The Experts below are selected from a list of 303 Experts worldwide ranked by ideXlab platform
M. O. Katanaev - One of the best experts on this subject based on the ideXlab platform.
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Point disclinations in the Chern–Simons Geometric Theory of defects
Modern Physics Letters B, 2020Co-Authors: M. O. Katanaev, B. O. VolkovAbstract:We use the Chern–Simons action for a 𝕊𝕆(3)-connection for the description of point disclinations in the Geometric Theory of defects. The most general spherically symmetric 𝕊𝕆(3)-connection with zer...
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The 't Hooft-Polyakov monopole in the Geometric Theory of defects
Modern Physics Letters B, 2020Co-Authors: M. O. KatanaevAbstract:The 't Hooft-Polyakov monopole solution in Yang-Mills Theory is given new physical interpretation in the Geometric Theory of defects. It describes solids with continuous distribution of dislocations and disclinations. The corresponding densities of Burgers and Frank vectors are computed. It means that the 't Hooft-Polyakov monopole can be seen, probably, in solids.
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Point disclinations in the Chern-Simons Geometric Theory of defects
arXiv: Mathematical Physics, 2019Co-Authors: M. O. Katanaev, B. O. VolkovAbstract:We use the Chern-Simons action for a SO(3)-connection for the description of point disclinations in the Geometric Theory of defects. The most general spherically symmetric SO(3)-connection with zero curvature is found. The corresponding orthogonal spherically symmetric SO(3) matrix and n-field are computed. Two examples of point disclinations are described.
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Chern-Simons term in the Geometric Theory of defects
Physical Review D, 2017Co-Authors: M. O. KatanaevAbstract:The Chern--Simons term is used in the Geometric Theory of defects. The equilibrium equations with $\ensuremath{\delta}$-function source are explicitly solved with respect to the $\mathbb{S}\mathbb{O}(3)$ connection. This solution describes one straight linear disclination and corresponds to the singularity in the connection but not the metric which is the flat Euclidean metric. This is the first example of a disclination described within the Geometric Theory of defects. The corresponding angular rotation field is computed.
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Geometric Theory of Defects
Physics-Uspekhi, 2005Co-Authors: M. O. KatanaevAbstract:A description of dislocations and disclinations defects in terms of Riemann--Cartan geometry is given, with the curvature and torsion tensors being interpreted as the surface densities of the Frank and Burgers vectors, respectively. A new free energy expression describing the static distribution of defects is presented, and equations of nonlinear elasticity Theory are used to specify the coordinate system. Application of the Lorentz gauge leads to equations for the principal chiral SO(3)-field. In the defect-free case, the Geometric model reduces to elasticity Theory for the displacement vector field and to a principal chiral SO(3)-field model for the spin structure. As illustrated by the example of a wedge dislocation, elasticity Theory reproduces only the linear approximation of the Geometric Theory of defects. It is shown that the equations of asymmetric elasticity Theory for the Cosserat media can also be naturally incorporated into the Geometric Theory as the gauge conditions. As an application of the Theory, phonon scattering on a wedge dislocation is considered. The energy spectrum of impurity in the field of a wedge dislocation is also discussed.
Oren Raz - One of the best experts on this subject based on the ideXlab platform.
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a Geometric Theory of swimming purcell s swimmer and its symmetrized cousin
New Journal of Physics, 2008Co-Authors: J E Avron, Oren RazAbstract:We develop a qualitative Geometric approach to swimming at low Reynolds numbers which avoids solving differential equations and uses instead landscape figures describing the swimming and dissipation. This approach gives complete information about swimmers that swim on a line without rotations and gives the main qualitative features of general swimmers that can also rotate. We illustrate this approach for a symmetric version of Purcell's swimmer, which we solve by elementary analytical means within slender body Theory. We then apply the Theory to derive the basic qualitative properties of Purcell's swimmer.
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a Geometric Theory of swimming purcell s swimmer and its symmetrized cousin
arXiv: Fluid Dynamics, 2007Co-Authors: J E Avron, Oren RazAbstract:We develop a qualitative Geometric approach to swimming at low Reynolds number which avoids solving differential equations and uses instead landscape figures of two notions of curvatures: The swimming curvature and the curvature derived from dissipation. This approach gives complete information for swimmers that swim on a line without rotations and gives the main qualitative features for general swimmers that can also rotate. We illustrate this approach for a symmetric version of Purcell's swimmer which we solve by elementary analytical means within slender body Theory. We then apply the Theory to derive the basic qualitative properties of Purcell's swimmer.
J E Avron - One of the best experts on this subject based on the ideXlab platform.
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a Geometric Theory of swimming purcell s swimmer and its symmetrized cousin
New Journal of Physics, 2008Co-Authors: J E Avron, Oren RazAbstract:We develop a qualitative Geometric approach to swimming at low Reynolds numbers which avoids solving differential equations and uses instead landscape figures describing the swimming and dissipation. This approach gives complete information about swimmers that swim on a line without rotations and gives the main qualitative features of general swimmers that can also rotate. We illustrate this approach for a symmetric version of Purcell's swimmer, which we solve by elementary analytical means within slender body Theory. We then apply the Theory to derive the basic qualitative properties of Purcell's swimmer.
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a Geometric Theory of swimming purcell s swimmer and its symmetrized cousin
arXiv: Fluid Dynamics, 2007Co-Authors: J E Avron, Oren RazAbstract:We develop a qualitative Geometric approach to swimming at low Reynolds number which avoids solving differential equations and uses instead landscape figures of two notions of curvatures: The swimming curvature and the curvature derived from dissipation. This approach gives complete information for swimmers that swim on a line without rotations and gives the main qualitative features for general swimmers that can also rotate. We illustrate this approach for a symmetric version of Purcell's swimmer which we solve by elementary analytical means within slender body Theory. We then apply the Theory to derive the basic qualitative properties of Purcell's swimmer.
Vakhtang Putkaradze - One of the best experts on this subject based on the ideXlab platform.
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Geometric Theory of Flexible and Expandable Tubes Conveying Fluid: Equations, Solutions and Shock Waves
Journal of Nonlinear Science, 2019Co-Authors: François Gay-balmaz, Vakhtang PutkaradzeAbstract:We present a Theory for the three-dimensional evolution of tubes with expandable walls conveying fluid. Our Theory can accommodate arbitrary deformations of the tube, arbitrary elasticity of the walls, and both compressible and incompressible flows inside the tube. We also present the Theory of propagation of shock waves in such tubes and derive the conservation laws and Rankine–Hugoniot conditions in arbitrary spatial configuration of the tubes and compute several examples of particular solutions. The Theory is derived from a variational treatment of Cosserat rod Theory extended to incorporate expandable walls and moving flow inside the tube. The results presented here are useful for biological flows and industrial applications involving high-speed motion of gas in flexible tubes.
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Exact Geometric Theory for flexible, fluid-conducting tubes
Comptes Rendus Mecanique, 2014Co-Authors: François Gay-balmaz, Vakhtang PutkaradzeAbstract:Abstract Instability of flexible tubes conducting fluid, or “garden hose instability”, is a phenomenon both familiar from everyday life and important for applications, which has been actively studied. However, previous works did not consider one of the most crucial physical effects — the dynamical change of the cross-section. We show how to consistently address this issue by coupling the Geometrically exact rod dynamics with the fluid motion via the use of a constrained Hamilton's variational principle. We find strong effect of this dynamics on stability, and derive a variety of exact nonlinear solutions of traveling-wave type.
Jean-michel Dion - One of the best experts on this subject based on the ideXlab platform.
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A comprehensive introduction to the Geometric Theory of linear multivariable systems
IEEE Transactions on Education, 1992Co-Authors: Christian Commault, Jean-michel DionAbstract:A simple tutorial introduction to the Geometric Theory of linear multivariable control is presented. This corresponds to approximately three two-hour lectures in a graduate-level course. The authors emphasise the intuitive control interpretation of the main Geometric concepts. To this end, the authors focus interest on trajectory formulation for subspace invariance and discrete-time interpretation of the basic subspaces and their construction algorithms. Application of Geometric Theory for solving the disturbance decoupling problem is illustrated via two pedagogical examples. >