Conformal invariance and Noether symmetry, Lie symmetry of holonomic mechanical systems in event space

This paper is devoted to studying the conformal invariance and Noether symmetry and Lie symmetry of a holonomic mechanical system in event space. The definition of the conformal invariance and the corresponding conformal factors of the holonomic system in event space are given. By investigating the relation between the conformal invariance and the Noether symmetry and the Lie symmetry, expressions of conformal factors of the system under these circumstances are obtained, and the Noether conserved quantity and the Hojman conserved quantity directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.     

Particle effects on the emissivity and temperature of optically thick, mixed media retrieved by mid-IR emission spectroscopy

Passive diagnostics offer new ways of obtaining real-time data for the control and modeling of industrial furnaces. It has been proposed elsewhere that from the intensity profile between 3.8 and 4.7 μm one may derive the temperature of a gas-particle medium and the particle emissivity (ε_p) at 3.95 μm. This technique applies to large columns of combustion products with enough CO₂. The temperature is retrieved by finding the best fit between Planck's function and the intensity profile between 4.56 and 4.7 μm, which is that of a blackbody due to CO₂ saturation. Here we consider the effect of particles on the intensity profile and, therefore, on the retrieved temperature and particle emissivity. We derive an analytic approximation of the effective emissivity for an optically thick gas-particle mixture that includes emission and absorption due to particles and gases, along with isotropic particle scattering. The derivation follows the method of embedded invariance and has been used already for particle-only clouds. It yields a spectral solution that is applicable in other infrared regions where gas and particle optical thicknesses are large. A key parameter (χ) is the ratio of the gas absorption coefficient to the particle extinction coefficient. For χ=1 and ε_p=0.5, particle effects decrease the gas band profile by 5% from that of a blackbody. For χ<1 and ε_p<0.5, particle effects on the calculated temperature and particle emissivity are noticeable and particle effects should be considered. If χ is known, an iterative procedure may be used to calculate temperature and particle emissivity. We illustrate this procedure with data from a coal-fired boiler. Accounting for particle effects, temperatures were 4% higher (at about 1500 K) and particle emissivities 28% lower (for ε_p within 0.3-05) than without considering these effects.     

Conformal Invariance and Noether Symmetry,Lie Symmetry of Birkhoffian Systems in Event Space

This paper focuses on studying a conformal invariance and a Noether symmetry, a Lie symmetry for a Birkhoffian system in event space. The definitions of the conformal invariance of the system are given. By investigation on the relations between the conformal invariance and the Noether symmetry, the conformal invariance and the Lie symmetry, the expressions of conformal factors of the system under these circumstances are obtained. The Noether conserved quantities and the Hojman conserved quantities directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.     

Dark matter and LHC phenomenology of a scale-invariant scotogenic model

We study the phenomenology of a model that addresses the neutrino mass, dark matter, and generation of the electroweak scale in a single framework. Electroweak symmetry breaking is realized via the Coleman-Weinberg mechanism in a classically scale invariant theory, while the neutrino mass is generated radiatively through interactions with dark matter in a typically scotogenic manner. The model introduces a scalar triplet and singlet and a vectorlike fermion doublet that carry an odd parity of Z_2, and an even parity scalar singlet that helps preserve classical scale invariance. We sample over the parameter space by taking into account various experimental constraints from the dark matter relic density and direct detection, direct scalar searches, neutrino mass, and charged lepton flavor violating decays. We then examine by detailed simulations possible signatures at the LHC to find some benchmark points of the free parameters. We find that the future high-luminosity LHC will have a significant potential in detecting new physics signals in the dilepton channel.     

On Propagation of Germ Invariance

We prove the theorems on propagation of C -solution germ invariance for one class of weakly nonlinear differential equations. This class includes generalized versions of KdV, NLS, Boussinesq and other equations of spreading nonlinear waves.     

Modal Interpretations and Relativity

A proof is given, at a greater level of generality than previous no-go theorems, of the impossibility of formulating a modal interpretation that exhibits serious Lorentz invariance at the fundamental level. Particular attention is given to modal interpretations of the type proposed by Bub.     

Weak convergence to the matrix stochastic integral ∫0 B dB′

The asymptotic theory of regression with integrated processes of the ARIMA type frequently involves weak convergence to stochastic integrals of the form ∫₀¹ W dW, where W(r) is standard Brownian motion. In multiple regressions and vector autoregressions with vector ARIMA processes, the theory involves weak convergence to matrix stochastic integrals of the form ∫₀¹ B dB′, where B(r) is vector Brownian motion with a non-scalar covariance matrix. This paper studies the weak convergence of sample covariance matrices to ∫₀¹ B dB′ under quite general conditions. The theory is applied to vector autoregressions with integrated processes.     

Quantum Ashkin-Teller model near the decoupling limit

The critical properties and the spectrum of the quantum Ashkin-Teller chain are investigated by perturbation expansion around the exactly soluble Ising decoupling limit. The critical exponents are found to satisfy the hyperscaling relation and they are consistent with the conjectured values. The critical Hamiltonian in the finite-size scaling limit is transformed into a two-band spin-1/2 Fermi system, where the interaction energy in first order is the product of the band magnetizations. The complete spectrum is shown to exhibit a conformal structure with infinite primary operators, the anomalous dimensions of which are consistent with a Gaussian form.