scholarly journals From kinetic to fluid models of liquid crystals by the moment method

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Pierre Degond ◽  
Amic Frouvelle ◽  
Jian-Guo Liu
Keyword(s):  
Liquid Crystals ◽  
Moment Method ◽  
Collision Operator ◽  
Expansion Method ◽  
Deborah Number ◽  
Navier Stokes ◽  
Leslie Model ◽  
Limit Model ◽  
Spatial Dimensions ◽  
The Moment

<p style='text-indent:20px;'>This paper deals with the convergence of the Doi-Navier-Stokes model of liquid crystals to the Ericksen-Leslie model in the limit of the Deborah number tending to zero. While the literature has investigated this problem by means of the Hilbert expansion method, we develop the moment method, i.e. a method that exploits conservation relations obeyed by the collision operator. These are non-classical conservation relations which are associated with a new concept, that of Generalized Collision Invariant (GCI). In this paper, we develop the GCI concept and relate it to geometrical and analytical structures of the collision operator. Then, the derivation of the limit model using the GCI is performed in an arbitrary number of spatial dimensions and with non-constant and non-uniform polymer density. This non-uniformity generates new terms in the Ericksen-Leslie model.</p>

scholarly journals The Uniaxial Limit of the Non-Inertial Qian–Sheng Model for Liquid Crystals

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 912
Author(s):  
Sirui Li ◽  
Fangxin Zhao
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystals ◽  
Elastic Constant ◽  
Nematic Liquid Crystal ◽  
Expansion Method ◽  
Inertial Effect ◽  
Rigorous Derivation ◽  
Leslie Model ◽  
Hilbert Expansion ◽  
Nematic Liquid Crystal Flows

In this article, we consider the Qian–Sheng model in the Landau–de Gennes framework describing nematic liquid crystal flows when the inertial effect is neglected. By taking the limit of elastic constant to zero (also called the uniaxial limit) and utilizing the so-called Hilbert expansion method, we provide a rigorous derivation from the non-inertial Qian–Sheng model to the Ericksen–Leslie model.

scholarly journals Spectral gap in random bipartite biregular graphs and applications

2021 ◽  
pp. 1-39
Author(s):  
Gerandy Brito ◽  
Ioana Dumitriu ◽  
Kameron Decker Harris
Keyword(s):  
Community Detection ◽  
Adjacency Matrix ◽  
Moment Method ◽  
Coding Theory ◽  
High Probability ◽  
Spectral Gap ◽  
Matrix Completion ◽  
Full Rank ◽  
The Moment ◽  
Deterministic Matrix

Abstract We prove an analogue of Alon’s spectral gap conjecture for random bipartite, biregular graphs. We use the Ihara–Bass formula to connect the non-backtracking spectrum to that of the adjacency matrix, employing the moment method to show there exists a spectral gap for the non-backtracking matrix. A by-product of our main theorem is that random rectangular zero-one matrices with fixed row and column sums are full rank with high probability. Finally, we illustrate applications to community detection, coding theory, and deterministic matrix completion.

Investigation of the Thermodynamic Properties of Anharmonic Crystals with Defects and Influence of Anharmonicity in Exafs by the Moment Method

1998 ◽  
Vol 12 (02) ◽  
pp. 191-205 ◽  
Author(s):  
Vu Van Hung ◽  
Nguyen Thanh Hai
Keyword(s):  
Thermal Expansion ◽  
Thermodynamic Properties ◽  
Phase Change ◽  
Specific Heat ◽  
Thermal Expansion Coefficient ◽  
Expansion Coefficient ◽  
Moment Method ◽  
Adiabatic Compressibility ◽  
Relative Displacement ◽  
The Moment

By the moment method established previously on the basis of the statistical mechanics, the thermodynamic properties of a strongly anharmonic face-centered and body-centered cubic crystal with point defect are considered. The thermal expansion coefficient, the specific heat Cv and Cp, the isothermal and adiabatic compressibility, etc. are calculated. Our calculated results of the thermal expansion coefficient, the specific heat Cv and Cp… of W, Nb, Au and Ag metals at various temperatures agrees well with the measured values. The anharmonic effects in extended X-ray absorption fine structure (EXAFS) in the single-shell model are considered. We have obtained a new formula for anharmonic contribution to the mean square relative displacement. The anharmonicity is proportional to the temperature and enters the phase change of EXAFS. Our calculated results of Debye–Waller factor and phase change in EXAFS of Cu at various temperatures agrees well with the measured values.

scholarly journals Os desafios atuais mais fundos à vida religiosa

2019 ◽  
Vol 64 (255) ◽  
pp. 638
Author(s):  
José María Vigil
Keyword(s):  
Religious Life ◽  
Present Situation ◽  
Symbolic Capital ◽  
Spatial Dimensions ◽  
The Moment ◽  
Third Moment

O artigo de José Maria Vigil, Claretiano, enumera, no momento “Ver”, os mais fundos desafios que a Vida Religiosa (VR) enfrenta em nossa época. A seguir, no momento “Julgar”, chama a atenção para as profundas e céleres mudanças que estão ocorrendo nesta “época-eixo”, tanto na dimensão temporal como na espacial. Num terceiro momento, o do “Agir”, identifica as tarefas que acredita poder deduzir desta situação para a VR. Em particular, sugere: a) recuperar a teologia da VR; b) recuperar a antropologia da vida radical; e c) adequar o capital simbólico da VR. Concluindo, sintetiza suas propostas em duas grandes tarefas: 1) “desabsolutizar o cristocentrismo da VR”, e 2) “reinocentralizar a VR”. Reflexão pertinente quando se pensa na “refundação” da VR!Abstract: The article by José Maria Vigil, a Claretian, lists, in the moment “See”, the gravest challenges faced by the Religious Life (RL) in our times. In the moment “Judge” he calls attention to the deep and fast changes that are taking place in this “axle-age” both in the temporal and in the spatial dimensions. In a third moment – that of “Act” – he identifies the tasks that, in his opinion, should be carried out by the RL in the present situation. In particular, he suggests: a) rescue the theology of the RL; b) rescue the anthropology of the radical life; c) adjust the symbolic capital of the RL. In the conclusion, he synthesizes his proposals into two large tasks, namely: 1) “make the Christ-centrism of the RL less absolute” and 2) “make the RL more Kingdom-centric”. A pertinent idea when one thinks of the “re-founding” of the RL!

Phase Field Modeling of Nonequilibrium Patterns on the Surface of a Liquid Film Under Lateral Oscillations at the Substrate

2014 ◽  
Vol 24 (09) ◽  
pp. 1450110 ◽  
Author(s):  
Rodica Borcia ◽  
Michael Bestehorn
Keyword(s):  
Liquid Film ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Solid Substrate ◽  
Navier Stokes ◽  
Bottom Plate ◽  
Navier Stokes Equation ◽  
Harmonic Vibrations ◽  
Spatial Dimensions

We use a phase field model which couples the generalized Navier–Stokes equation (including the Korteweg stress tensor) with the continuity equation for studying nonlinear pattern formation on the surface of a liquid film under (linear and circular) lateral harmonic vibrations at the solid substrate. First, we prove the thermodynamic consistency of our phase field model. Next, we present computer simulations in three spatial dimensions. We illustrate nonequilibrium patterns at the instability onset, confirming in this way the results recently reported in Phys. Rev. E 88, 023025 (2013). The lateral profiles of the deflected surface are compared with those reported in J. Fluid Mech. 686, 409 (2011) for Faraday instability excited by vertical harmonic vibrations at the bottom plate.

Sign in / Sign up

Export Citation Format

Share Document