMO: A New Design for 5G and Beyond

Physical layer network coding (PNC) has been studied to serve wireless network MIMO systems with much lower backhaul load than approaches such as Cloud Radio Access Network (Cloud-RAN) and coordinated multipoint (CoMP). In this paper, we present a design guideline of engineering applicable PNC to fulfil the request of high user densities in 5G wireless RAN infrastructure. We show that the proposed design criteria guarantee that: 1) the whole system operates over binary system; 2) the PNC functions utilized at each access point overcome all singular fade states; and 3) the destination can unambiguously recover all source messages, while the overall backhaul load remains at the lowest level. We then develop a two-stage search algorithm to identify the optimum PNC mapping functions which greatly reduces the real-time computational complexity. The impact of estimated channel information and reduced number of singular fade states in different QAM modulation schemes are studied in this paper. Numerical results show that the proposed schemes achieve low outage probability with reduced backhaul load.

Signature of quantum Griffiths singularity state in a layered quasi-one-dimensional superconductor

Quantum Griffiths singularity was theoretically proposed to interpret the phenomenon of divergent dynamical exponent in quantum phase transitions. It has been discovered experimentally in three-dimensional (3D) magnetic metal systems and two-dimensional (2D) superconductors. But, whether this state exists in lower dimensional systems remains elusive. Here, we report the signature of quantum Griffiths singularity state in quasi-one-dimensional (1D) Ta2PdS5 nanowires. The superconducting critical field shows a strong anisotropic behavior and a violation of the Pauli limit in a parallel magnetic field configuration. Current-voltage measurements exhibit hysteresis loops and a series of multiple voltage steps in transition to the normal state, indicating a quasi-1D nature of the superconductivity. Surprisingly, the nanowire undergoes a superconductor-metal transition when the magnetic field increases. Upon approaching the zero-temperature quantum critical point, the system uncovers the signature of the quantum Griffiths singularity state arising from enhanced quenched disorders, where the dynamical critical exponent becomes diverging rather than being constant.

Study and Application of Intelligent Sliding Mode Control for Voltage Source Inverters

In this paper, an intelligent sliding mode controlled voltage source inverter (VSI) is developed to achieve not only quick transient behavior, but satisfactory steady-state response. The presented approach combines the respective merits of a nonsingular fast terminal attractor (NFTA) as well as an adaptive neuro-fuzzy inference system (ANFIS). The NFTA allows no singularity and error states to be converged to the equilibrium within a finite time, while conventional sliding mode control (SMC) leads to long-term (infinite) convergent behavior. However, there is the likelihood of chattering or steady-state error occurring in NFTA due to the overestimation or underestimation of system uncertainty bound. The ANFIS with accurate estimation and the ease of implementation is employed in NFTA for suppressing the chatter or steady-state error so as to improve the system’s robustness against uncertain disturbances. Simulation results display that this described approach yields low distorted output wave shapes and quick transience in the presence of capacitor input rectifier loading as well as abrupt connection of linear loads. Experimental results conducted on a 1 kW VSI prototype with control algorithm implementation in Texas Instruments DSP (digital signal processor) support the theoretic analysis and reaffirm the robust performance of the developed VSI. Because the proposed VSI yields remarkable benefits over conventional terminal attractor VSIs on the basis of computational quickness and unsophisticated realization, the presented approach is a noteworthy referral to the designers of correlated VSI applications in future, such as DC (direct current) microgrids and AC (alternating current) microgrids, or even hybrid AC/DC microgrids.

Fractional-order singular logistic map: Stability, bifurcation and chaos analysis

Recently fractional calculus started to gain much importance due to its applications to the mathematical modeling of real phenomena with memory effect. Besides, singular modeling, which has been accompanied by exhibiting more complicated dynamics rather than standard models, can reveal the instability mechanism of wide-range of physical systems. Utilizing these two applicable techniques of modeling, a generalization of the logistic growth model, which takes into account the effects of memory and economic interest, is suggested in this paper. Besides mathematical analysis and extracting new results on the equilibrium points and local stability studies of discrete-time commensurate fractional-order singular (FOS) state space systems, some basic dynamical properties and qualitative analysis of the new chaotic FOS logistic map are studied, either numerically or analytically, to explore the impacts of real order and economic interest on the presented system in biological contexts.

Mechanical Systems with Singular Equilibria and the Coulomb Dynamics of Three Charges

We consider mechanical systems for which the matrices of second partial derivatives of the potential energies at equilibria have zero eigenvalues. It is assumed that their potential energies are holomorphic functions in these singular equilibrium states. For these systems, we prove the existence of proper bounded (for positive time) solutions of the Newton equations of motion convergent to equilibrium in the infinite-time limit. These results are applied to the Coulomb systems of three point charges with singular equilibrium in a line.

Electrically induced 2D half-metallic antiferromagnets and spin field effect transistors

Engineering the electronic band structure of material systems enables the unprecedented exploration of new physical properties that are absent in natural or as-synthetic materials. Half metallicity, an intriguing physical property arising from the metallic nature of electrons with singular spin polarization and insulating for oppositely polarized electrons, holds a great potential for a 100% spin-polarized current for high-efficiency spintronics. Conventionally synthesized thin films hardly sustain half metallicity inherited from their 3D counterparts. A fundamental challenge, in systems of reduced dimensions, is the almost inevitable spin-mixed edge or surface states in proximity to the Fermi level. Here, we predict electric field-induced half metallicity in bilayer A-type antiferromagnetic van der Waals crystals (i.e., intralayer ferromagnetism and interlayer antiferromagnetism), by employing density functional theory calculations on vanadium diselenide. Electric fields lift energy levels of the constituent layers in opposite directions, leading to the gradual closure of the gap of singular spin-polarized states and the opening of the gap of the others. We show that a vertical electrical field is a generic and effective way to achieve half metallicity in A-type antiferromagnetic bilayers and realize the spin field effect transistor. The electric field-induced half metallicity represents an appealing route to realize 2D half metals and opens opportunities for nanoscale highly efficient antiferromagnetic spintronics for information processing and storage.

Spacecraft angular velocity trajectory planning for SGCMG singularity avoidance

A trajectory planning method for angular velocity of spacecraft is developed to avoid the impassable singular states for singular gimbal control moment gyroscope (SGCMG) systems in this paper. A new set of attitude parameters, named σ-parameters, is first developed. Based on the properties of σ-parameters, two approximate decoupled rotations are presented. To achieve a rapid attitude maneuver, both of the decoupled motions are designed as simple bang-off-bang type maneuvers. Then, a type of SGCMG singularity-free angular velocity trajectory on the conic surface is developed. Thereafter, an attitude controller based on σ-parameters is developed to track the reference trajectory. To avoid the impassable singular state, suitable axes of the approximate decoupled two rotations are chosen to achieve the fastest maneuver under the condition that the minimum distance from the angular momentum trajectory to the impassable surface is greater than a safety distance. Finally, simulations are performed to verify the effectiveness of the proposed SGCMG singularity avoidance method.

State Capitalism and Entertainment Markets: The Socialist Transformation of Quyi in Tianjin, 1949–1964

This article explores the relationship between the state and a persistent entertainment market during the socialist transformation period of 1949–1964. Drawing on the competing narratives in state archives and the oral accounts of performers and Chinese Communist Party cadres, the article examines the interplay of central policies, local practices, and personal experiences in the formation of state-run troupes and new quyi in Tianjin. It reveals that state-run troupes applied various marketing strategies to fulfill the task that the Center had assigned them: achieving self-sufficiency amid local economic difficulties. The central government promoted a state capitalist policy, and yet provided little funding. To support themselves, local leaders employed such marketing approaches as performing for pay at parties (“party performances”), staging quyi opera, and charging audiences on a pay-by-time basis. In a process of policy testing and negotiating among multiple levels of government, central policies were adjusted. This study demonstrates that the cultural reform was not simply a contest between a singular state and the market, but rather that the state existed at multiple levels and the lack of state funding facilitated a market economy. State capitalism laid a foundation for the socialist cultural transformation.

Cosmological model with variable deceleration parameter in f(R,T) modified gravity

A study is made of the LRS Bianchi type-I cosmological model in [Formula: see text] modified gravity theory. Einstein’s field equations in [Formula: see text] gravity are solved by taking [Formula: see text] and the deceleration parameter [Formula: see text] to be a linear function of the Hubble parameter [Formula: see text]. The universe begins with an initial singular state and changes with time from an early deceleration phase to a late time acceleration phase. We have found that the jerk parameter [Formula: see text] in the model approaches that of the [Formula: see text] model at late times. We also discuss the physical and geometrical properties of the model.

First-principles study of graphene nanoflakes with large spin property

Based on density functional theory, the extraordinary magnetic properties of finite graphene fragments (graphene nanoflake, GNF) with different shapes are studied by first-principles electronic structure calculations with all electron numerical-orbital basis set scheme as implemented in DMol3 code of Materials Studio 8.0 software package. According to the graph theory, the spin characteristics of several typical hydrogen-terminated GNF shaped into 3-fold and 6-fold highly rotational symmetries as well as two specific geometrical structures related to graphene nanoribbon are analyzed and verified by first-principles calculations. In some characteristic GNFs shaped into a singular graph, the electron energy matrix becomes singular and multiple states of zero eigenvalue appear which is called nonbonding state (NBS). In these singular graph structures, all the -bonds cannot be satisfied simultaneously and spin-aligned singly occupied molecular orbitals are generated from degeneracy at Fermi-level, which means that the topological frustration occurs. It is proved that the electronic spin magnetic order of GNF originates from topological frustration of conjugate -bonds determined by its shape. The net spin of triangular GNF with zigzag edges is not zero, like an artificial ferromagnetic atom, increasing proportionally with its linear dimension. According to the principle of topological frustration, the large net spins and specific spin distributions can be reasonably introduced into graphene nanocrystals, such as by triangulation. The NBSs of zigzag-edged triangular GNFs with nanoscale dimension create 0.4-0.7 eV energy gaps at Fermi-level to achieve stable spin-alignment at ambient temperature. Even though the linear size of zigzag-edged triangular GNF increases beyond nanoscale, the maximum energy gap is still ~0.68 eV and thus the magnetic moment measurement is feasible at room ambient temperature. The total spin of the complex fractal structure constructed by zigzag-edged triangular GNF unit increases exponentially with the fractal level, due to the increased possibility of topological frustration from aggrandizing boundary. In addition, a large net spin can also be acquired by hollowed-out zigzag triangle in graphene with a net spin value of at least 1.00 and a spin-polarization split band gap of ~0.40 eV. The basic design principle for obtaining large spin and controlling spin state distribution by etching GNF of various patterns in graphene atomic layer is presented. In contrast to traditional chemical synthesis of obtaining large spin limited by complicated reaction pathways, the GNF with large spin easily exceeding the reported highest spin in conjugated polymers can be practically produced by carving lithography. It is suggested that the GNF with designed topological structures fabricated by pattern carving technique can be efficiently used to realize the controllable spintronic nanomaterials and devices.

Entanglement and non-classical properties of generalized supercoherent states

Three classes of generalized supercoherent states have been recently introduced, degenerate, singular and generic. We have studied the entanglement, squeezing and statistical properties of these supercoherent states. Using concurrence, we calculate the entanglement of these states. We find that the degenerate and the generic supercoherent states classes may be entangled and squeezed. While the singular supercoherent states generally have Poissonian statistics, the degenerate and generic classes have sub-Poissonian statistics in some ranges of the parameters. Also, we have optimized the super-annihilation operator which has been used to obtain maximum of entanglement.

Synchronous dynamics in the Kuramoto model with biharmonic interaction and bimodal frequency distribution.

In this work, we study the Kuramoto model with biharmonic interaction and bimodal frequency distribution. Rich synchronous dynamics, such as standing wave states, stationary partial synchronous dynamics, and multiplicity of singular synchronous dynamics, are found. Notably, we find a symmetry-breaking synchronous dynamics when the peaks in frequency distribution are not well separated. We present the phase diagrams for two cases: the peaks in the frequency distribution are well separated and the peaks are not well separated. We find that reducing peak distance tends to make the transition between standing wave states and stationary partial synchronous states to be continuous when the multiplicity of singular synchronous state is present or to be discontinuous when the multiplicity is absent.

A singular one-dimensional bound state problem and its degeneracies

We give a brief exposition of the formulation of the bound state problem for the one-dimensional system of N attractive Dirac delta potentials, as an $N \times N$ matrix eigenvalue problem ( $\Phi A =\omega A$ ). The main aim of this paper is to illustrate that the non-degeneracy theorem in one dimension breaks down for the equidistantly distributed Dirac delta potential, where the matrix $\Phi$ becomes a special form of the circulant matrix. We then give elementary proof that the ground state is always non-degenerate and the associated wave function may be chosen to be positive by using the Perron-Frobenius theorem. We also prove that removing a single center from the system of N delta centers shifts all the bound state energy levels upward as a simple consequence of the Cauchy interlacing theorem.

Construction of type II blow-up solutions for a semilinear parabolic system with higher dimension

This paper is concerned with blow-up solutions for a semilinear parabolic system with a power type nonlinearity. Non self-similar blow-up solution is constructed by the matched asymptotic expansions. One component of this solution converges to the singular steady state, and another component converges to zero in self-similar variables.

Structural Evolution of Flower Defects and Effects on the Electronic Structures of Epitaxial Graphene

The structural evolution processes of flower defects in epitaxial graphene at high temperature annealing are investigated by using scanning tunneling microscopy, Raman spectroscopy, and the density functional theory calculations. The experimental results reveal that flower defects can increase in amount with the increasing of annealing time until they nucleate and evolve into complex defect structures. As the direct evidence of the structural development for flower defects evolving into the complex structures, the conjoined-twin defect is detected in epitaxial graphene with two of 2/3 flower defects joined together. The theoretical calculations show that the conjoined-twin defect has a calculated energy 2.7 eV smaller than that of two isolated flower defects. And the conjoined-twin defect as a new topological defect in graphene can bring about a bandgap of 50 meV. The calculation results also demonstrate that new van Hove singularity states will be generated in the vicinity of + (0.4–0.7) and −0.4 eV in t...

Quantum measurable cardinals

We investigate states on von Neumann algebras which are not normal but enjoy various forms of infinite additivity, and show that these exist on B(H) if and only if the cardinality of an orthonormal basis of H satisfies various large cardinal conditions. For instance, there is a singular countably additive pure state on B(l2(κ)) if and only if κ is Ulam measurable, and there is a singular <κ-additive pure state on B(l2(κ)) if and only if κ is measurable. The proofs make use of Farah and Weaver's theory of quantum filters [12]. We can generalize some of these characterizations to arbitrary von Neumann algebras. Applications to Ueda's peak set theorem for von Neumann algebras are discussed in the final section.

A novel size independent symplectic analytical singular element for inclined crack terminating at bimaterial interface

• The analytical symplectic eigen expansion for inclined bimaterial interface crack is solved. • Stress intensity factors for the inclined bimaterial crack derived from the proposed method are provided and discussed. • A novel singular finite element is constructed based on the symplectic eigen solution. • It is proven that the stiffness matrix of the proposed singular element is independent of the element's size. • Stress intensity factors can be calculated directly without any post-processing. Cracks often exist in composite structures, especially at the interface of two different materials. These cracks can significantly affect the load bearing capacity of the structure and lead to premature failure of the structure. In this paper, a novel element for modeling the singular stress state around the inclined interface crack which terminates at the interface is developed. This new singular element is derived based on the explicit form of the high order eigen solution which is, for the first time, determined by using a symplectic approach. The developed singular element is then applied in finite element analysis and the stress intensity factors (SIFs) for a number of crack configurations are derived. It has been concluded that composites with complex geometric configurations of inclined interface cracks can be accurately simulated by the developed method, according to comparison of the results against benchmarks. It has been found that the stiffness matrix of the proposed singular element is independent of the element size and the SIFs of the crack can be solved directly without any post-processing.

Singularity and steering logic for control moment gyros on flexible space structures

Control moment gyros (CMGs) are a widely used device for generating control torques for spacecraft attitude control without expending propellant. Because of its effectiveness and cleanness, it has been considered to be mounted on a space structure for active vibration suppression. The resultant system is the so-called gyroelastic body. Since CMGs could exert both torque and modal force to the structure, it can also be used to simultaneously achieve attitude maneuver and vibration reduction of a flexible spacecraft. In this paper, we consider the singularity problem in such application of CMGs. The dynamics of an unconstrained gyroelastic body is established, from which the output equations of the CMGs are extracted. Then, torque singular state and modal force singular state are defined and visualized to demonstrate the singularity. Numerical examples of several typical CMGs configurations on a gyroelastic body are given. Finally, a steering law allowing output error is designed and applied to the vibration suppression of a plate with distributed CMGs.

Anisotropic deformations of spatially open cosmology in massive gravity theory

We combine analytical and numerical methods to study anisotropic deformations of the spatially open homogeneous and isotropic cosmology in the ghost free massive gravity theory with flat reference metric. We find that if the initial perturbations are not too strong then the physical metric relaxes back to the isotropic de Sitter state. However, the dumping of the anisotropies is achieved at the expense of exciting the Stueckelberg fields in such a way that the reference metric changes and does not share anymore with the physical metric the same rotational and translational symmetries. As a result, the universe evolves towards a fixed point which does not coincide with the original solution, but for which the physical metric is still de Sitter. If the initial perturbation is strong, then its evolution generically leads to a singular anisotropic state or, for some parameter values, to a decay into flat spacetime. We also present an infinite dimensional family of new homogeneous and isotropic cosmologies in the theory.

„The singular state of the ice“. Das kartografische Wissen des Walfängers William Scoresby

Abstract“The singular state of the ice”. The Cartographic Knowledge of the Whaler William Scoresby. The English whaler William Scoresby, Jr. (1790–1857) made use of his annual voyages to the Greenland Sea for distinguished scientific work, detailed records and the production of amazing maps. Due to his intensive contacts to scientists as Robert Jameson and politicians as Joseph Banks and John Barrow his research achieved a great deal of attention and set a benchmark for at least half a century. Scoresby combined the adventurous world of Arctic fishery with academic sciences. He attained the northernmost point anybody reached in his time, he extended the cartographic knowledge and forced the conquest and utilisation of the oceans for commercial fishing. But his biography enquires also about who got an opportunity for research and for what. Especially it demonstrates the strong impact practical knowledge of a whaler could have on geographic research and Arctic cartography.