scholarly journals THE LONG-RANGE INTERACTION IN MASSLESS (λΦ4)4THEORY

2009 ◽  
Vol 24 (04) ◽  
pp. 261-271 ◽  
Author(s):  
P. M. STEVENSON
Keyword(s):  
Field Theory ◽  
Symmetry Breaking ◽  
Long Range ◽  
Low Energy ◽  
Effective Theory ◽  
Range Interaction ◽  
Nonlocal Field Theory ◽  
Long Range Interaction ◽  
Nonlocal Field ◽  
Pointlike Interaction

Does massless (λΦ4)4theory exhibit spontaneous symmetry breaking (SSB)? The raw one-loop result implies that it does, but the "RG-improved" result implies the opposite. We argue that the appropriate "low-energy effective theory" is a nonlocal field theory involving an attractive, long-range interaction Φ2(x)Φ2(y)/|x-y|4. RG improvement then requires running couplings for both this interaction and the original pointlike interaction. A crude calculation in this framework yields SSB even after "RG improvement" and closely agrees with the raw one-loop result.

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 Nonlocal elastodynamics and fracture

2021 ◽  
Vol 28 (3) ◽  
Author(s):  
Robert P. Lipton ◽  
Prashant K. Jha
Keyword(s):  
Field Theory ◽  
Brittle Fracture ◽  
A Priori ◽  
Nonlocal Model ◽  
Elastic Fields ◽  
Nonlocal Field Theory ◽  
Nonlocal Field ◽  
Increasing Function ◽  
Non Locality

AbstractA nonlocal field theory of peridynamic type is applied to model the brittle fracture problem. The elastic fields obtained from the nonlocal model are shown to converge in the limit of vanishing non-locality to solutions of classic plane elastodynamics associated with a running crack. We carry out our analysis for a plate subject to mode one loading. The length of the crack is prescribed a priori and is an increasing function of time.

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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