Construction of a nonisothermal model of electrohydrodynamics with a nonsymmetric stress tensor

1980 ◽  
Vol 16 (4) ◽  
pp. 352-357
Author(s):  
L. G. Petrosyan
Keyword(s):  
Stress Tensor ◽  
Nonsymmetric Stress ◽  
Nonsymmetric Stress Tensor

Smoothness of Malliavin derivatives and dissipativity of solutions to two-dimensional micropolar fluid system

2017 ◽  
Vol 25 (3) ◽  
Author(s):  
Kazuo Yamazaki
Keyword(s):  
Micropolar Fluid ◽  
Kinematic Viscosity ◽  
Periodic Boundary Condition ◽  
Random Noise ◽  
Two Dimensional ◽  
Fluid System ◽  
Micropolar Fluids ◽  
Viscosity Coefficients ◽  
Nonsymmetric Stress ◽  
Nonsymmetric Stress Tensor

AbstractMicropolar fluids have microstructure and belong to a class of fluids with nonsymmetric stress tensor. We study the incompressible two-dimensional micropolar fluid system with periodic boundary condition forced by random noise that is white-in-time. In particular, we obtain a sufficient condition on the size of the angular viscosity coefficients in comparison to the vortex and kinematic viscosity coefficients so that the solution to this system is smooth in the Malliavin sense. In addition, we prove a result concerning an orthogonal projection onto a finite number of Fourier modes, taking advantage of the dissipative nature of the system.

Gluing Solutions

2017 ◽  
Author(s):  
Philip Isett
Keyword(s):  
Stress Tensor ◽  
Compact Support ◽  
Smooth Solution ◽  
Continuous Solution ◽  
Total Momentum ◽  
Frame Of Reference ◽  
Galilean Transformation ◽  
Hölder Continuous ◽  
Pressure Form ◽  
Original Frame

This chapter deals with the gluing of solutions and the relevant theorem (Theorem 12.1), which states the condition for a Hölder continuous solution to exist. By taking a Galilean transformation if necessary, the solution can be assumed to have zero total momentum. The cut off velocity and pressure form a smooth solution to the Euler-Reynolds equations with compact support when coupled to a smooth stress tensor. The proof of Theorem (12.1) proceeds by iterating Lemma (10.1) just as in the proof of Theorem (10.1). Applying another Galilean transformation to return to the original frame of reference, the theorem is obtained.

An Extension of Burzyński Hypothesis of Material Effort Accounting for the Third Invariant of Stress Tensor

2011 ◽  
Vol 56 (2) ◽  
pp. 503-508 ◽  
Author(s):  
R. Pęcherski ◽  
P. Szeptyński ◽  
M. Nowak
Keyword(s):  
Stress Tensor ◽  
Elastic Energy ◽  
Yield Condition ◽  
The Third ◽  
Third Invariant ◽  
Lode Angle

An Extension of Burzyński Hypothesis of Material Effort Accounting for the Third Invariant of Stress Tensor The aim of the paper is to propose an extension of the Burzyński hypothesis of material effort to account for the influence of the third invariant of stress tensor deviator. In the proposed formulation the contribution of the density of elastic energy of distortion in material effort is controlled by Lode angle. The resulted yield condition is analyzed and possible applications and comparison with the results known in the literature are discussed.

scholarly journals One-loop string corrections to AdS amplitudes from CFT

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
J.M. Drummond ◽  
H. Paul
Keyword(s):  
Stress Tensor ◽  
Analytic Structure ◽  
Position Space ◽  
Yang Mills ◽  
String Corrections ◽  
The One ◽  
Loop Amplitudes

Abstract We consider α′ corrections to the one-loop four-point correlator of the stress- tensor multiplets in $$ \mathcal{N} $$ N = 4 super Yang-Mills at order 1/N4. Holographically, this is dual to string corrections of the one-loop supergravity amplitude on AdS5 × S5. While this correlator has been considered in Mellin space before, we derive the corresponding position space results, gaining new insights into the analytic structure of AdS loop amplitudes. Most notably, the presence of a transcendental weight three function involving new singularities is required, which has not appeared in the context of AdS amplitudes before. We thereby confirm the structure of string corrected one-loop Mellin amplitudes, and also provide new explicit results at orders in α′ not considered before.

scholarly journals Driving stress and seismotectonic implications of the 2013 Mw5.8 Awaji Island earthquake, southwestern Japan, based on earthquake focal mechanisms before and after the mainshock

2020 ◽  
Vol 72 (1) ◽  
Author(s):  
Kazutoshi Imanishi ◽  
Makiko Ohtani ◽  
Takahiko Uchide
Keyword(s):  
Stress Field ◽  
Stress Tensor ◽  
Nankai Trough ◽  
Source Region ◽  
Local Scale ◽  
Southwest Japan ◽  
Stress Tensor Inversion ◽  
Earthquake Fault ◽  
Reverse Faulting ◽  
Before And After

Abstract A driving stress of the Mw5.8 reverse-faulting Awaji Island earthquake (2013), southwest Japan, was investigated using focal mechanism solutions of earthquakes before and after the mainshock. The seismic records from regional high-sensitivity seismic stations were used. Further, the stress tensor inversion method was applied to infer the stress fields in the source region. The results of the stress tensor inversion and the slip tendency analysis revealed that the stress field within the source region deviates from the surrounding area, in which the stress field locally contains a reverse-faulting component with ENE–WSW compression. This local fluctuation in the stress field is key to producing reverse-faulting earthquakes. The existing knowledge on regional-scale stress (tens to hundreds of km) cannot predict the occurrence of the Awaji Island earthquake, emphasizing the importance of estimating local-scale (< tens of km) stress information. It is possible that the local-scale stress heterogeneity has been formed by local tectonic movement, i.e., the formation of flexures in combination with recurring deep aseismic slips. The coseismic Coulomb stress change, induced by the disastrous 1995 Mw6.9 Kobe earthquake, increased along the fault plane of the Awaji Island earthquake; however, the postseismic stress change was negative. We concluded that the gradual stress build-up, due to the interseismic plate locking along the Nankai trough, overcame the postseismic stress reduction in a few years, pushing the Awaji Island earthquake fault over its failure threshold in 2013. The observation that the earthquake occurred in response to the interseismic plate locking has an important implication in terms of seismotectonics in southwest Japan, facilitating further research on the causal relationship between the inland earthquake activity and the Nankai trough earthquake. Furthermore, this study highlighted that the dataset before the mainshock may not have sufficient information to reflect the stress field in the source region due to the lack of earthquakes in that region. This is because the earthquake fault is generally locked prior to the mainshock. Further research is needed for estimating the stress field in the vicinity of an earthquake fault via seismicity before the mainshock alone.

scholarly journals Defect CFT techniques in the 6d $$ \mathcal{N} $$ = (2, 0) theory

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Nadav Drukker ◽  
Malte Probst ◽  
Maxime Trépanier
Keyword(s):  
Stress Tensor ◽  
Unitary Representations ◽  
Point Function ◽  
Displacement Operator ◽  
Expectation Value ◽  
Operator Expansion ◽  
Bulk Stress ◽  
Defect Operator ◽  
Tensor Multiplet

Abstract Surface operators are among the most important observables of the 6d $$ \mathcal{N} $$ N = (2, 0) theory. Here we apply the tools of defect CFT to study local operator insertions into the 1/2-BPS plane. We first relate the 2-point function of the displacement operator to the expectation value of the bulk stress tensor and translate this relation into a constraint on the anomaly coefficients associated with the defect. Secondly, we study the defect operator expansion of the stress tensor multiplet and identify several new operators of the defect CFT. Technical results derived along the way include the explicit supersymmetry tranformations of the stress tensor multiplet and the classification of unitary representations of the superconformal algebra preserved by the defect.

scholarly journals Hyperbolic cylinders and entanglement entropy: gravitons, higher spins, p-forms

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Justin R. David ◽  
Jyotirmoy Mukherjee
Keyword(s):  
Stress Tensor ◽  
Entanglement Entropy ◽  
Partition Functions ◽  
Point Function ◽  
Expectation Value ◽  
Massive Spin ◽  
Twist Operator ◽  
Higher Spins ◽  
Hyperbolic Cylinders ◽  
Kaluza Klein

Abstract We show that the entanglement entropy of D = 4 linearized gravitons across a sphere recently computed by Benedetti and Casini coincides with that obtained using the Kaluza-Klein tower of traceless transverse massive spin-2 fields on S1× AdS3. The mass of the constant mode on S1 saturates the Brietenholer-Freedman bound in AdS3. This condition also ensures that the entanglement entropy of higher spins determined from partition functions on the hyperbolic cylinder coincides with their recent conjecture. Starting from the action of the 2-form on S1× AdS5 and fixing gauge, we evaluate the entanglement entropy across a sphere as well as the dimensions of the corresponding twist operator. We demonstrate that the conformal dimensions of the corresponding twist operator agrees with that obtained using the expectation value of the stress tensor on the replica cone. For conformal p-forms in even dimensions it obeys the expected relations with the coefficients determining the 3-point function of the stress tensor of these fields.

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