Global renormalized solutions and Navier–Stokes limit of the Boltzmann equation with incoming boundary condition for long range interaction

2019 ◽  
Vol 266 (5) ◽  
pp. 2597-2637 ◽  
Author(s):  
Ning Jiang ◽  
Xu Zhang
Keyword(s):  
Boundary Condition ◽  
Boltzmann Equation ◽  
Long Range ◽  
Navier Stokes ◽  
Renormalized Solutions ◽  
Range Interaction ◽  
The Boltzmann Equation ◽  
Long Range Interaction

Phase transformation and Raman spectra in BaTiO3 nanocrystals

2002 ◽  
Vol 718 ◽  
Author(s):  
Jian Yu ◽  
X. J. Meng ◽  
J.L. Sun ◽  
G.S. Wang ◽  
J.H. Chu
Keyword(s):  
Particle Size ◽  
Phase Transformation ◽  
Low Temperature ◽  
Long Range ◽  
Lattice Expansion ◽  
Inversion Symmetry ◽  
Range Interaction ◽  
Cooperative Phenomena ◽  
Long Range Interaction ◽  
Hydrothermal Methods

AbstractIn this paper, size-induced ferroelectricit yweakening, phase transformation, and anomalous lattice expansion are observed in nanocrystalline BaTiO3 (nc-BaTiO3) deriv ed b y low temperature hydrothermal methods, and they are w ellunderstood using the terms of the long-range interaction and its cooperative phenomena altered by particle size in covalen t ionic nanocrystals. In cubic nc-BaTiO3, five modes centerd at 186, 254, 308, 512 and 716 cm-1 are observed Raman active in cubic nanophase, and they are attributed to local rhombohedral distortion breaking inversion-symmetry in cubic nanophase. The254 and 308 cm-1 modes are significantly affected not only by the concentration of hydroxyl defects, but also their particular configuration. And the 806 cm-1 modes found to be closely associated with OH - absorbed on grain boundaries.

scholarly journals Inverse Problem for Ising Connection Matrix with Long-Range Interaction

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1624
Author(s):  
Leonid Litinskii ◽  
Boris Kryzhanovsky
Keyword(s):  
Inverse Problem ◽  
Long Range ◽  
Random Number ◽  
Connection Matrix ◽  
Range Interaction ◽  
Connection Matrices ◽  
Ising Systems ◽  
Long Range Interaction ◽  
Matrix Spectrum ◽  
Analytical Expressions

In the present paper, we examine Ising systems on d-dimensional hypercube lattices and solve an inverse problem where we have to determine interaction constants of an Ising connection matrix when we know a spectrum of its eigenvalues. In addition, we define restrictions allowing a random number sequence to be a connection matrix spectrum. We use the previously obtained analytical expressions for the eigenvalues of Ising connection matrices accounting for an arbitrary long-range interaction and supposing periodic boundary conditions.

scholarly journals HiChIP and Hi-C Protocol Optimized for Primary Murine T Cells

2021 ◽  
Vol 4 (3) ◽  
pp. 49
Author(s):  
Tomas Zelenka ◽  
Charalampos Spilianakis
Keyword(s):  
T Cells ◽  
Long Range ◽  
Three Dimensional ◽  
Cell Types ◽  
Range Interaction ◽  
Chromatin Interactions ◽  
Optimized Protocol ◽  
Long Range Interaction ◽  
Chromatin Compactness ◽  
Detailed Protocol

The functional implications of the three-dimensional genome organization are becoming increasingly recognized. The Hi-C and HiChIP research approaches belong among the most popular choices for probing long-range chromatin interactions. A few methodical protocols have been published so far, yet their reproducibility and efficiency may vary. Most importantly, the high frequency of the dangling ends may dramatically affect the number of usable reads mapped to valid interaction pairs. Additionally, more obstacles arise from the chromatin compactness of certain investigated cell types, such as primary T cells, which due to their small and compact nuclei, impede limitations for their use in various genomic approaches. Here we systematically optimized all the major steps of the HiChIP protocol in T cells. As a result, we reduced the number of dangling ends to nearly zero and increased the proportion of long-range interaction pairs. Moreover, using three different mouse genotypes and multiple biological replicates, we demonstrated the high reproducibility of the optimized protocol. Although our primary goal was to optimize HiChIP, we also successfully applied the optimized steps to Hi-C, given their significant protocol overlap. Overall, we describe the rationale behind every optimization step, followed by a detailed protocol for both HiChIP and Hi-C experiments.

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