scholarly journals Degrees of freedom of MIMO X networks: Spatial scale invariance, one-sided decomposability and linear feasibility

2012 ◽  
Author(s):  
Hua Sun ◽  
Chunhua Geng ◽  
Tiangao Gou ◽  
Syed A. Jafar
Keyword(s):  
Spatial Scale ◽  
Scale Invariance ◽  
Degrees Of Freedom ◽  
Linear Feasibility

All-atomistic molecular dynamics study of the glass transition of amorphous polymers

2021 ◽  
Author(s):  
Zhiye Tang ◽  
Susumu Okazaki
Keyword(s):  
Molecular Dynamics ◽  
Glass Transition ◽  
Spatial Scale ◽  
Degrees Of Freedom ◽  
Main Chain ◽  
Polymer Materials ◽  
Coarse Grained ◽  
Mode Analysis ◽  
Radius Of Gyration ◽  
Chemical Structures

Glass transition is an important phenomenon of polymer materials and it has been intensively studied over the past a few decades. However, the influencing factors arising from the chemical structures of the polymers are often ignored due to a continuous or coarse-grained description of the polymer. Here, we approached this phenomenon using all-atomistic molecular dynamics (MD) simulations and two conventionally used polymer materials, polycarbonate (PC) and poly-(methyl methacrylate) (PMMA). We reproduced the glass transition temperatures (Tg) of the two materials reasonably well. Then we characterized and investigated the glass transition process by looking at the changes of potential energy, dihedral transition, and thermal fluctuation of the individual degrees of freedom in the systems, over the entire temperature range of glass transition. As previously reported, the dihedral angles stop their conformational changes gradually at the Tg, especially for the main chain dihedrals, and sidechain rotations immediately rooting from the main chain. The volumetric change during the temperature decrease is confirmed to be because of conformational adjustment, probably due to the tendency of chain stretching for the maintenance of the radius of gyration, and the loss of thermal energy. The strength of motions of single degrees of freedom and polymer chains, and overall slow motions obtained by normal mode analysis (NMA) shows that different motions at different spatial scale may gradually stop at distinct temperature in the MD simulation temporal and spatial scales. Presumably, the small spatial scale do not contribute to the glass transition at the experimental scale since the timescale is much longer than their relaxation time.

Neighbourhood rules make or break spatial scale invariance in a classic model of contagious disturbance

2011 ◽  
Vol 8 (4) ◽  
pp. 347-356 ◽  
Author(s):  
Matthias M. Boer ◽  
Paul Johnston ◽  
Rohan J. Sadler
Keyword(s):  
Spatial Scale ◽  
Scale Invariance ◽  
Classic Model

scholarly journals Spatial scale invariance of southern Australian forest fires mirrors the scaling behaviour of fire-driving weather events

2008 ◽  
Author(s):  
Matthias M. Boer ◽  
Rohan J. Sadler ◽  
Ross A. Bradstock ◽  
A. Malcolm Gill ◽  
Pauline F. Grierson
Keyword(s):  
Spatial Scale ◽  
Forest Fires ◽  
Scale Invariance ◽  
Scaling Behaviour ◽  
Weather Events

QUINTESSENTIAL POTENTIAL, FERMION FAMILIES AND SPONTANEOUS BREAKING OF SCALE SYMMETRY

2002 ◽  
Vol 17 (29) ◽  
pp. 4419-4424 ◽  
Author(s):  
E. I. GUENDELMAN ◽  
A. B. KAGANOVICH
Keyword(s):  
Scale Invariance ◽  
Degrees Of Freedom ◽  
Field Potential ◽  
Momentum Tensor ◽  
Kinetic Term ◽  
Spontaneous Breaking ◽  
Exponential Potential ◽  
Covariant Model ◽  
Fermion Masses ◽  
Generally Covariant

We study a generally covariant model with SSB of scale invariance where two measures of integration in the action enter: the standard [Formula: see text] and a new Φd4x, where Φ is a density built out of degrees of freedom independent of the metric. The theory demonstrates a new mechanism for generation of the exponential potential: in the conformal Einstein frame, after SSB of scale invariance, the theory develops the exponential potential and, in general, non-linear kinetic term is generated as well. The scale symmetry does not allow the appearance of terms breaking the exponential shape of the potential that solves the problem of the flatness of the scalar field potential in the context of quintessential scenarios. Under normal laboratory conditions where the fermionic matter dominates, it is found that starting from a single fermionic field we obtain exactly three different types of spin 1/2 particles which can be identified with known fermion families. It is automatically achieved that for two of them, fermion masses are constants, the energy-momentum tensor is canonical and the "fifth force" is absent. For the third family, a self-interaction appears as a result of SSB of scale invariance.

scholarly journals SCALE INVARIANCE, NEW INFLATION AND DECAYING Λ-TERMS

1999 ◽  
Vol 14 (16) ◽  
pp. 1043-1052 ◽  
Author(s):  
E. I. GUENDELMAN
Keyword(s):  
Scale Invariance ◽  
Degrees Of Freedom ◽  
Vacuum Energy ◽  
Scalar Potential ◽  
Field Potential ◽  
Vacuum State ◽  
Gravitational Theory ◽  
Global Scale ◽  
Kinetic Term ◽  
Decaying Λ

Realizations of scale invariance are studied in the context of a gravitational theory where the action (in the first-order formalism) is of the form [Formula: see text] where Φ is a density built out of degrees of freedom, the "measure fields" independent of gμν and matter fields appearing in L1, L2. If L1 contains the curvature, scalar potential V(ϕ) and kinetic term for ϕ, L2 another potential for ϕ, U(ϕ), then the true vacuum state has zero energy density, when theory is analyzed in the conformal Einstein frame (CEF), where the equations assume the Einstein form. Global scale invariance is realized when V(ϕ)=f1eαϕ and U(ϕ)=f2e2αϕ. In the CEF the scalar field potential energy V eff (ϕ) has, in addition to a minimum at zero, a flat region for αϕ→∞, with nonzero vacuum energy, which is suitable for either a new inflationary scenario for the early universe or for a slowly rolling decaying Λ-scenario for the late universe, where the smallness of the vacuum energy can be understood as a kind of seesaw mechanism.

FERMION FAMILIES AND LONG-RANGE FORCE PROBLEMS: INTERRELATION AND RESOLUTION

2002 ◽  
Vol 11 (10) ◽  
pp. 1591-1595
Author(s):  
E. I. GUENDELMAN ◽  
A. B. KAGANOVICH
Keyword(s):  
Scale Invariance ◽  
Degrees Of Freedom ◽  
Momentum Tensor ◽  
Covariant Model ◽  
Fermion Masses ◽  
Different Types ◽  
Two Measures ◽  
Generally Covariant ◽  
Range Force ◽  
Normal Laboratory

We study a generally covariant model with SSB of scale invariance where two measures of integration in the action enter: the standard [Formula: see text] and a new Φd4x, where Φ is a density built out of degrees of freedom independent of the metric. Under normal laboratory conditions where the fermionic matter dominates, it is found that starting from a single fermionic field we obtain exactly three different types of spin 1/2 particles which can be identified with known fermion families. It is automatically achieved that for two of them, fermion masses are constants, the energy-momentum tensor is canonical and the "fifth force" is absent. For the third family, a self-interaction appears as a result of SSB of scale invariance.

scholarly journals SCALE INVARIANCE AND VACUUM ENERGY

1999 ◽  
Vol 14 (21) ◽  
pp. 1397-1401 ◽  
Author(s):  
E. I. GUENDELMAN
Keyword(s):  
Scale Invariance ◽  
Degrees Of Freedom ◽  
Vacuum Energy ◽  
Gravitational Theory ◽  
Global Scale ◽  
Scale Invariant ◽  
Mass Generation ◽  
First Order ◽  
Mass Terms ◽  
Generally Covariant

The possibility of mass in the context of scale-invariant, generally covariant theories, is discussed. Scale invariance is considered in the context of a gravitational theory where the action, in the first-order formalism, is of the form [Formula: see text] where Φ is a density built out of degrees of freedom independent of the metric. For global scale invariance, a "dilaton" ϕ has to be introduced, with nontrivial potentials V(ϕ)=f1eαϕ in L1 and U(ϕ)=f2e2αϕ in L2. This leads to nontrivial mass generation and a potential for ϕ which is interesting for new inflation. Scale invariant mass terms for fermions lead to a possible explanation of the present day accelerated universe and of cosmic coincidences.

scholarly journals Scale invariant distribution functions in quantum systems with few degrees of freedom

2018 ◽  
Vol 5 (3) ◽  
Author(s):  
Emanuele Dalla Torre
Keyword(s):  
Scale Invariance ◽  
Degrees Of Freedom ◽  
Quantum Systems ◽  
Distribution Functions ◽  
Matter Wave ◽  
Classical Dynamics ◽  
Scale Invariant ◽  
New Type ◽  
Stable Points ◽  
Linear Quantum

Scale invariance usually occurs in extended systems where correlation functions decay algebraically in space and/or time. Here we introduce a new type of scale invariance, occurring in the distribution functions of physical observables. At equilibrium these functions decay over a typical scale set by the temperature, but they can become scale invariant in a sudden quantum quench. We exemplify this effect through the analysis of linear and non-linear quantum oscillators. We find that their distribution functions generically diverge logarithmically close to the stable points of the classical dynamics. Our study opens the possibility to address integrability and its breaking in distribution functions, with immediate applications to matter-wave interferometers.

scholarly journals GEOMETRICAL ORIGIN OF FERMION FAMILIES IN SU(2) × U(1) GAUGE THEORY

2002 ◽  
Vol 17 (19) ◽  
pp. 1227-1237 ◽  
Author(s):  
E. I. GUENDELMAN ◽  
A. B. KAGANOVICH
Keyword(s):  
Gauge Theory ◽  
Particle Physics ◽  
Scale Invariance ◽  
Degrees Of Freedom ◽  
Global Scale ◽  
Covariant Theory ◽  
Fermion Field ◽  
Mass Generation ◽  
Classical Level ◽  
Satisfactory Answer

A spontaneously broken SU (2) × U (1) gauge theory with just one "primordial" generation of fermions is formulated in the context of generally covariant theory which contains two measures of integration in the action: the standard [Formula: see text] and a new Φd4x, where Φ is a density built out of degrees of freedom independent of the metric. Such type of models are known to produce a satisfactory answer to the cosmological constant problem. Global scale invariance is implemented. After SSB of scale invariance and gauge symmetry it is found that with the conditions appropriate to laboratory particle physics experiments, to each primordial fermion field corresponds three physical fermionic states. Two of them correspond to particles with different constant masses and they are identified with the first two generations of the electroweak theory. The third fermionic states at the classical level get nonpolynomial interactions which indicate the existence of fermionic condensate and fermionic mass generation.

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