scholarly journals A self-similarity model for the occupancy frequency distribution

2007 ◽  
Vol 71 (1) ◽  
pp. 61-70 ◽  
Author(s):  
Cang Hui ◽  
Melodie A. McGeoch
Keyword(s):  
Frequency Distribution ◽  
Self Similarity ◽  
Similarity Model

scholarly journals Self-similarity model of nonsingular perfect gas universe

2008 ◽  
Vol 57 (12) ◽  
pp. 7955
Author(s):  
Lai Xiao-Ming ◽  
Bian Bao-Min ◽  
Yang Ling ◽  
Yang Juan ◽  
Bian Niu ◽  
...  
Keyword(s):  
Perfect Gas ◽  
Self Similarity ◽  
Similarity Model

Effective Subgrid Modeling From the ILES Simulation of Compressible Turbulence

2007 ◽  
Vol 129 (12) ◽  
pp. 1493-1496 ◽  
Author(s):  
William J. Rider
Keyword(s):  
Incompressible Flows ◽  
Stokes Equations ◽  
Standard Form ◽  
Large Eddy Simulations ◽  
Compressible Turbulence ◽  
Navier Stokes ◽  
Subgrid Scale ◽  
Self Similarity ◽  
Large Eddy ◽  
Similarity Model

Implicit large eddy simulation (ILES) has provided many computer simulations with an efficient and effective model for turbulence. The capacity for ILES has been shown to arise from a broad class of numerical methods with specific properties producing nonoscillatory solutions using limiters that provide these methods with nonlinear stability. The use of modified equation has allowed us to understand the mechanisms behind the efficacy of ILES as a model. Much of the understanding of the ILES modeling has proceeded in the realm of incompressible flows. Here, we extend this analysis to compressible flows. While the general conclusions are consistent with our previous findings, the compressible case has several important distinctions. Like the incompressible analysis, the ILES of compressible flow is dominated by an effective self-similarity model (Bardina, J., Ferziger, J. H., and Reynolds, W. C., 1980, “Improved Subgrid Scale Models for Large Eddy Simulations,” AIAA Paper No. 80–1357; Borue, V., and Orszag, S. A., 1998, “Local Energy Flux and Subgrid-Scale Statistics in Three Dimensional Turbulence,” J. Fluid Mech., 366, pp. 1–31; Meneveau, C., and Katz, J., 2000, “Scale-Invariance and Turbulence Models for Large-Eddy Simulations,” Annu. Rev. Fluid. Mech., 32, pp. 1–32). Here, we focus on one of these issues, the form of the effective subgrid model for the conservation of mass equations. In the mass equation, the leading order model is a self-similarity model acting on the joint gradients of density and velocity. The dissipative ILES model results from the limiter and upwind differencing resulting in effects proportional to the acoustic modes in the flow as well as the convective effects. We examine the model in several limits including the incompressible limit. This equation differs from the standard form found in the classical Navier–Stokes equations, but generally follows the form suggested by Brenner (2005, “Navier-Stokes Revisited,” Physica A, 349(1–2), pp. 60–133) in a modification of Navier–Stokes necessary to successfully reproduce some experimentally measured phenomena. The implications of these developments are discussed in relation to the usual turbulence modeling approaches.

A self-similarity model for effective thermal conductivity of porous media

2003 ◽  
Vol 36 (17) ◽  
pp. 2157-2164 ◽  
Author(s):  
Yongting Ma ◽  
Boming Yu ◽  
Duanming Zhang ◽  
Mingqing Zou
Keyword(s):  
Thermal Conductivity ◽  
Porous Media ◽  
Effective Thermal Conductivity ◽  
Self Similarity ◽  
Similarity Model

A self-similarity model for dielectric constant of porous ultra low-kdielectrics

2007 ◽  
Vol 40 (17) ◽  
pp. 5377-5382 ◽  
Author(s):  
Yanni Tang ◽  
Boming Yu ◽  
Yifan Hu ◽  
Jianchao Cai ◽  
Yongjin Feng ◽  
...  
Keyword(s):  
Dielectric Constant ◽  
Self Similarity ◽  
Similarity Model

Fractal Organization of the Human T Cell Repertoire in Health and Following Stem Cell Transplantation

Blood ◽  
2012 ◽  
Vol 120 (21) ◽  
pp. 4193-4193
Author(s):  
Jeremy Meier ◽  
Allison F Hazlett ◽  
Kassi Avent ◽  
Jennifer Berrie ◽  
Kyle Payne ◽  
...  
Keyword(s):  
Stem Cell ◽  
T Cell ◽  
Frequency Distribution ◽  
Gene Segment ◽  
T Cell Repertoire ◽  
Self Similarity ◽  
Cell Repertoire ◽  
Cell Clones ◽  
Tcr Repertoire ◽  
Proportional Distribution

Abstract Abstract 4193 T cell repertoire diversity is generated by recombination of variable (V), diversity (D) and joining (J) segments in the T cell receptor (TCR) locus. Further variability and antigen recognition capacity is introduced by nucleotide insertion (NI) in the recombined sequences resulting in a complex repertoire, the organization of which is poorly understood. We postulate that TCR b D, J and V gene segment usage in an individual would result in a TCR repertoire with a fractal, self-similar frequency distribution of T cell clones with respect to gene segment usage. To determine this, the TCR repertoire of donors and recipients of HLA matched-related and unrelated allogeneic stem cell transplantation (SCT) was evaluated by high-throughput (HT) sequencing of the CDR3 region of TCR b. Ten SCT donor-recipient pairs were selected for HT-TCR b sequencing. cDNA was isolated from T cells obtained from the donors at baseline and recipients at day 100, 1 year post SCT or at the time of graft-versus-host disease (GVHD) diagnosis. HT-TCR β sequencing was performed and analyzed using the ImmunoSEQ analyzer tool (Adaptive Biotechnologies, Seattle, WA). TCR b clone frequencies were used to determine the TCR self-similarity score (SSS = log clone frequency × log scale), evaluating clonal frequency at each gene segment-scale (J, VJ and VJ+NI). This revealed a TCR SSS with a relatively narrow distribution of 1.64 ± 0.1 (mean ± SD) for J, 1.69 ± 0.2 for VJ, and 1.41 ± 0.01 for VJ+NI, which was consistent between all normal stem cell donors analyzed. Relative proportional distribution (RPD) graphs were then generated to allow for the depiction of the TCR b D, J, V distribution for simultaneous comparison at an individual level. Representative data in Figure 1 shows the relatedness across donors at the TCR b J segment level. Relative clonal frequency was determined for each unique TCR clone at the specified segment level and plotted according to frequency-rank. Slope of the resulting linear regression lines from log-log plots of rank-frequency was used to determine self-similarity and fractal dimension. These plots were comparable among donors with resulting slopes of 1.6 ± 0.01 and 1.8 ± 0.1, respectively for TCR J and VJ containing clones (Figure 2). The plots also revealed a hierarchy of T cell clones, with few dominant clones occupying the high ranks and a multitude of clones in the later ranks. For donor-recipient comparisons, we examined the dominant ranking clones which would be most likely to be involved in GVHD and response to infection. The ordered TCR clonal frequency distribution seen in donors was perturbed in recipients following SCT, with recipients demonstrating a lower level of complexity in their TCR repertoire, and a large shift in the frequency distribution of the dominant T cell clones compared to the donor. When dominant clones were compared between donors and recipients, recipients shared only a small proportion of TCR clonotypes with their donors despite full donor T cell chimerism. This difference did not change over time, suggesting an alternate T cell clonal hierarchy and repertoire develops in transplant recipients when compared with their donors. Using simple mathematical analysis, we demonstrate that the TCR b repertoire has a fractal, self-similar pattern with a hierarchy of dominant and minor clones. We note that the complexity of the TCR repertoire is diminished and TCR b hierarchy is altered following SCT. Restoration of this order may serve as a marker for post-SCT immune reconstitution. Further, by demonstrating shifts in TCR clonal dominance, fractal analysis comparing donor and recipient T cell repertoire may allow for more accurate monitoring of immunotherapy of malignancies in general, beyond allogeneic SCT. Figure 1. Graphical representation of self-similarity in TCR b J gene segment usage across segments and individuals. Relative-proportional-distribution (RPD) graph depicting TCR b J segment usage in ten hematopoietic stem cell donors. Each ring in the graph represents J segment usage frequency in a single donor, showing similarity in J segment frequency across ten different donors. Figure 1. Graphical representation of self-similarity in TCR b J gene segment usage across segments and individuals. Relative-proportional-distribution (RPD) graph depicting TCR b J segment usage in ten hematopoietic stem cell donors. Each ring in the graph represents J segment usage frequency in a single donor, showing similarity in J segment frequency across ten different donors. Figure 2. Log-Log plot depicting linear distribution of frequency ranked TCR b DJ (top panels) and VDJ (bottom panels) clones in two stem cell donors. Figure 2. Log-Log plot depicting linear distribution of frequency ranked TCR b DJ (top panels) and VDJ (bottom panels) clones in two stem cell donors. Disclosures: No relevant conflicts of interest to declare.

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