scholarly journals On the Hamiltonian approach: Applications to geophysical flows

1998 ◽  
Vol 5 (4) ◽  
pp. 219-240 ◽  
Author(s):  
V. Goncharov ◽  
V. Pavlov
Keyword(s):  
Degrees Of Freedom ◽  
Fluid Motion ◽  
Gauge Transformations ◽  
Motion Models ◽  
Canonical Variables ◽  
Long Time ◽  
Minimum Number ◽  
Nonlinear Gauge ◽  
Hydrodynamical System ◽  
General Method

Abstract. This paper presents developments of the Harniltonian Approach to problems of fluid dynamics, and also considers some specific applications of the general method to hydrodynamical models. Nonlinear gauge transformations are found to result in a reduction to a minimum number of degrees of freedom, i.e. the number of pairs of canonically conjugated variables used in a given hydrodynamical system. It is shown that any conservative hydrodynamic model with additional fields which are in involution may be always reduced to the canonical Hamiltonian system with three degrees of freedom only. These gauge transformations are associated with the law of helicity conservation. Constraints imposed on the corresponding Clebsch representation are determined for some particular cases, such as, for example. when fluid motions develop in the absence of helicity. For a long time the process of the introduction of canonical variables into hydrodynamics has remained more of an intuitive foresight than a logical finding. The special attention is allocated to the problem of the elaboration of the corresponding regular procedure. The Harniltonian Approach is applied to geophysical models including incompressible (3D and 2D) fluid motion models in curvilinear and lagrangian coordinates. The problems of the canonical description of the Rossby waves on a rotating sphere and of the evolution of a system consisting of N singular vortices are investigated.

scholarly journals Hamiltonian analysis of a topological theory in the presence of boundaries

2019 ◽  
Vol 28 (06) ◽  
pp. 1950075 ◽  
Author(s):  
Alejandro Corichi ◽  
Tatjana Vukašinac
Keyword(s):  
Boundary Conditions ◽  
Degrees Of Freedom ◽  
Boundary Theory ◽  
Gauge Transformations ◽  
Canonical Variables ◽  
Dimensional Spacetime ◽  
Constraint Structure ◽  
Generic Boundary ◽  
The One ◽  
Hamiltonian Analysis

We perform the canonical Hamiltonian analysis of a topological gauge theory, that can be seen both as a theory defined on a four-dimensional spacetime region with boundaries — the bulk theory —, or as a theory defined on the boundary of the region — the boundary theory —. In our case, the bulk theory is given by the 4-dimensional [Formula: see text] Pontryagin action and the boundary one is defined by the [Formula: see text] Chern–Simons action. We analyze the conditions that need to be imposed on the bulk theory so that the total Hamiltonian, smeared constraints and generators of gauge transformations be well defined (differentiable) for generic boundary conditions. We pay special attention to the interplay between the constraints and boundary conditions in the bulk theory on the one side, and the constraints in the boundary theory, on the other side. We illustrate how both theories are equivalent, despite the different canonical variables and constraint structure, by explicitly showing that they both have the same symmetries, degrees of freedom and observables.

CONSISTENT CANONICAL QUANTIZATION OF THE CHIRAL SCHWINGER MODEL

1991 ◽  
Vol 06 (21) ◽  
pp. 3823-3841 ◽  
Author(s):  
FUAD M. SARADZHEV
Keyword(s):  
Canonical Quantization ◽  
Bound State ◽  
Gauge Invariant ◽  
Gauge Transformations ◽  
Schwinger Model ◽  
Canonical Variables ◽  
Bound State Spectrum

For the chiral Schwinger model, the canonical quantization formulation consistent with the Gauss law constraint is developed. This requires modification of the canonical variables of the model. The formulation presented is unitary and gauge-invariant under modified gauge transformations. The bound state spectrum of the model is established.

Systematic Synthesis and Applications of Novel Multi-Degree-of-Freedom Differential Systems

1992 ◽  
Author(s):  
Sridhar Kota ◽  
Srinivas Bidare
Keyword(s):  
Degrees Of Freedom ◽  
Building Blocks ◽  
Degree Of Freedom ◽  
Differential Systems ◽  
Practical Applications ◽  
Epicyclic Gear ◽  
Differential Mechanism ◽  
Long Time ◽  
Gear Trains ◽  
Drive Systems

Abstract A two-degree-of-freedom differential system has been known for a long time and is widely used in automotive drive systems. Although higher degree-of-freedom differential systems have been developed in the past based on the well-known standard differential, the number of degrees-of-freedom has been severely restricted to 2n. Using a standard differential mechanism and simple epicyclic gear trains as differential building blocks, we have developed novel whiffletree-like differential systems that can provide n-degrees of freedom, where n is any integer greater than two. Symbolic notation for representing these novel differentials is also presented. This paper presents a systematic method of deriving multi-degree-of-freedom differential systems, a three and four output differential systems and some of their practical applications.

scholarly journals Degrees-Of-Freedom in Multi-Cloud Based Sectored Cellular Networks

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 668
Author(s):  
Samet Gelincik ◽  
Ghaya Rekaya-Ben Othman
Keyword(s):  
Cellular Networks ◽  
Degrees Of Freedom ◽  
Signal To Noise Ratio ◽  
Base Stations ◽  
Processing Capacity ◽  
Coding Schemes ◽  
Minimum Number ◽  
Cut Set ◽  
Base Band ◽  
Multi Cloud

This paper investigates the achievable per-user degrees-of-freedom (DoF) in multi-cloud based sectored hexagonal cellular networks (M-CRAN) at uplink. The network consists of N base stations (BS) and K ≤ N base band unit pools (BBUP), which function as independent cloud centers. The communication between BSs and BBUPs occurs by means of finite-capacity fronthaul links of capacities C F = μ F · 1 2 log ( 1 + P ) with P denoting transmit power. In the system model, BBUPs have limited processing capacity C BBU = μ BBU · 1 2 log ( 1 + P ) . We propose two different achievability schemes based on dividing the network into non-interfering parallelogram and hexagonal clusters, respectively. The minimum number of users in a cluster is determined by the ratio of BBUPs to BSs, r = K / N . Both of the parallelogram and hexagonal schemes are based on practically implementable beamforming and adapt the way of forming clusters to the sectorization of the cells. Proposed coding schemes improve the sum-rate over naive approaches that ignore cell sectorization, both at finite signal-to-noise ratio (SNR) and in the high-SNR limit. We derive a lower bound on per-user DoF which is a function of μ BBU , μ F , and r. We show that cut-set bound are attained for several cases, the achievability gap between lower and cut-set bounds decreases with the inverse of BBUP-BS ratio 1 r for μ F ≤ 2 M irrespective of μ BBU , and that per-user DoF achieved through hexagonal clustering can not exceed the per-user DoF of parallelogram clustering for any value of μ BBU and r as long as μ F ≤ 2 M . Since the achievability gap decreases with inverse of the BBUP-BS ratio for small and moderate fronthaul capacities, the cut-set bound is almost achieved even for small cluster sizes for this range of fronthaul capacities. For higher fronthaul capacities, the achievability gap is not always tight but decreases with processing capacity. However, the cut-set bound, e.g., at 5 M 6 , can be achieved with a moderate clustering size.

scholarly journals Two degrees of freedom, dynamic, hand-wrist EMG-force using a minimum number of electrodes

2019 ◽  
Vol 47 ◽  
pp. 10-18 ◽  
Author(s):  
Chenyun Dai ◽  
Ziling Zhu ◽  
Carlos Martinez-Luna ◽  
Thane R. Hunt ◽  
Todd R. Farrell ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Two Degrees Of Freedom ◽  
Minimum Number

Best Structural Theories for Free Vibrations of Sandwich Composites via Machine Learning

2019 ◽  
Author(s):  
Marco Petrolo ◽  
Erasmo Carrera
Keyword(s):  
Degrees Of Freedom ◽  
Computational Cost ◽  
Free Vibrations ◽  
Numerical Results ◽  
Design Parameters ◽  
Sandwich Composites ◽  
Accuracy Requirement ◽  
Minimum Number ◽  
Carrera Unified Formulation ◽  
Structural Theories

Abstract This work presents a novel methodology for the development of refined structural theories for the modal analysis of sandwich composites. Such a methodology combines three well-established techniques, namely, the Carrera Unified Formulation (CUF), the Axiomatic/Asymptotic Method (AAM), and Artificial Neural Networks (NN). CUF generates structural theories and finite element arrays hierarchically. CUF provides the training set for the NN in which the structural theories are inputs and the natural frequencies targets. AAM evaluates the influence of each generalized displacement variable, and NN provides Best Theory Diagrams (BTD), i.e., curves providing the minimum number of nodal degrees of freedom required to satisfy a given accuracy requirement. The aim is to build BTD with far less computational cost than in previous works. The numerical results consider sandwich spherical shells with soft cores and different features, such as thickness and curvature to investigate their influence on the choice of generalized displacement variables. The numerical results show the importance of third-order generalized displacement variables and prove that the present framework can be of interest to evaluate the performance of any structural theory as typical design parameters change and provide guidelines to the analysts on the most convenient computational model to save computational cost without accuracy penalties.

scholarly journals Structure of nonlinear gauge transformations

1998 ◽  
Vol 57 (4) ◽  
pp. R2263-R2266 ◽  
Author(s):  
Marek Czachor
Keyword(s):  
Gauge Transformations ◽  
Nonlinear Gauge
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