Poisson bracket formulation of viscoelastic flow equations of differential type: A unified approach

1990 ◽  
Vol 34 (4) ◽  
pp. 503-538 ◽  
Author(s):  
Anthony N. Beris ◽  
Brian J. Edwards
Keyword(s):  
Poisson Bracket ◽  
Type A ◽  
Viscoelastic Flow ◽  
Unified Approach ◽  
Flow Equations ◽  
Differential Type

scholarly journals SYMPLECTIC GEOMETRY AND HAMILTONIAN FLOW OF THE RENORMALIZATION GROUP EQUATION

1995 ◽  
Vol 10 (18) ◽  
pp. 2703-2732 ◽  
Author(s):  
BRIAN P. DOLAN
Keyword(s):  
Renormalization Group ◽  
Phase Space ◽  
Poisson Bracket ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Identity Operator ◽  
Group Equation ◽  
Renormalization Group Flow ◽  
Flow Equations ◽  
Group Flow

It is argued that renormalization group flow can be interpreted as a Hamiltonian vector flow on a phase space which consists of the couplings of the theory and their conjugate “momenta,” which are the vacuum expectation values of the corresponding composite operators. The Hamiltonian is linear in the conjugate variables and can be identified with the vacuum expectation value of the trace of the energy-momentum operator. For theories with massive couplings the identity operator plays a central role and its associated coupling gives rise to a potential in the flow equations. The evolution of any quantity, such as N-point Green functions, under renormalization group flow can be obtained from its Poisson bracket with the Hamiltonian. Ward identities can be represented as constants of the motion which act as symmetry generators on the phase space via the Poisson bracket structure.

Attenuation by squirt flow in undersaturated gas sands

Geophysics ◽  
1980 ◽  
Vol 45 (12) ◽  
pp. 1780-1792 ◽  
Author(s):  
I. D. Palmer ◽  
M. L. Traviolia
Keyword(s):  
Wave Attenuation ◽  
Water Saturation ◽  
Type A ◽  
Type B ◽  
Flow Equations ◽  
Contact Points ◽  
Aspect Ratios ◽  
Unconsolidated Sand ◽  
Normal Spectrum ◽  
Log Normal

In unconsolidated sand at low saturations, water exists in pendular rings at grain contact points. As the grains are pressed together by a passing wave, the squirt flow will contribute to wave attenuation. In a model which consists of a sphere‐pack framework, fluid flow equations are solved under certain approximations to calculate the viscous losses and, hence, attenuation. Attenuation is negligible for a sphere‐pack composed of equal‐sized spherical grains. The model is extended to include a spectrum of grain contact geometries, in particular a log‐normal spectrum of aspect ratios. The attenuation is substantial and depends markedly upon a lower limit imposed on the aspect ratios. For contacts of Type B (water separating two grains) only, results at 1 Hz are consistent with those of Mavko and Nur (1979) based on two‐dimensional (2-D) cracks. If contacts of Type A (two grains in contact) and Type B are present, the attenuation is greater by 2–3 orders of magnitude. The model with Type B contacts displays a dependence of attenuation on water saturation in the range 1–10 percent; the model with Type A and B contacts does not. When the results were fitted to the measurements of absolute attenuation and saturation dependence at kHz frequencies by Gardner et al. (1964), only the model with Type B contacts with aspect ratios [Formula: see text] could fit the data.

Biological and Morphological Studies on Low-Leukemia-Strain Mice with Hodgkin's-Like Neoplasia Induced by Serial Cell-Free Transmission of Leukemic Organs of SJL/J Strain Mice

1968 ◽  
Vol 26 ◽  
pp. 210-211
Author(s):  
S. Fujinaga ◽  
K. Maruyama ◽  
C.W. Williams ◽  
K. Sekhri ◽  
L. Dmochowski
Keyword(s):  
Tissue Culture ◽  
Type A ◽  
Reticulum Cell ◽  
Type B ◽  
Viral Origin ◽  
Serial Transfer ◽  
Strain Mouse ◽  
Morphological Studies ◽  
Cell Neoplasm ◽  
Free Material

Yumoto and Dmochowski (Cancer Res.27, 2098 (1967)) reported the presence of mature and immature type C leukemia virus particles in leukemic organs and tissues such as lymph nodes, spleen, thymus, liver, and kidneys of SJL/J strain mice with Hodgki's-like disease or reticulum cell neoplasm (type B). In an attempt to ascertain the possibility that this neoplasia may be of viral origin, experiments with induction and transmission of this neoplasm were carried out using cell-free extracts of leukemic organs from an SJL/J strain mouse with spontaneous disease.It has been possible to induce the disease in low-leukemia BALB/c and C3HZB strain mice and serially transfer the neoplasia by cell-free extracts of leukemic organs of these mice. Histological examination revealed the neoplasia to be of either reticulum cell-type A or type B. Serial transfer is now in its fifth passage. In addition leukemic spleen from another SJL/J strain mouse with spontaneous reticulum cell neoplasm (type A) was set up in tissue culture and is now in its 141st serial passage in vitro. Preliminary results indicate that cell-free material of 39th tissue culture passage can reproduce neoplasia in BALB/c mice.

Hepatitis A Antigen in Liver, Bile and Stool

1975 ◽  
Vol 33 ◽  
pp. 340-341
Author(s):  
D.R. Jackson ◽  
J.H. Hoofnagle ◽  
A.N. Schulman ◽  
J.L. Dienstag ◽  
R.H. Purcell ◽  
...  
Keyword(s):  
Hepatitis A ◽  
Liver Enzymes ◽  
Hepatitis A Virus ◽  
Type A ◽  
Initial Study ◽  
Virus Like Particle ◽  
Elevated Liver Enzymes ◽  
Ag Particles ◽  
Ag Particle ◽  
Human Stool

Using immune electron microscopy Feinstone et. al. demonstrated the presence of a 27 nm virus-like particle in acute-phase stools of patients with viral hepatitis, type A, These hepatitis A antigen (HA Ag) particles were aggregated by convalescent serum from patients with type A hepatitis but not by pre-infection serum. Subsequently Dienstag et. al. and Maynard et. al. produced acute hepatitis in chimpanzees by inoculation with human stool containing HA Ag. During the early acute disease, virus like particles antigenically, morphologically and biophysically identical to the human HA Ag particle were found in chimpanzee stool. Recently Hilleman et. al. have described similar particles in liver and serum of marmosets infected with hepatitis A virus (HAV). We have investigated liver, bile and stool from chimpanzees and marmosets experimentally infected with HAV. In an initial study, a chimpanzee (no.785) inoculated with HA Ag-containing stool developed elevated liver enzymes 21 days after exposure.

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