scholarly journals A Simple Construction of a Thermodynamically Consistent Mathematical Model for Non-Isothermal Flows of Dilute Compressible Polymeric Fluids

Fluids ◽  
2020 ◽  
Vol 5 (3) ◽  
pp. 133
Author(s):  
Mark Dostalík ◽  
Josef Málek ◽  
Vít Průša ◽  
Endre Süli
Keyword(s):  
Finite Amplitude ◽  
Homogeneous State ◽  
Cauchy Stress ◽  
Polymeric Fluids ◽  
Classical Models ◽  
Explicit Formulae ◽  
Isothermal Flows ◽  
Elementary Manner ◽  
Production Mechanisms ◽  
Thermodynamic Basis

We revisit some classical models for dilute polymeric fluids, and we show that thermodynamically consistent models for non-isothermal flows of these fluids can be derived in a very elementary manner. Our approach is based on the identification of energy storage mechanisms and entropy production mechanisms in the fluid of interest, which, in turn, leads to explicit formulae for the Cauchy stress tensor and for all of the fluxes involved. Having identified these mechanisms and derived the governing equations, we document the potential use of the thermodynamic basis of the model in a rudimentary stability analysis. In particular, we focus on finite amplitude (nonlinear) stability of a stationary spatially homogeneous state in a thermodynamically isolated system.

Independence polynomial and matching polynomial of the Koch network

2015 ◽  
Vol 29 (32) ◽  
pp. 1550234
Author(s):  
Yunhua Liao ◽  
Xiaoliang Xie
Keyword(s):  
Lattice Gas ◽  
Small World ◽  
Partition Functions ◽  
Complete Class ◽  
Dimer Model ◽  
Scale Free ◽  
Matching Polynomial ◽  
Independence Polynomial ◽  
Classical Models ◽  
Explicit Formulae

The lattice gas model and the monomer-dimer model are two classical models in statistical mechanics. It is well known that the partition functions of these two models are associated with the independence polynomial and the matching polynomial in graph theory, respectively. Both polynomials have been shown to belong to the “[Formula: see text]-complete” class, which indicate the problems are computationally “intractable”. We consider these two polynomials of the Koch networks which are scale-free with small-world effects. Explicit recurrences are derived, and explicit formulae are presented for the number of independent sets of a certain type.

Internal waves of finite amplitude and permanent form

1966 ◽  
Vol 25 (2) ◽  
pp. 241-270 ◽  
Author(s):  
T. Brooke Benjamin
Keyword(s):  
Internal Waves ◽  
Present Theory ◽  
Boussinesq Approximation ◽  
Finite Amplitude ◽  
Physical Models ◽  
Physical Conditions ◽  
Explicit Formulae ◽  
The Waves ◽  
Wave Phenomena ◽  
Permanent Form

A theory is derived for the class of long two-dimensional waves, comprising solitary and periodic cnoidal waves, that can propagate with unchanging form in heterogeneous fluids. The treatment is generalized to the extent that the waves are supposed to arise on a horizontal stream of incompressible fluid whose density and velocity are arbitrary functions of height, and the upper surface of the fluid is allowed either to be free or to be fixed in a horizontal plane. Explicit formulae for the wave properties and a general interpretation of the physical conditions for the occurrence of the waves are achieved without need to specify particular physical models; but in a later part of the paper, §4, the results are applied to three examples that have been worked out by other means and so provide checks on the present theory. These general results are also shown to accord nicely with the principle of ‘conjugate-flow pairs’ which was explained by Benjamin (1962b) with reference to swirling flows along cylindrical ducts, but which is known to apply equally well to flow systems of the kind in question here.The theory reveals certain physical peculiarities of a type of flow model often used in theoretical studies of internal-wave phenomena, being specified so as to make the equation for the stream-function linear. In an appendix, some observations are also made regarding the ‘Boussinesq approximation’, which too is often used as a simplifying assumption in this field. It is shown, adding to a recent discussion by Long (1965), that finite internal waves may depend crucially on small effects neglected in this approximation.

scholarly journals A multi-scale method for complex flows of non-Newtonian fluids

2021 ◽  
Vol 4 (6) ◽  
pp. 1-22
Author(s):  
Francesca Tedeschi ◽  
◽  
Giulio G. Giusteri ◽  
Leonid Yelash ◽  
Mária Lukáčová-Medvid'ová ◽  
...  
Keyword(s):  
Newtonian Fluids ◽  
Cauchy Stress ◽  
Complex Flows ◽  
Polymeric Fluids ◽  
Local Flow ◽  
Micro Scale ◽  
Multi Scale ◽  
Scale Method ◽  
Model Free ◽  
Macro Scale

<abstract><p>We introduce a new heterogeneous multi-scale method for the simulation of flows of non-Newtonian fluids in general geometries and present its application to paradigmatic two-dimensional flows of polymeric fluids. Our method combines micro-scale data from non-equilibrium molecular dynamics (NEMD) with macro-scale continuum equations to achieve a data-driven prediction of complex flows. At the continuum level, the method is model-free, since the Cauchy stress tensor is determined locally in space and time from NEMD data. The modelling effort is thus limited to the identification of suitable interaction potentials at the micro-scale. Compared to previous proposals, our approach takes into account the fact that the material response can depend strongly on the local flow type and we show that this is a necessary feature to correctly capture the macroscopic dynamics. In particular, we highlight the importance of extensional rheology in simulating generic flows of polymeric fluids.</p></abstract>

Simulation Tool for Assignment Models: SIMASI

2014 ◽  
Vol 13 (8) ◽  
pp. 4723-4728
Author(s):  
Pratiksha Saxena ◽  
Smt. Anjali
Keyword(s):  
Optimization Procedure ◽  
Simulation Tool ◽  
Optimization Strategy ◽  
Performance Measurements ◽  
Integrated Simulation ◽  
Assignment Model ◽  
Classical Models ◽  
Simulation Results ◽  
User Friendly ◽  
Assignment Models

In this paper, an integrated simulation optimization model for the assignment problems is developed. An effective algorithm is developed to evaluate and analyze the back-end stored simulation results. This paper proposes simulation tool SIMASI (Simulation of assignment models) to simulate assignment models. SIMASI is a tool which simulates and computes the results of different assignment models. This tool is programmed in DOT.NET and is based on analytical approach to guide optimization strategy. Objective of this paper is to provide a user friendly simulation tool which gives optimized assignment model results. Simulation is carried out by providing the required values of matrix for resource and destination requirements and result is stored in the database for further comparison and study. Result is obtained in terms of the performance measurements of classical models of assignment system. This simulation tool is interfaced with an optimization procedure based on classical models of assignment system. The simulation results are obtained and analyzed rigorously with the help of numerical examples. 

Finite amplitude disturbances in a rotating fluid

Tellus ◽  
1971 ◽  
Vol 23 (1) ◽  
pp. 82-86
Author(s):  
Robert R. Long
Keyword(s):  
Finite Amplitude ◽  
Rotating Fluid
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