Lagrangian observations of homogeneous random environments

2001 ◽  
Vol 33 (4) ◽  
pp. 810-835 ◽  
Author(s):  
Craig L. Zirbel

This article deals with the distribution of the view of a random environment as seen by an observer whose location at each moment is determined by the environment. The main application is in statistical fluid mechanics, where the environment consists of a random velocity field and the observer is a particle moving in the velocity field, possibly subject to molecular diffusion. Several results on such Lagrangian observations of the environment have appeared in the literature, beginning with the 1957 dissertation of J. L. Lumley. This article unites these results into a simple unified framework and rounds out the theory with new results in several directions. When the environment is homogeneous, the problem can be re-cast in terms of certain random mappings on the physical space that are based on the random location of the observer. If these mappings preserve the invariant measure on the physical space, then the view from the random location has the same distribution as the view from the origin. If these mappings satisfy the flow property and the environment is stationary, then the succession of Lagrangian observations over time forms a strictly stationary process. In particular, for motion in a homogeneous, stationary, and nondivergent velocity field, the Lagrangian velocity (the velocity of the particle) is strictly stationary, which was first observed by Lumley. In the compressible case, the distribution of a Lagrangian observation has a density with respect to the distribution of the view from the origin, and in some cases convergence in distribution of the Lagrangian observations as time tends to infinity can be shown.

2001 ◽  
Vol 33 (04) ◽  
pp. 810-835 ◽  
Author(s):  
Craig L. Zirbel

This article deals with the distribution of the view of a random environment as seen by an observer whose location at each moment is determined by the environment. The main application is in statistical fluid mechanics, where the environment consists of a random velocity field and the observer is a particle moving in the velocity field, possibly subject to molecular diffusion. Several results on such Lagrangian observations of the environment have appeared in the literature, beginning with the 1957 dissertation of J. L. Lumley. This article unites these results into a simple unified framework and rounds out the theory with new results in several directions. When the environment is homogeneous, the problem can be re-cast in terms of certain random mappings on the physical space that are based on the random location of the observer. If these mappings preserve the invariant measure on the physical space, then the view from the random location has the same distribution as the view from the origin. If these mappings satisfy the flow property and the environment is stationary, then the succession of Lagrangian observations over time forms a strictly stationary process. In particular, for motion in a homogeneous, stationary, and nondivergent velocity field, the Lagrangian velocity (the velocity of the particle) is strictly stationary, which was first observed by Lumley. In the compressible case, the distribution of a Lagrangian observation has a density with respect to the distribution of the view from the origin, and in some cases convergence in distribution of the Lagrangian observations as time tends to infinity can be shown.


Author(s):  
Bagus Putra Muljadi ◽  
Jaw-Yen Yang

The unsteady shock wave diffraction by a square cylinder in gases of arbitrary particle statistics is simulated using an accurate and direct algorithm for solving the semiclassical Boltzmann equation with relaxation time approximation in phase space. The numerical method is based on the discrete ordinate method for discretizing the velocity space of the distribution function and high-resolution method is used for evolving the solution in physical space and time. The specular reflection surface boundary condition is employed. The complete diffraction patterns including regular reflection, triple Mach reflection, slip lines, vortices and their complex nonlinear manifestations are recorded using various flow property contours. Different ranges of relaxation times corresponding to different flow regimes are considered, and the equilibrium Euler limit solution is also computed for comparison. The effects of gas particles that obey the Maxwell–Boltzmann, Bose–Einstein and Fermi—Dirac statistics are examined and depicted.


Author(s):  
Avilash Carpenter ◽  
M.K. Gupta ◽  
Neetesh Kumar Jain ◽  
Urvashi Sharma ◽  
Rahul Sisodiya

Aim: The main of the study is to formulate and develop orally disintegrating fast dissolving tablet of Metoclopramide hydrochloride. Material & Methods: Before formulation and development of selected drug, the standard curve in buffer was prepared and absorbance at selected maxima was taken. Then two different disintegrating agents were selected and drug was mixed with disintegrating agents in different ratio. Various Preformulation parameters and evaluation of tablet i.e. disintegration time, dissolution time, friability, hardness, thickness were measured by standard procedure. Result & Discussion: The angle of repose for all the batches prepared. The values were found to be in the range of 30.46 to 36.45, which indicates good flow property for the powder blend according to the USP. The bulk density and tapped density for all the batches varied from 0.49 to 0.54 g/mL and 0.66 to 0.73, respectively. Carr’s index values were found to be in the range of 23.33 to 25.88, which is satisfactory for the powders as well as implies that the blends have good compressibility. Hausner ratio values obtained were in the range of 1.22 to 1.36, which shows a passable flow property for the powder blend based on the USP. The results for tablet thickness and height for all batches was found to range from 4.45 to 4.72 mm and 3.67 to 3.69 mm, respectively. Hardness or breaking force of tablets for all batches was found to range from 32.8 to 36.2 N. Tablet formulations must show good mechanical strength with sufficient hardness in order to handle shipping and transportation. Friability values for all the formulations were found to be in the range of 0.22 % to 0.30 %. Conclusion: Orally disintegrating tablets were compressed in order to have sufficient mechanical strength and integrity to withstand handling, shipping and transportation. The formulation was shown to have a rapid disintegration time that complied with the USP (less than one minute). The data obtained from the stability studies indicated that the orally disintegrating mini-tablets of MTH were stable under different environmental storage conditions. Keywords: Formulation & Development, Fast Dissolving Tablet, Metoclopramide, Anti-Emetic Drug, Oral Disintegrating Tablet


2020 ◽  
Vol 10 (2) ◽  
pp. 151-173
Author(s):  
Min-Su Jung ◽  
◽  
Hang-Bae Chang
Keyword(s):  

2018 ◽  
Vol 12 (1) ◽  
pp. 26-36 ◽  
Author(s):  
Richard B. Apgar

As destination of choice for many short-term study abroad programs, Berlin offers students of German language, culture and history a number of sites richly layered with significance. The complexities of these sites and the competing narratives that surround them are difficult for students to grasp in a condensed period of time. Using approaches from the spatial humanities, this article offers a case study for enhancing student learning through the creation of digital maps and itineraries in a campus-based course for subsequent use during a three-week program in Berlin. In particular, the concept of deep mapping is discussed as a means of augmenting understanding of the city and its history from a narrative across time to a narrative across the physical space of the city. As itineraries, these course-based projects were replicated on site. In moving from the digital environment to the urban landscape, this article concludes by noting meanings uncovered and narratives formed as we moved through the physical space of the city.


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