Velocity,temperature, and Reynolds-stress scaling in the wall region of turbulent boundary layer on a permeable surface

A finite total number of flow parameters in the wall region of a turbulent boundary layer points to universal behavior of turbulent shear stress as a function of mean-velocity gradient and turbulent heat flux as a function of both mean-velocity and mean-temperature gradients. Combined with dimensional arguments, this fact is used to reduce the momentum and heat equations to first-order ordinary differential equations for temperature and velocity profiles amenable to general analysis. Scaling laws for velocity and temperature in boundary layer flows with transpiration are obtained as generalizations of well-known logarithmic laws. Scaling relations are also established for shear stress and rms transverse velocity fluctuation. The proposed method has substantial advantages as compared to the classical approach (which does not rely on fluid-dynamics equations [1–3]). It can be applied to establish scaling laws for a broader class of near-wall turbulence problems without invoking closure hypotheses.     

A general theory of conservation laws,their violation,and spontaneous phenomena

We formulate a general theory of conservation laws and other invariants for a physical system through equivalence relations. The conservation laws are classified according to the type of equivalence relation, with group equivalence, homotopical equivalence, and other types of equivalence relations giving respective kinds of conservation laws. The stability properties in the topological (and differentiable) sense are discussed using continuous deformations with respect to control parameters. The conservation laws due to the Abelian symmetries are shown to be stable through application of well-known theorems.     

Vectorial laws of refraction and reflection using the cross product and dot product

We demonstrate that published vectorial laws of reflection and refraction of light based solely on the cross product do not, in general, uniquely determine the direction of the reflected and refracted waves without additional information. This is because the cross product does not have a unique inverse operation, which is explained in this Letter in linear algebra terms. However, a vector is in fact uniquely determined if both the cross product (vector product) and dot product (scalar product) with a known vector are specified, which can be written as a single equation with a left-invertible matrix. It is thus possible to amend the vectorial laws of reflection and refraction to incorporate both the cross and dot products for a complete specification with unique solution. This enables highly efficient, unambiguous computation of reflected and refracted wave vectors from the incident wave and surface normal.     

Thermodynamics and Preferred Frame

The Lorentz covariant statistical physics and thermodynamics is formulated within the preferred frame approach. The transformation laws for geometrical and mechanical quantities such as volume and pressure as well as the Lorentz-invariant measure on the phase space are found using Lorentz transformations in absolute synchronization. Next, the probability density and partition function are investigated using the preferred frame approach, and the transformation laws for internal energy, entropy, temperature and other thermodynamical potentials are established. The Lorentz covariance of basic thermodynamical relations, including Clapeyron's equation and Maxwell's relations is shown. Finally, the relation of presented approach to the previous approaches to relativistic thermodynamics is briefly discussed.     

Are There Dynamical Laws?

The nature of a physical law is examined, and it is suggested that there may not be any fundamental dynamical laws. This explains the intrinsic indeterminism of quantum theory. The probabilities for transition from a given initial state to a final state then depends on the quantum geometry that is determined by symmetries, which may exist as relations between states in the absence of dynamical laws. This enables the experimentally well-confirmed quantum probabilities to be derived from the geometry of Hilbert space and gives rise to effective probabilistic laws. An arrow of time which is consistent with the one given by the second law of thermodynamics, regarded as an effective law, is obtained. Symmetries are used as the basis for a new proposed paradigm of physics. This naturally gives rise to the gravitational and gauge fields from the symmetry group of the standard model and a general procedure for obtaining interactions from any symmetry group.     

Approximation of Green's functions

Special symmetries of the Green's functions of a non-relativistic many fermion-system and conservation laws, expressible by hermitian generators, are formulated as relations for a Green's function operator. Approximations for the Green's functions, defined as partial summations of the perturbation expansion, and consistent with the symmetries and conservation laws are presented.     

Über die Beziehungen zwischen raumladungsbegrenzten Dunkelströmen und gesättigten Photoströmen

The current-voltage characteristics of trap-free photoconductors with ohmic contacts are calculated for large applied voltages. No restriction is made with respect to the magnitude of the excitation rate. However, the recombination rate is assumed to be linear. It is shown that also under these much more general conditions one has to distinguish between the same groups of photoconductors and one obtains essentially the same expressions for the saturated parts of the photocurrent as they were found earlier for low excitation rates and neutral contacts. In particular it is concluded that to each group belongs one of the different laws for space-charge-limited currents. Therefore, the range of validity of these different laws is defined by the same conditions as the different groups of photoconductors, namely by order-of-magnitude relations between the dielectric relaxation time and the carrier life time on one hand and the transit times of both carriers on the other hand.     

Newtonian gravitational field theory

A field theory for gravitation is developed within the framework of the special theory of relativity. This is achieved by exploiting the similarity in mathematical structure of two relations which are found in both Newton's gravitational theory and Maxwell's electromagnetic theory. These relations are: (1) the law of force between the relevant physical entities (mass and electric charge), and (2) the equation of continuity (conservation of charge). The field equations describe the propagation of gravitational waves with the velocity of light in much the same way that Maxwell's field equations describe electromagnetic waves. Both fields have such similar mathematical structures that they are developed in parallel up to the point where their inherently different physical content cause their paths of evolution to diverge. At this stage, the field equations for both theories are determined. The physical significance of the field variables of both theories imposes a mathematical formalism which doesnot give rise to self-interactions. A calculation for the energy in the field of two particles representative of either the electromagnetic or gravitational field is shown to give the correct finite value. The reason that conventional calculations yield an infinite energy is readily seen to lie in the calculation of a physically meaningless quantity. The mathematical formalism required by the field theories is used to develop generalizations of the usual conservation laws. Two conservation laws are derived which are consequences of the consistent physical interpretation of the field variables. These laws do not appear in conventional theory. The approach followed here in developing the field theories leads to the appearance of forces dual to the well-known forces. Thus, for the electromagnetic field, we find a dual to the Lorentz force and, in the gravitational field, we find a dual to Newton's law of gravitation. These results are not due to the introduction of the fields, for they can be expressed in terms of the particle variables. They emerge from the consistent application of the physical interpretation of the particle and field variables. A basic physical principle, which underlies both theories, is best expressed by the statement: It is the interactions between the elements of a physical event and not the elements themselves which are the physical observables.     

Constraints,dissipation functions and cholesteric liquid crystals

Our recently introduced dissipation function theory of molecular liquids and solids is extended to include constrained motions. Lagrangian multipliers are used in the reversible parts of the field equations of motion. Conservation laws of mass, momentum, energy and angular momentum are derived (in both the material and spatial frames) and shown to hold under the same general conditions as in the unconstrained case. Our theory is then applied to liquid crystals. Within our formalism, constitutive relations characterizing linear and nonlinear liquid crystals are given. In the linear regime, for cholesterics, depending on whether the heat flux or the temperature gradient is used in the dissipation function we show that different reciprocal relations follow. Our results for incompressible nematics and cholesterics are compared with the Ericksen-Leslie theory and others.     

Continuous Correspondence of Conservation Laws of the Semi-discrete AKNS System

In this paper we investigate the semi-discrete Ablowitz–Kaup–Newell–Segur (sdAKNS) hierarchy, and specifically their Lax pairs and infinitely many conservation laws, as well as the corresponding continuum limits. The infinitely many conserved densities derived from the Ablowitz-Ladik spectral problem are trivial, in the sense that all of them are shown to reduce to the first conserved density of the AKNS hierarchy in the continuum limit. We derive new and nontrivial infinitely many conservation laws for the sdAKNS hierarchy, and also the explicit combinatorial relations between the known conservation laws and our new ones. By performing a uniform continuum limit, the new conservation laws of the sdAKNS system are then matched with their counterparts of the continuous AKNS system.     

腔QED中超导量子干涉仪概率克隆机的物理实现

提出一个量子概率克隆机的物理实现方案,该方案首先将高Q腔中的两个超导量子干涉仪分别作为初始比特和目标比特,腔模作为测量比特,通过腔模和经典微波脉冲与超导量子干涉仪的多种相互作用实现量子概率克隆机的幺正演化;然后将腔模态映射到另一个超导量子干涉仪上,通过对该超导量子干涉仪磁通量的测量完成状态坍缩,从而以最优的成功概率实现量子态的精确克隆.本方案采用双光子拉曼共振过程加快单比特门的操作速率,并且总操作时间远小于自发辐射和腔模衰变时间,因而在实验上是可行的.     

The effect of temperature on laws of minor hysteresis loops in nickel single crystals with compressive deformation

The temperature dependence of minor hysteresis loops of compressively deformed nickel single crystals has been investigated in a wide temperature range below the Curie temperature of 628 K. There exist power-law relations between the field-dependent parameters of minor-loops, and their exponents are independent of both temperature and strain after the compressive deformation. These observations indicate the presence of universal power laws in minor hysteresis loops. The minor-loop coefficients of the power laws show a similar temperature dependence of the coercive force, which is quantitatively related to the dislocation density. These properties of minor hysteresis loops are useful for the accurate and quantitative nondestructive evaluation of age degradation in ferromagnetic materials.     

A spatial network explanation for a hierarchy of urban power laws

Power laws in socioeconomic systems are generally explained as being generated by multiplicative growth of aggregate objects. In this paper we formulate a model of geographic activity distribution with spatial correlations on the level of land lots where multiplicative growth is assumed to be dominant but not exclusive. The purpose is to retain the explanatory power of earlier models due to Simon, Gibrat and others while attaining some additional properties that are attractive for both empirical and modelling purposes. In this sense, the model presented here is a combination of the two factors that have been identified as central to urban evolution but rarely appear unified in the same model: transportation costs and multiplicative growth. The model is an elaboration of a previously reported complex network model of geographical land value evolution. We reproduce statistical properties of an empirical geographical distribution of land values on multiple hierarchical levels: land value per unit area, cluster areas, aggregated land value per cluster and cluster area/perimeter ratios. It is found that transportation effects are not strong enough to disturb the power law distribution of land values per unit area but strong enough to sort nodes to generate a new set of power laws on a higher level of aggregation. The main hypothesis is that all these relations can be understood as consequences of an underlying growing scale-free network of geographic economic interdependencies.     

Micromorphic Electromagnetic Theory and Waves

This paper introduces a continuum microelectromagnetic theory (also called micromorphic electromagnetic theory), to discuss electromagnetic phenomena in bodies with microstructures. Balance laws of microelectromagnetic media of the first-grade are given. Constitutive equations are developed. The field equations are obtained . It has been shown that, this theory gives rise to several new vector and tensor waves. A theorem of conservation of energy (Poynting type) is proved. Dispersion relations are obtained for both vector and tensor waves. Relations of tensor waves to microscopic phenomena (such as spin waves) are discussed.     

Onsager Relations and Eulerian Hydrodynamic Limit for Systems with Several Conservation Laws

We present the derivation of the hydrodynamic limit under Eulerian scaling for a general class of one-dimensional interacting particle systems with two or more conservation laws. Following Yau's relative entropy method it turns out that in case of more than one conservation laws, in order that the system exhibit hydrodynamic behaviour, some particular identities reminiscent of Onsager's reciprocity relations must hold. We check validity of these identities whenever a stationary measure with product structure exists. It also follows that, as a general rule, the equilibrium thermodynamic entropy (as function of the densities of the conserved variables) is a globally convex Lax entropy of the hyperbolic systems of conservation laws arising as hydrodynamic limit. As concrete examples we also present a number of models modeling deposition (or domain growth) phenomena. The Onsager relations arising in the context of hydrodynamic limits under hyperbolic scaling seem to be novel. The fact that equilibrium thermodynamic entropy is Lax entropy for the arising Euler equations was noticed earlier in the context of Hamiltonian systems with weak noise, see ref. 7.     

Conservation laws in de Sitter space from action principles in five-space

By recognizing the resemblance of the de Sitter group algebra to that of the conformal group, the method by which manifestly conformally covariant field equations in sixdimensional space are rewritten in Minkowski space is adapted to fields in flat five-dimensional space, the embedding space of de Sitter space. A quantum action principle based solely on rotational invariance in five-dimensional space is devised, and the resulting commutation relations are shown to correspond to the correct ones in curved four-space. As well as recovering the ten conservation laws associated with de Sitter group invariance, the five extra conservation laws present whenever conformal symmetry holds are determined directly in five-space. The derivation is found to be complicated by a new feature—the Lagrangian density does not transform as a field either for special conformal transformations or for dilations; this is true only for the former transformations in flat space.     

Conformal Symmetry and Quantum Relativity

The relativistic conception of space and time is challenged by the quantum nature of physical observables. It has been known for a long time that Poincare symmetry of field theory can be extended to the larger conformal symmetry. We use these symmetries to define quantum observables associated with positions in space-time, in the spirit of Einstein theory of relativity. This conception of localization may be applied to massive as well as massless fields. Localization observables are defined as to obey Lorentz covariant commutation relations and in particular include a time observable conjugated to energy. While position components do not commute in the presence of a nonvanishing spin, they still satisfy quantum relations which generalize the differential laws of classical relativity. We also give of these observables a representation in terms of canonical spatial positions, canonical spin components, and a proper time operator conjugated to mass. These results plead for a new representation not only of space-time localization but also of motion.