Multivalued Functions, Branch-Points, and Branch-Cuts

2010 ◽  
pp. 105-120
Keyword(s):  
Branch Points ◽  
Multivalued Functions ◽  
Branch Cuts

Analysis of Surface Wave Generation by Laser Interference

1990 ◽  
Vol 57 (2) ◽  
pp. 415-418 ◽  
Author(s):  
K. J. Faran ◽  
R. J. Dwayne Miller ◽  
S. M. Gracewski
Keyword(s):  
Rapid Heating ◽  
Free Edge ◽  
Elastic Half Space ◽  
Temperature Fields ◽  
Thermal Excitation ◽  
Complex Frequency ◽  
Branch Points ◽  
Laser Interference ◽  
Wave Speeds ◽  
Branch Cuts

An analytical solution for thermal excitation of elastic waves in an homogeneous, isotropic, elastic half-space resulting from a pulsed laser interference pattern incident on the solid surface is presented. The spacially-periodic laser field absorbed by the surface causes rapid heating within the optical penetration depth. Thus, a temperature field is generated which can be modeled as being spacially harmonic along the free edge, decaying exponentially with depth, and having a Heaviside dependence on time. Transform techniques yield expressions for the resulting transverse and normal displacements within the laser interference region in terms of infinite integrals over frequency. The integrands contain poles indicating the expected Rayleigh waves propagating along the surface, as well as branch points corresponding to the bulk longitudinal and transverse wave speeds. The solution is obtained by integrating numerically in the complex frequency plane with an appropriate contour around the poles and branch cuts. Normal and transverse displacements are plotted as functions of time and depth for various materials and temperature fields.

ON THE SUP-MEASURABILITY OF MULTIVALUED FUNCTIONS

1996 ◽  
Vol 22 (1) ◽  
pp. 102
Author(s):  
Kwiecińska
Keyword(s):  
Multivalued Functions

scholarly journals Pentagon functions for scattering of five massless particles

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
D. Chicherin ◽  
V. Sotnikov
Keyword(s):  
Phase Space ◽  
Numerical Evaluation ◽  
Public Library ◽  
Basis Set ◽  
Particle Scattering ◽  
Minimal Basis ◽  
Feynman Integrals ◽  
Analytic Expressions ◽  
Transcendental Functions ◽  
Branch Cuts

Abstract We complete the analytic calculation of the full set of two-loop Feynman integrals required for computation of massless five-particle scattering amplitudes. We employ the method of canonical differential equations to construct a minimal basis set of transcendental functions, pentagon functions, which is sufficient to express all planar and nonplanar massless five-point two-loop Feynman integrals in the whole physical phase space. We find analytic expressions for pentagon functions which are manifestly free of unphysical branch cuts. We present a public library for numerical evaluation of pentagon functions suitable for immediate phenomenological applications.

scholarly journals Treating branch cuts in quantum trajectory models for photoelectron holography

2018 ◽  
Vol 98 (6) ◽  
Author(s):  
A. S. Maxwell ◽  
S. V. Popruzhenko ◽  
C. Figueira de Morisson Faria
Keyword(s):  
Quantum Trajectory ◽  
Trajectory Models ◽  
Branch Cuts

scholarly journals Actin-binding protein promotes the bipolar and perpendicular branching of actin filaments.

1980 ◽  
Vol 87 (3) ◽  
pp. 841-848 ◽  
Author(s):  
J H Hartwig ◽  
J Tyler ◽  
T P Stossel
Keyword(s):  
Actin Filaments ◽  
Actin Polymerization ◽  
Average Length ◽  
Binding Protein ◽  
Actin Binding ◽  
Branch Points ◽  
Heavy Meromyosin ◽  
Actin Binding Protein ◽  
Protein Dimers ◽  
Protein Molecules

Branching filaments with striking perpendicularity form when actin polymerizes in the presence of macrophage actin-binding protein. Actin-binding protein molecules are visible at the branch points. Compared with actin polymerized in the absence of actin-binding proteins, not only do the filaments branch but the average length of the actin filaments decreases from 3.2 to 0.63 micrometer. Arrowhead complexes formed by addition of heavy meromyosin molecules to the branching actin filaments point toward the branch points. Actin-binding protein also accelerates the onset of actin polymerization. All of these findings show that actin filaments assemble from nucleating sites on actin-binding protein dimers. A branching polymerization of actin filaments from a preexisting lattice of actin filaments joined by actin-binding protein molecules could generate expansion of cortical cytoplasm in amoeboid cells.

An airfoil theory of bifurcating laminar separation from thin obstacles

1990 ◽  
Vol 216 ◽  
pp. 255-284 ◽  
Author(s):  
C. J. Lee ◽  
H. K. Cheng
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Steady State ◽  
Steady State Solution ◽  
Equation System ◽  
Branch Points ◽  
Laminar Separation ◽  
Kutta Condition ◽  
Numerical Studies ◽  
Steady State Solutions

Global interaction of the boundary layer separating from an obstacle with resulting open/closed wakes is studied for a thin airfoil in a steady flow. Replacing the Kutta condition of the classical theory is the breakaway criterion of the laminar triple-deck interaction (Sychev 1972; Smith 1977), which, together with the assumption of a uniform wake/eddy pressure, leads to a nonlinear equation system for the breakaway location and wake shape. The solutions depend on a Reynolds numberReand an airfoil thickness ratio or incidence τ and, in the domain$Re^{\frac{1}{16}}\tau = O(1)$considered, the separation locations are found to be far removed from the classical Brillouin–Villat point for the breakaway from a smooth shape. Bifurcations of the steady-state solution are found among examples of symmetrical and asymmetrical flows, allowing open and closed wakes, as well as symmetry breaking in an otherwise symmetrical flow. Accordingly, the influence of thickness and incidence, as well as Reynolds number is critical in the vicinity of branch points and cut-off points where steady-state solutions can/must change branches/types. The study suggests a correspondence of this bifurcation feature with the lift hysteresis and other aerodynamic anomalies observed from wind-tunnel and numerical studies in subcritical and high-subcriticalReflows.

scholarly journals Different Angiogenic Potentials of Mesenchymal Stem Cells Derived from Umbilical Artery, Umbilical Vein, and Wharton’s Jelly

2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Lu Xu ◽  
Jianjun Zhou ◽  
Jingyu Liu ◽  
Yong Liu ◽  
Lei Wang ◽  
...  
Keyword(s):  
Stem Cells ◽  
Mesenchymal Stem Cells ◽  
Umbilical Vein ◽  
Wharton’S Jelly ◽  
Tube Length ◽  
Branch Points ◽  
Differentiation Potential ◽  
Wharton's Jelly ◽  
Allogeneic Cell Therapy ◽  
Perivascular Stem Cells

Human mesenchymal stem cells derived from the umbilical cord (UC) are a favorable source for allogeneic cell therapy. Here, we successfully isolated the stem cells derived from three different compartments of the human UC, including perivascular stem cells derived from umbilical arteries (UCA-PSCs), perivascular stem cells derived from umbilical vein (UCV-PSCs), and mesenchymal stem cells derived from Wharton’s jelly (WJ-MSCs). These cells had the similar phenotype and differentiation potential toward adipocytes, osteoblasts, and neuron-like cells. However, UCA-PSCs and UCV-PSCs had more CD146+ cells than WJ-MSCs (P<0.05). Tube formation assay in vitro showed the largest number of tube-like structures and branch points in UCA-PSCs among the three stem cells. Additionally, the total tube length in UCA-PSCs and UCV-PSCs was significantly longer than in WJ-MSCs (P<0.01). Microarray, qRT-PCR, and Western blot analysis showed that UCA-PSCs had the highest expression of the Notch ligand Jagged1 (JAG1), which is crucial for blood vessel maturation. Knockdown of Jagged1 significantly impaired the angiogenesis in UCA-PSCs. In summary, UCA-PSCs are promising cell populations for clinical use in ischemic diseases.

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