Quantum Space-Time as the Set of Shapeless Finite Fundamental Elements

The idea of space-time as a combination of shapeless fundamental elements is proposed.The history of the development of ideas about the discrete space-time structure is analyzed.Quantum space-time is considered as a set of quantum states defined on a set of discretizations with an arbitrary shape of the boundaries of regions.The fundamental element of such space-time is described by the totality of its probabilistic characteristics.We consider a concept in which space-time is the only quantum object,and all material particles and interaction carriers are described as excited states of the fundamental elements of this quantum object.

Optimal dynamical systems of Navier-Stokes equations based on generalized helical-wave bases and the fundamental elements of turbulence

In this paper, we present the theory of constructing optimal generalized helical-wave coupling dynamical systems. Applying the helical-wave decomposition method to Navier-Stokes equations, we derive a pair of coupling dynamical systems based on optimal generalized helical-wave bases. Then with the method of multi-scale global optimization based on coarse graining analysis, a set of global optimal generalized helical-wave bases is obtained. Optimal generalized helical-wave bases retain the good properties of classical helical-wave bases. Moreover, they are optimal for the dynamical systems of Navier-Stokes equations, and suitable for complex physical and geometric boundary conditions. Then we find that the optimal generalized helical-wave vortexes fitted by a finite number of optimal generalized helical-wave bases can be used as the fundamental elements of turbulence, and have important significance for studying physical properties of complex flows and turbulent vortex structures in a deeper level.

Toward the complete relational graph of fundamental circuit elements

A complete and harmonized fundamental circuit relational graph with four linear and four memory elements is con- structed based on some newly defined elements, which provides a guide to developing novel circuit functionalities in the future. In addition to resistors, capacitors, and inductors, which are defined in terms of a linear relationship between charge q, current i, voltage v, and magnetic flux φ, Chua proposed in 1971 a fourth linear circuit element to directly relate φ and q. A nonlinear resistive device defined in memory i-v relation and dubbed memristor, was later attributed to such an element and has been realized in various material structures. Here we clarify that the memristor is not the true fourth fundamen- tal circuit element but the memory extension to the concept of resistor, in analogy to the extension of memcapacitor to capacitor and meminductor to inductor. Instead, a two-terminal device employing the linear ME effects, termed transtor, directly relates φ and q and should be recognized as the fourth linear element. Moreover, its memory extension, termed memtranstor, is proposed and analyzed here.

Realization of a flux-driven memtranstor at room temperature

The memtranstor has been proposed to be the fourth fundamental circuit memelement in addition to the memristor,memcapacitor, and meminductor. Here, we demonstrate the memtranstor behavior at room temperature in a device made of the magnetoelectric hexaferrite（Ba_（0.5）Sr_（1.5）Co_2Fe_（11） AlO_（22）） where the electric polarization is tunable by external magnetic field. This device shows a nonlinear q–р relationship with a butterfly-shaped hysteresis loop, in agreement with the anticipated memtranstor behavior. The memtranstor, like other memelements, has a great potential in developing more advanced circuit functionalities.

Boundary element analysis for elastic and elastoplastic problems of 2D orthotropic media with stress concentration

Both the orthotropy and the stress concentration are common issues in modem structural engineering. This paper introduces the boundary element method （BEM） into the elastic and elastoplastic analyses for 2D orthotropic media with stress concentration. The discretized boundary element formulations are established, and the stress formulae as well as the fundamental solutions are derived in matrix notations. The numerical procedures are proposed to analyze both elastic and elastoplastic problems of 2D orthotropic me- dia with stress concentration. To obtain more precise stress values with fewer elements, the quadratic isoparametric element formulation is adopted in the boundary discretization and numerical procedures. Numerical examples show that there are significant stress concentrations and different elastoplastic behaviors in some orthotropic media, and some of the computational results are compared with other solutions. Good agreements are also observed, which demonstrates the efficiency and reliability of the present BEM in the stress concentration analysis for orthotropic media.

A hierarchical path-segmentation movement ecology framework

This paper lays out a hierarchical,appropriate-complexity framework for conceptualizing movement-path segments at different spatiotemporal scales in a way that facilitates comparative analyses and bridges behavior and mathematical concepts.It then outlines a process for generating a multimode,multiscale stochastic simulation model that can be used to test animal movement hypotheses and make predictions of movement responses to management and global change.Many methods for analyzing movement data begin by generating step-length(SL)and turning-angle(TA)distributions from relocation time-series data,some of which are linked to ecological,landscape,and environmental covariates.The frequency at which these data are collected may vary from sub-seconds to several hours.The kinds of questions that may be asked of these data,however,are very much scale dependent.The hierarchical path-segmentation(HPS)framework presented here clarifies how the scale at which SL and TA data are collected relates to other sub-and super-diel scales.Difficulties arise because the information contained in SL and TA time series are often not directly relatable to the physiological,ecological,and sociological factors that drive the structure of movement paths at longer scales.These difficulties are overcome by anchoring the classification of movement types around the concept of fixed-period(24 h)diel activity routines and providing a bridge between behavioral/ecological and stochastic-walk concepts(means,variances,correlations,individual-state and local environmental covariates).This bridge is achieved through the generation of relatively short segments conceived as characteristic sequences of fundamental movement elements.These short segments are then used to characterize longer canonical-activity-mode segments that emerge through movement at behaviorally relevant sub-diel scales.HPS thus provides a novel system for integrating sub-minute movement sequences into canonical activity modes(CAMs)that,in turn,can be strung together into various types of diel activity routines(DARs).These DARs both vary among individuals within a given day,and for any given individual across time and under the influence of landscape factors.An understanding of how DARs are influenced by environmental inputs will help us predict the response of supra-diel lifetime movement phases(LiMPs)of individuals,as well as their complete lifetime tracks(LiTs),to anthropogenically induced global change.