Comparative Analysis of the Generalized Omega Equation and Generalized Vertical Motion Equation

Research on vertical motion in mesoscale systems is an extraordinarily challenging effort.Allowing for fewer assumptions,a new form of generalized vertical motion equation and a generalized Omega equation are derived in the Cartesian coordinate system(nonhydrostatic equilibrium)and the isobaric coordinate system(hydrostatic equilibrium),respectively.The terms on the right-hand side of the equations,which comprise the Q vector,are composed of three factors:dynamic,thermodynamic,and mass.A heavy rain event that occurred from 18 to 19 July 2021 in southern Xinjiang was selected to analyze the characteristics of the diagnostic variable in the generalized vertical motion equation(Qz)and the diagnostic variable in the generalized Omega equation(Qp)using high-resolution model data.The results show that the horizontal distribution of the Qz-vector divergence at 5.5 km is roughly similar to the distribution of the Qp-vector divergence at 500 hPa,and that both relate well to the composite radar reflectivity,vertical motion,and hourly accumulated precipitation.The Qz-vector divergence is more effective in indicating weak precipitation.In vertical cross sections,regions with alternating positive and negative large values that match the precipitation are mainly concentrated in the middle levels for both forms of Q vectors.The temporal evolutions of vertically integrated Qz-vector divergence and Qp-vector divergence are generally similar.Both perform better than the classical quasigeostrophic Q vector and nongeostrophic Q vector in indicating the development of the precipitation system.

Adaptive Walking of a Quadrupedal Robot Based on Layered Biological Reflexes

A multiple-legged robot is traditionally controlled by using its dynamic model.But the dynamic-model-based approach fails to acquire satisfactory performances when the robot faces rough terrains and unknown environments.Referring animals＇ neural control mechanisms,a control model is built for a quadruped robot walking adaptively.The basic rhythmic motion of the robot is controlled by a well-designed rhythmic motion controller（RMC） comprising a central pattern generator（CPG） for hip joints and a rhythmic coupler（RC） for knee joints.CPG and RC have relationships of motion-mapping and rhythmic couple.Multiple sensory-motor models,abstracted from the neural reflexes of a cat,are employed.These reflex models are organized and thus interact with the CPG in three layers,to meet different requirements of complexity and response time to the tasks.On the basis of the RMC and layered biological reflexes,a quadruped robot is constructed,which can clear obstacles and walk uphill and downhill autonomously,and make a turn voluntarily in uncertain environments,interacting with the environment in a way similar to that of an animal.The paper provides a biologically inspired architecture,with which a robot can walk adaptively in uncertain environments in a simple and effective way,and achieve better performances.

The Fractal Dimensions of the Level Sets of the Generalized Iterated Brownian Motion

Let{W1（t）, t∈R＋} and {W2（t）, t∈R＋} be two independent Brownian motions with W1（0） = W2（0） = 0. {H （t） = W1（｜W2（t）｜）, t ∈R＋} is called a generalized iterated Brownian motion. In this paper, the Hausdorff dimension and packing dimension of the level sets {t ∈[0, T ], H（t） = x} are established for any 0 T ≤ 1.

Gravidynamics,spinodynamics and electrodynamics within the framework of gravitational quantum field theory

By noticing the fact that the charged leptons and quarks in the standard model are chirality-based Dirac spinors since their weak interaction violates maximally parity symmetry though they behave as Dirac fermions in electromagnetic interaction,we show that such a chirality-based Dirac spinor possesses not only electric charge gauge symmetry U(1)but also inhomogeneous spin gauge symmetry WS(1,3)=SP(1,3)?W1,3,which reveals the nature of gravity and spacetime.The gravitational force and spin gauge force are governed by the gauge symmetries W1,3and SP(1,3),respectively,and a biframe spacetime with globally fiat Minkowski spacetime as base spacetime and locally fiat gravigauge spacetime as a fiber is described by the gravigauge field through emergent non-commutative geometry.The gauge-geometry duality and renormalizability in gravitational quantum field theory(GQFT)are carefully discussed.A detailed analysis and systematic investigation on gravidynamics and spinodynamics as well as electrodynamics are carried out within the framework of GQFT.A full discussion on the generalized Dirac equation and Maxwell equation as well as Einstein equation and spin gauge equation is made in biframe spacetime.New effects of gravidynamics as extension of general relativity are particularly analyzed.All dynamic equations of basic fields are demonstrated to preserve the spin gauge covariance and general coordinate covariance due to the spin gauge symmetry and emergent general linear group symmetry GL(1,3,R),so they hold naturally in any spinning reference frame and motional reference frame.