An Overall Approach for Microcrack and Inhomogeneity Toughening in Brittle Solids

1999 ◽  
Vol 15 (2) ◽  
pp. 57-68
Author(s):  
Huang Hsing Pan
Keyword(s):  
Poisson Ratio ◽  
Crack Density ◽  
Mean Field ◽  
Analytic Form ◽  
Density Parameter ◽  
Brittle Solids ◽  
The Matrix ◽  
Microcrack Toughening ◽  
Average Quantity ◽  
The Mean

ABSTRACTBased on the weight function theory and Hutchinson's technique, the analytic form of the toughness change near a crack-tip is derived. The inhomogeneity toughening is treated as an average quantity calculated from the mean-field approach. The solutions are suitable for the composite materials with moderate concentration as compared with Hutchinson's lowest order formula. The composite has the more toughened property if the matrix owns the higher value of the Poisson ratio. The composite with thin-disc inclusions obtains the highest toughening and that with spheres always provides the least effective one. For the microcrack toughening, the variations of the crack shape do not significantly affect the toughness change if the Budiansky and O'Connell crack density parameter is used. The explicit forms for three types of the void toughening and two types of the microcrack toughening are also shown.

scholarly journals WRITING ELECTRONIC FERROMAGNETIC STATES IN A HIGH-TEMPERATURE PARAMAGNETIC NUCLEAR SPIN SYSTEM

2011 ◽  
Vol 09 (04) ◽  
pp. 1047-1056 ◽  
Author(s):  
D. O. SOARES-PINTO ◽  
J. TELES ◽  
A. M. SOUZA ◽  
E. R. DEAZEVEDO ◽  
R. S. SARTHOUR ◽  
...  
Keyword(s):  
Magnetic Field ◽  
High Temperature ◽  
Mean Field ◽  
Field Approximation ◽  
Order Transition ◽  
Mean Field Approximation ◽  
Temperature Hysteresis ◽  
First Case ◽  
The Matrix ◽  
The Mean

In this paper, we use Nuclear Magnetic Resonance (NMR) to write electronic states of a ferromagnetic system into high-temperature paramagnetic nuclear spins. Through the control of phase and duration of radio frequency pulses, we set the NMR density matrix populations, and apply the technique of quantum state tomography to experimentally obtain the matrix elements of the system, from which we calculate the temperature dependence of magnetization for different magnetic fields. The effects of the variation of temperature and magnetic field over the populations can be mapped in the angles of spin rotations, carried out by the RF pulses. The experimental results are compared to the Brillouin functions of ferromagnetic ordered systems in the mean field approximation for two cases: the mean field is given by (i) B = B0 + λM and (ii) B = B0 + λM + λ′M3, where B0 is the external magnetic field, and λ, λ′ are mean field parameters. The first case exhibits second order transition, whereas the second case has first order transition with temperature hysteresis. The NMR simulations are in good agreement with the magnetic predictions.

scholarly journals SEMICLASSICAL DESCRIPTION OF AVERAGE PAIRING PROPERTIES IN NUCLEI

2011 ◽  
Vol 20 (02) ◽  
pp. 399-405 ◽  
Author(s):  
X. VIÑAS ◽  
P. SCHUCK ◽  
M. FARINE
Keyword(s):  
Size Dependence ◽  
Local Density ◽  
Level Density ◽  
Mean Field ◽  
Matrix Elements ◽  
Fermi Systems ◽  
New Approach ◽  
The Matrix ◽  
The Mean ◽  
Arch Structure

We present a new semiclassical theory for describing pairing in finite Fermi systems. It is based on taking the ħ → 0, i.e. Thomas-Fermi, limit of the gap equation written in the basis of the mean field (weak coupling). In addition to the position dependence of the Fermi momentum, the size dependence of the matrix elements of the pairing force is also taken into account in this theory. An example typical for the nuclear situation shows the improvment of this new approach over the standard Local Density Approximation. We also show that if in this approach some shell fluctuations are introduced in the level density, the arch structure displayed by the quantal gaps along isotopic chains is almost recovered. We also point out that in heavy drip line nuclei pairing is strongly reduced.

Development of Prolonged Delivery of Tramadol and Dissolution Translation by Statistical Data Treatment

2011 ◽  
Vol 4 (1) ◽  
pp. 1331-1337
Author(s):  
P B Parejiya ◽  
B S Barot ◽  
P K Shelat
Keyword(s):  
Drug Release ◽  
Study Data ◽  
Stability Study ◽  
Dissolution Time ◽  
Matrix Tablet ◽  
Burst Effect ◽  
The Matrix ◽  
The Mean ◽  
The Difference ◽  
Dissolution Efficiency

The present study was carried out to fabricate a prolonged design for tramadol using Kollidon SR (Polyvinyl acetate and povidone based matrix retarding polymer). Matrix tablet formulations were prepared by direct compression of Kollidon SR of a varying proportion with a fixed percentage of tramadol. Tablets containing a 1:0.5 (Drug: Kollidon SR) ratio exhibited a rapid rate of drug release with an initial burst effect. Incorporation of more Kollidon SR in the matrix tablet extended the release of drug with subsequent minimization of the burst effect as confirmed by the mean dissolution time, dissolution efficiency and f2 value. Among the formulation batches, a direct relationship was obtained between release rate and the percentage of Kollidon SR used. The formulation showed close resemblance to the commercial product Contramal and compliance with USP specification. The results were explored and explained by the difference of micromeritic characteristics of the polymers and blend of drug with excipients. Insignificant effects of various factors, e.g. pH of dissolution media, ionic strength, speed of paddle were found on the drug release from Kollidon-SR matrix. The formulation followed the Higuchi kinetic model of drug release. Stability study data indicated stable character of Batch T6 after short-term stability study.

Classical Kinetic Theory

2018 ◽  
Author(s):  
Klaus Morawetz
Keyword(s):  
Kinetic Equation ◽  
Equation Of State ◽  
Mean Field ◽  
Ideal Gas ◽  
Hydrodynamic Equations ◽  
Free Particles ◽  
Internal Mechanism ◽  
The Mean ◽  
Energy Gains ◽  
Non Locality

The classical non-ideal gas shows that the two original concepts of the pressure based of the motion and the forces have eventually developed into drift and dissipation contributions. Collisions of realistic particles are nonlocal and non-instant. A collision delay characterizes the effective duration of collisions, and three displacements, describe its effective non-locality. Consequently, the scattering integral of kinetic equation is nonlocal and non-instant. The non-instant and nonlocal corrections to the scattering integral directly result in the virial corrections to the equation of state. The interaction of particles via long-range potential tails is approximated by a mean field which acts as an external field. The effect of the mean field on free particles is covered by the momentum drift. The effect of the mean field on the colliding pairs causes the momentum and the energy gains which enter the scattering integral and lead to an internal mechanism of energy conversion. The entropy production is shown and the nonequilibrium hydrodynamic equations are derived. Two concepts of quasiparticle, the spectral and the variational one, are explored with the help of the virial of forces.

scholarly journals Evidence of exactness of the mean-field theory in the nonextensive regime of long-range classical spin models

2000 ◽  
Vol 61 (17) ◽  
pp. 11521-11528 ◽  
Author(s):  
Sergio A. Cannas ◽  
A. C. N. de Magalhães ◽  
Francisco A. Tamarit
Keyword(s):  
Field Theory ◽  
Long Range ◽  
Mean Field Theory ◽  
Mean Field ◽  
Spin Models ◽  
Classical Spin ◽  
The Mean ◽  
Classical Spin Models

scholarly journals The Mean-field Behavior of Processor Sharing Systems with General Job Lengths Under the SQ(d) Policy

2019 ◽  
Vol 46 (3) ◽  
pp. 54-55
Author(s):  
Thirupathaiah Vasantam ◽  
Arpan Mukhopadhyay ◽  
Ravi R. Mazumdar
Keyword(s):  
Mean Field ◽  
Processor Sharing ◽  
Field Behavior ◽  
The Mean

scholarly journals The Microscopic Derivation and Well-Posedness of the Stochastic Keller–Segel Equation

2020 ◽  
Vol 31 (1) ◽  
Author(s):  
Hui Huang ◽  
Jinniao Qiu
Keyword(s):  
Existence Of Solutions ◽  
Particle System ◽  
Mean Field ◽  
Field Limit ◽  
Mean Field Limit ◽  
Unique Existence ◽  
Interacting Particle ◽  
Microscopic Derivation ◽  
The Mean ◽  
Limit Result

AbstractIn this paper, we propose and study a stochastic aggregation–diffusion equation of the Keller–Segel (KS) type for modeling the chemotaxis in dimensions $$d=2,3$$ d = 2 , 3 . Unlike the classical deterministic KS system, which only allows for idiosyncratic noises, the stochastic KS equation is derived from an interacting particle system subject to both idiosyncratic and common noises. Both the unique existence of solutions to the stochastic KS equation and the mean-field limit result are addressed.

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