Two New Universal Relations in Nonlinear Elasticity and Some Related Matters

1994 ◽  
Vol 61 (4) ◽  
pp. 784-787 ◽  
Author(s):  
M. Aron ◽  
S. Aizicovici
Keyword(s):  
Nonlinear Elasticity ◽  
Ground State ◽  
Mean Stress ◽  
The Mean

Two inequalities which for certain deformation classes may be viewed as universal relations are shown to hold for two distinct subclasses of unconstrained rubberlike solids. The inequalities express the fact that the mean stress corresponding to any purely distortional deformation originating from a given ground state is dominated by (and, respectively, dominates) the mean stress in that ground state. Also discussed is a case in which the deformations involved are necessarily homogeneous.

scholarly journals Two-term expansion of the ground state one-body density matrix of a mean-field Bose gas

2021 ◽  
Vol 60 (3) ◽  
Author(s):  
Phan Thành Nam ◽  
Marcin Napiórkowski
Keyword(s):  
Density Matrix ◽  
Ground State ◽  
Mean Field ◽  
Interaction Strength ◽  
Bose Gas ◽  
Body Density ◽  
The Mean ◽  
The One ◽  
Mean Field Regime ◽  
Number Of Particles

AbstractWe consider the homogeneous Bose gas on a unit torus in the mean-field regime when the interaction strength is proportional to the inverse of the particle number. In the limit when the number of particles becomes large, we derive a two-term expansion of the one-body density matrix of the ground state. The proof is based on a cubic correction to Bogoliubov’s approximation of the ground state energy and the ground state.

Ground state of one-dimension repulsing particles on disordered lattice

2014 ◽  
Vol 25 (08) ◽  
pp. 1450028 ◽  
Author(s):  
L. A. Pastur ◽  
V. V. Slavin ◽  
A. A. Krivchikov
Keyword(s):  
Ground State ◽  
Domain Walls ◽  
Host Lattice ◽  
One Dimension ◽  
Weak Disorder ◽  
Interacting Particles ◽  
One Dimensional ◽  
Lattice Disorder ◽  
Disordered Lattice ◽  
The Mean

The ground state (GS) of interacting particles on a disordered one-dimensional (1D) host-lattice is studied by a new numerical method. It is shown that if the concentration of particles is small, then even a weak disorder of the host-lattice breaks the long-range order of Generalized Wigner Crystal (GWC), replacing it by the sequence of blocks (domains) of particles with random lengths. The mean domains length as a function of the host-lattice disorder parameter is also found. It is shown that the domain structure can be detected by a weak random field, whose form is similar to that of the ground state but has fluctuating domain walls positions. This is because the generalized magnetization corresponding to the field has a sufficiently sharp peak as a function of the amplitude of fluctuations for small amplitudes.

scholarly journals Study on the Mechanical Criterion of Ice Lens Formation Based on Pore Size Distribution

2020 ◽  
Vol 10 (24) ◽  
pp. 8981
Author(s):  
Yuhang Liu ◽  
Dongqing Li ◽  
Lei Chen ◽  
Feng Ming
Keyword(s):  
Pore Size Distribution ◽  
Pore Size ◽  
Water Content ◽  
Size Distribution ◽  
Initial Water Content ◽  
Mean Stress ◽  
Initial Water ◽  
Unfrozen Water Content ◽  
The Mean ◽  
Lens Formation

Ice lens is the key factor which determines the frost heave in engineering construction in cold regions. At present, several theories have been proposed to describe the formation of ice lens. However, most of these theories analyzed the ice lens formation from a macroscopic view and ignored the influence of microscopic pore sizes and structures. Meanwhile, these theories lacked the support of measured data. To solve this problem, the microscopic crystallization stress was converted into the macro mean stress through the principle of statistics with the consideration of pore size distribution. The mean stress was treated as the driving force of the formation of ice lens and induced into the criterion of ice lens formation. The influence of pore structure and unfrozen water content on the mean stress was analyzed. The results indicate that the microcosmic crystallization pressure can be converted into the macro mean stress through the principle of statistics. Larger mean stress means the ice lens will be formed easier in the soil. The mean stress is positively correlated with initial water content. At the same temperature, an increase to both the initial water content and the number of pores can result in a larger mean stress. Under the same initial water content, mean stress increases with decreasing temperature. The result provides a theoretical basis for studying ice lens formation from the crystallization theory.

MODULATION OF ORDER PARAMETER OF EXCITON BOSE-EINSTEIN CONDENSATE IN A RING

2004 ◽  
Vol 18 (27n29) ◽  
pp. 3797-3802 ◽  
Author(s):  
S.-R. ERIC YANG ◽  
Q-HAN PARK ◽  
J. YEO
Keyword(s):  
Ground State ◽  
Order Parameter ◽  
Weak Magnetic Field ◽  
Random Potential ◽  
Einstein Condensate ◽  
Einstein Condensation ◽  
Random Potentials ◽  
Bose Einstein Condensate ◽  
The Mean ◽  
Bose Einstein

We have studied theoretically the Bose-Einstein condensation (BEC) of two-dimensional excitons in a ring with a random variation of the effective exciton potential along the circumference. We derive a nonlinear Gross-Pitaevkii equation (GPE) for such a condensate, which is valid even in the presence of a weak magnetic field. For several types of the random potentials our numerical solution of the ground state of the GPE displays a necklace-like structure. This is a consequence of the interplay between the random potential and a strong nonlinear repulsive term of the GPE. We have investigated how the mean distance between modulation peaks depends on properties of the random potentials.

An investigation of wind structure in the trades: anegada 1953

1956 ◽  
Vol 249 (963) ◽  
pp. 179-234 ◽  
Keyword(s):  
Wind Velocity ◽  
Pressure Field ◽  
Surface Wind ◽  
Fair Agreement ◽  
Vertical Shear ◽  
Mean Stress ◽  
Mean Motion ◽  
Horizontal Pressure ◽  
The Mean ◽  
Made In

This paper describes an observational study of the mean and larger-scale turbulent structure of the wind in the lowest 1500 m of the North-East Trades. The observed motions are used both alone and in conjunction with the horizontal pressure field to deduce values of the vertical transport of momentum; the pattern of cumulus cloud convection is borne in mind throughout. Sections 1 and 2 provide a brief survey of the background to the expedition and of the simplified equations by which the observations are interpreted. Section 3 describes the site and observations in detail. 466 double-theodolite pilot-balloon soundings were made in the spring of 1953 from the small flat island of Anegada (18°N, 64° W). Soundings were made on 15 days over a 27-day period, balloons being released at intervals of 5 to 15 min. The balloons, rising at about 150 m/min, were observed every 20s for 9 min, to obtain the three components of the motion in 50 m layers over the lowest 1350 m. Special observations of pressure were made in a network of neighbouring islands. The derivation of component air velocities and of the horizontal pressure gradient as a function of height is described in §4. Difficulty was experienced in obtaining the pressure field with requisite accuracy. Surface observations of the weather in relation to the main aim of the study are discussed in §5. The mean angle between surface wind and isobar over the 15-day period was 13°, notably less than the climatological value of about 33°. Section 6 discusses the properties of the mean horizontal motion for the whole period of observation. The easterly component of wind velocity was greatest at 350 m, and the wind veered with height through 24° in the first 1350 m. There was also a veer of geostrophic wind in this layer of about 13° so that some down-gradient motion remained at the top of the layer. It is shown that the mean values of the local and advective components of acceleration were negligible compared with others terms in the momentum balance. Section 7 uses the wind profiles of §6 together with the mean horizontal pressure field to find the distribution of shearing stress with height, assuming that ageostrophic flow is balanced by internal friction. The mean stress in the direction of the surface wind varied from 0-41 dyn/cm2 at the surface to —0.37 dyn/cm 2 at 1300 m. The former provides a coefficient of surface stress, based on the anemometer windspeed, c = 1.5 x 10- 3 . The mean stress in the direction normal to the surface wind varied from zero (assumed) at the surface to 0.17 dyn/cm 2 at 200 m, and was small above 800 m, but internal consistency is only obtained by assuming the horizontal gradient of temperature near the surface to be appreciably greater than the climatological value for the general area. The stresses and related gradients of mean motion imply eddy viscosities of order 10 5 cm 2 / s throughout the layer. Section 8 discusses the vertical profiles of daily mean wind, which are variable from day to day. It was not possible to analyze the profiles to find shearing forces because of uncertainty in the acceleration terms, and in the pressure field. Section 9 is concerned with the analysis of fluctuations of wind at heights up to 1350 m, using averaging periods increasing from about 3 h up to the whole 27-day period. For none of these averaging periods was there equipartition of eddying energy in the three velocity components; w2 the vertical intensity, was one to two orders of magnitude lower than u2, the horizontal intensities, the difference being greater the longer the averaging periods. The covariances uv,uw were also evaluated for various heights and averaging periods, uw increased with averaging period and from their variation crude estimates are made of lag covariances which are equivalent to spectra. Values of uv for the larger components of the motion sampled were in fair agreement with those of early workers, uw and vw were in general less than uv and did not vary systematically with averaging period. The values for the smaller scale components of the motion sampled were in fair agreement with shearing stresses computed by the method of geostrophic departure (§7). The direction of the resultant of uw and vw agreed surprisingly well with the direction of the vertical shear vector of the mean wind velocity, the implied coefficient of eddy viscosity for the spectral range sampled again being about I0 5 cm 2/s over the whole range of height. An appendix considers the effect of the island, about 30 km 2 in area, on the oceanic Trades; the land was strongly heated by the sun and a particular pattern of convective cloud was usually set up. The associated field of mean vertical motion, of the order of 10 cm/s, and the disturbance of the field of horizontal mean motion have been partly evaluated. It is found that the velocities measured on the upwind shore were fairly representative of those over the open ocean, even though slow steady rising and sinking motions were detected.

Fatigue Life Prediction of Vortex Reducer Based on Stress Gradient

2018 ◽  
Author(s):  
Yanbin Luo ◽  
Yanrong Wang ◽  
Bo Zhong ◽  
Jiazhe Zhao ◽  
Xiaojie Zhang
Keyword(s):  
Fatigue Life ◽  
Size Effect ◽  
Stress Gradient ◽  
Fatigue Crack Initiation ◽  
High Stress ◽  
Stress Effect ◽  
Mean Stress ◽  
Notched Specimens ◽  
Life Model ◽  
The Mean

The effects of stress gradient and size effect on fatigue life are investigated based on the distributions of stress at notch root of the notched specimens of GH4169 alloy. The relationship between the life of the notched specimens and the smooth specimens is correlated by introducing the stress gradient effect factor, and a new life model of predicting the notched specimens based on the Walker modification for the mean stress effect is established. In order to improve the prediction precision of life model with the equation parameters having a definite physical significance, the relationships among fatigue parameters, monotonic ultimate tensile strength and reduction of area are established. Three-dimensional elastic finite element (FE) analysis of a vortex reducer is carried out to obtain the data of stress and strain for predicting its life. The results show that there is a high-stress gradient at the edge of the air holes of the vortex reducer, and it is thus a dangerous point for fatigue crack initiation. The prediction result of the vortex reducer is more reasonable if the mean stress, stress gradient and size effect are considered comprehensively. The developed life model can reflect the effects of many factors well, especially the stress concentration. The life of the notched specimens predicted by this model give a high estimation precision, and the prediction life data mainly fall into the scatter band of factor 2.

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