Conformal invariance of Mei symmetry for discrete Lagrangian systems

The conformal invariance of the Mei symmetry and the conserved quantities are investigated for discrete Lagrangian systems under the infinitesimal transformation of the Lie group. The difference Euler–Lagrange equations on regular lattices of the discrete Lagrangian systems are presented via the transformation operators in the space of the discrete variables. The conformal invariance of the Mei symmetry is defined for the discrete Lagrangian systems. The criterion equations and the determining equations are proposed. The conserved quantities of the systems are derived from the structure equation governing the gauge function. Two examples are given to illustrate the application of the results.     

Emergent physics: Fermi-point scenario

The Fermi-point scenario of emergent gravity has the following consequences: gravity emerges together with fermionic and bosonic matter; emergent fermionic matter consists of massless Weyl fermions; emergent bosonic matter consists of gauge fields; Lorentz symmetry persists well above the Planck energy; space-time is naturally four dimensional; the Universe is naturally flat; the cosmological constant is naturally small or zero; the underlying physics is based on discrete symmetries; 'quantum gravity' cannot be obtained by quantization of Einstein equations; and there is no contradiction between quantum mechanics and gravity, etc.     

Conformal invariance and conserved quantity of Mei symmetry for higher-order nonholonomic system

The conformal invariance and conserved quantity of Mei symmetry for a higher-order nonholonomic mechanical system are presented. Introducing an infinitesimal transformation group and infinitesimal generator vector, the definition of conformal invariance of Mei symmetry and the determining equation for the holonomic system which corresponds to a higher-order nonholonomic system are provided, and the relationship between Mei symmetry and conformal invariance of the system is discussed. The basis of restriction equations and additional restriction equations, the conformal invariance of weak and strong Mei symmetry for the higher-order nonholonomic mechanical system is constructed. With the aid of a structure equation that the gauge function satisfies, the system’s corresponding conserved quantity is derived. Finally, an example is given to illustrate the application of the method and its result.     

Effects of Radiative Corrections on a Quantum Disordered Self-dual Josephson Junction Array

The quantum effective potential of a three-dimensional Abelian Maxwell-mixed-Chern-Simons gauge theory coupled to complex fields and massless fermions is investigated at zero temperature. The insulating phase of the related self-dual Josephson junction array is found to be stable against gauge field fluctuations since these do not induce symmetry breaking terms in the one-loop effective potential. Conversely, coupling to gapless fermions is shown to generate correction terms in the effective potential which change the symmetry of the ground state and favor transitions between the insulating and superconducting states.     

Symmetry and structure: an overview

The many aspects of symmetry are reviewed as a unifying principle in science. Discrete symmetry groups dictate the structures of physical objects and continuous space-time symmetries are the generators of special relativity and quantum operators. Internal symmetry and gauge invariance provide the basis of quantum theory and the electromagnetic field. Approximate global symmetries underpin the formulation of conservations and natural laws in terms of field densities and conserved currents. Symmetry breaking elucidates phenomena such as phase transition, nucleation and crystal growth, superconductivity, the arrow of time and chirality.     

Parameter-free effective potential method for use in particle-based device simulations

We propose a novel parameter-free effective potential scheme for use in conjunction with particle-based simulations. The method is based on a perturbation theory around thermodynamic equilibrium and leads to an effective potential scheme in which the size of the electron depends upon its energy. The approach has been tested on the example of a MOS-capacitor by retrieving the correct sheet electron density. It has also been used in simulations of a 25-nm n-channel nano-MOSFET that requires very high substrate doping to prevent the punch-through effect which, on the other hand, leads to pronounced quantum mechanical space-quantization effects. We find that the use of the new effective potential approach gives correct experimentally verified threshold voltage shifts of about 220 mV and drain current degradation of about 30%. The largest contribution comes from the barrier field which is precomputed in the initial stages of the simulation. Thus, rough estimates on the role of quantum effects on device operation can be made by using the barrier field only.     

Quantisation of the free electromagnetic field implies quantisation of its angular momentum

It is shown that when the gauge-invariant Bohr–Rosenfeld commutators of the free electromagnetic field are applied to the expressions for the linear and angular momentum of the electromagnetic field interpreted as operators then, in the absence of electric and magnetic charge densities, these operators satisfy the canonical commutation relations for momentum and angular momentum. This confirms their validity as operators that can be used in quantum mechanical calculations of angular momentum.     

Angular momentum of light

By means of the Helmholtz theorem on the decomposition of vector fields, the angular momentum of the classical electromagnetic field is decomposed, in a general and manifestly gauge invariant manner, into a spin component and an orbital component. The method is applied to linearly and circularly polarized plane waves in their classical and quantum forms.     

Micro-scale modeling of anisotropy effects on undrained behavior of granular soils

This paper presents a micro-scale modeling of fabric anisotropy effects on the mechanical behavior of granular assembly under undrained conditions using discrete element method. The initial fabrics of the numerical samples engendered from the deposition under gravity are measured, quantified and compared, where the gravitational field can be applied in different directions to generate varying anisotropy orientations. The samples are sheared under undrained biaxial compression, and identical testing conditions are applied, with samples having nearly the same anisotropy intensities, but with different anisotropy directions. The macroscopic behaviors are discussed for the samples, such as the dilatancy characteristics and responses at the critical state. And the associated microstructure changes are further examined, in terms of the variables in the particulate scale, with the focus on the fabric evolution up to a large deformation reaching the critical state. The numerical analysis results compare reasonably well with available experimental data. It is also observed that at critical state, in addition to the requirements by classical critical state theory, a unique fabric structure has also been developed, and might be independent of its initial fabric. This observation is coincided with the recent theoretical achievement of anisotropic critical state theory. Finally, a general framework is introduced for quantifying and modeling the anisotropy effects.     

Relativistic shear-free fluids with symmetry

We study the complete conformal geometry of shear-free spacetimes with spherical symmetry and do not specify the form of the matter content. The equation governing the general conformal Killing symmetry is solved, and we explicitly exhibit the conformal vector. The existence of a conformal symmetry places restrictions on the model. The conditions on the gravitational potentials are expressed as a system of integrability conditions. Timelike sectors and inheriting conformal symmetry vectors, which map fluid flow lines conformally onto fluid flow lines, are generated, and the integrability conditions are shown to be satisfied. As an example, a spacetime, which is expanding and accelerating, is identified that contains a spherically symmetric conformal symmetry.     

On a modified electrodynamics

A modification of electrodynamics is proposed, motivated by previously unremarked paradoxes that can occur in the standard formulation. It is shown by specific examples that gauge transformations exist that radically alter the nature of a problem, even while maintaining the values of many measurable quantities. In one example, a system with energy conservation is transformed to a system where energy is not conserved. The second example possesses a ponderomotive potential in one gauge, but this important measurable quantity does not appear in the gauge-transformed system. A resolution of the paradoxes comes from noting that the change in total action arising from the interaction term in the Lagrangian density cannot always be neglected, contrary to the usual assumption. The problem arises from the information lost by employing an adiabatic cutoff of the field. This is not necessary. Its replacement by a requirement that the total action should not change with a gauge transformation amounts to a supplementary condition for gauge invariance that can be employed to preserve the physical character of the problem. It is shown that the adiabatic cutoff procedure can also be eliminated in the construction of quantum transition amplitudes, thus retaining consistency between the way in which asymptotic conditions are applied in electrodynamics and in quantum mechanics. The ‘gauge-invariant electrodynamics’ of Schwinger is shown to depend on an ansatz equivalent to the condition found here for maintenance of the ponderomotive potential in a gauge transformation. Among the altered viewpoints required by the modified electrodynamics, in addition to the rejection of the adiabatic cutoff, is the recognition that the electric and magnetic fields do not completely determine a physical problem, and that the electromagnetic potentials supply additional information that is required for completeness of electrodynamics.     

Elliptical inclusion problem in antiplane piezoelectricity: Implications for fracture mechanics

An elliptical piezoelectric inclusion embedded in an infinite piezoelectric matrix is analyzed in the framework of linear piezoelectricity. Using the conformal mapping technique, a closed-form solution is obtained for the case of a far-field antiplane mechanical load and an inplane electrical load. The solution to a permeable elliptical hole problem is obtained as a limiting case of vanishing elastic modulus of the inclusion. This enables the study of the nature of crack tip electric field singularity which is shown to depend on the electrical boundary condition imposed on the crack faces. The energy release rate of a self-similarly expanding slender crack in the presence of electric fields is obtained by using the generalized M-integral. The energy release rate expression indicates that the electric field has a crack-arresting influence. This effect is inferred to have a more fundamental physical origin in the interaction between the applied electric field and the induced surface charges on the crack faces. An experimental result contradicting the theoretical prediction on the crack-arresting effect is also discussed.     

Tensors-structured numerical methods in scientific computing: Survey on recent advances

In the present paper, we give a survey of the recent results and outline future prospects of the tensor-structured numerical methods in applications to multidimensional problems in scientific computing. The guiding principle of the tensor methods is an approximation of multivariate functions and operators relying on a certain separation of variables. Along with the traditional canonical and Tucker models, we focus on the recent quantics-TT tensor approximation method that allows to represent N-d tensors with log-volume complexity, O(d log N). We outline how these methods can be applied in the framework of tensor truncated iteration for the solution of the high-dimensional elliptic/parabolic equations and parametric PDEs. Numerical examples demonstrate that the tensor-structured methods have proved their value in application to various computational problems arising in quantum chemistry and in the multi-dimensional/parametric FEM/BEM modeling—the tool apparently works and gives the promise for future use in challenging high-dimensional applications.     

Material symmetry optimization by Kelvin modes

Pointwise optimization of the material symmetry of an anisotropic elastic material with respect to fixed and specified stress (or strain) states is accomplished. The conceptual variables in this problem are the type of material symmetry and the orientation of the canonical symmetry axis for the material at a point in the material. The actual variables are the coefficients of the elasticity (or compliance) matrix. The results are presented in the form of the elasticity (or compliance) matrices that minimize the strain energy with respect to specified, but arbitrary, stress (or strain) states.     

Vibrational Diver

The paper is concerned with dynamics of light solid in cavity with liquid subjected to rotational vibration in the external force field. New vibrational phenomenon – diving of a light cylinder to the cavity bottom is found. The experimental investigation of a horizontal annulus with a partition has shown that under vibration a light body situated in the upper part of the layer is displaced in a threshold manner some distance away from the boundary. In this case the body executes symmetric tangential oscillations. An increase of the vibration intensity leads to a tangential displacement of the body near the external boundary. This displacement is caused by the tangential component of the vibrational lift force, which appears as soon as the oscillations lose symmetry. In this case the trajectory of the body oscillatory motion has the form of a loop. The tangential lift force makes stable the position of the body on the inclined section of the layer and even in its lower part. A theoretical interpretation has been proposed, which explains stabilization of a quasi-equilibrium state of a light body near the cavity bottom in the framework of vibrational hydromechanics.     

Interplay of quantum size effect,anisotropy and surface stress shapes the instability of thin metal films

We show how the conformal mapping technique can be applied to analyse specific problems in the context of viscous gravity current theory. We examine the edge of steady thin planar viscous gravity currents in the presence of complex external low Reynolds flows. In addition to the uniform ambient flow we look at the case of viscous gravity currents spreading in positively strained flows and around cylindrical bodies. These external flows exert shear stress on the gravity current, which drives it in the streamwise direction. The idealised conditions are re-created in the laboratory using a Hele–Shaw cell with a point source on the bottom plate where the saline is introduced into the flow. The mapped laboratory results are compared to a known similarity solution and the agreement is good. We conclude by identifying a broad class of viscous gravity current problems where this technique may be applied.     

Dehnungsmessung mit Hochtemperatur-Dehnungsmeßstreifen im instationären Temperaturfeld unter Berücksichtigung eines zweiachsigen Dehnungszustandes

Strain Measurement with High-Temperature Strain Gauges in a Non Steady Temperature Field Considering a Two Dimensional Strain Field To confirm a FEM-simulation the strain fields at the surface of the hub of a shrink fit are measured during the thermal fitting process. The temperature changes during the fitting process between 420°C and 20°C. Because of the rotation symmetry a two dimensional strain field yields on the surface of the hub. The strain gauge type LF 30 is used. The temperature-dependence could not compensate in a half-bridge compensation-circuit. Because of this each strain gauge application must be calibrated individually. The experimental data is extremely close to the results predicted by the numerical simulation. This is an experimental confirmation of the FEM-simulation.     

Magnetic Quantum Tunneling in the Single-Molecule Magnet Mn12-Acetate

The symmetry of magnetic quantum tunneling (MQT) in the single molecule magnet Mn₂-acetate has been determined by sensitive low-temperature magnetic measurements in the pure quantum tunneling regime and high frequency EPR spectroscopy in the presence of large transverse magnetic fields. The combined data set definitely establishes the transverse anisotropy terms responsible for the low temperature quantum dynamics. MQT is due to a disorder induced locally varying quadratic transverse anisotropy associated with rhombic distortions in the molecular environment (2nd order in the spin-operators). This is superimposed on a 4th order transverse magnetic anisotropy consistent with the global (average) S₄ molecule site symmetry. These forms of the transverse anisotropy are incommensurate, leading to a complex interplay between local and global symmetries, the consequences of which are analyzed in detail. The resulting model explains: (1) the observation of a twofold symmetry of MQT as a function of the angle of the transverse magnetic field when a subset of molecules in a single crystal are studied; (2) the non-monotonic dependence of the tunneling probability on the magnitude of the transverse magnetic field, which is ascribed to an interference (Berry phase)effect; and (3) the angular dependence of EPR absorption peaks, including the fine structure in the peaks, among many other phenomena. This work also establishes the magnitude of the 2nd and 4th order transverse anisotropy terms for Mn₁₂-acetate single crystals and the angle between the hard magnetic anisotropy axes of these terms. EPR as a function of the angle of the field with respect to the easy axes (close to the hard-medium plane) confirms that there are discrete tilts of the molecular magnetic easy axis from the global (average) easy axis of a crystal, also associated with solvent disorder. The latter observation provides a very plausible explanation for the lack of MQT selection rules, which has been a puzzle for many years.