DYNAMICS OF CREMONA MAPS FROM PHYSICAL MODELS

2001 ◽  
Vol 15 (24n25) ◽  
pp. 3279-3286
Author(s):  
W. SCHWALM ◽  
B. MORITZ ◽  
M. SCHWALM
Keyword(s):  
Dynamical Systems ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Physical Models ◽  
Invariant Curves ◽  
Chiral Potts Model ◽  
Cremona Transformation ◽  
Rational Mapping ◽  
Area Preserving Maps ◽  
The Matrix

A Cremona transformation X=f(x, y), Y=g(x, y) is a rational mapping (meaning that f and g are ratios of polynomials) with rational inverse x=F(X, Y), y=G(X, Y). Discrete dynamical systems defined by such transformations are well studied. They include symmetries of the Yang-Baxter equations and their generalizations. In this paper we comment on two types of dynamical systems based on Cremona transformations. The first is the P1 case of Bellon et al. which pertains to the inversion relation for the matrix of Boltzmann weights of the 4-state chiral Potts model. The resulting dynamical system decouples completely to one in a single variable. The sub case z=x corresponds to the symmetric Ashkin-Teller model. We solve this case explicitly giving orbits as closed formulas in the number n of iterations. The second type of system treated is an extension from the famous example due to McMillan of invariant curves of area preserving maps in two dimensions to the case of invariant curves and surfaces of three dimensional Cremona maps that preserve volume. The trace map of the renormalization of transmission through a Fibonacci chain, first introduced by Kohmoto, Kadanoff and Tang, is considered as an example of such a system.

scholarly journals Responsiveness and Renewal in Canada's Community Colleges: A Study of Change in Organizations

1989 ◽  
Vol 19 (2) ◽  
Author(s):  
John S. Levin ◽  
John D. Dennison
Keyword(s):  
Community Colleges ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Developmental Models ◽  
Managing Change ◽  
The Matrix ◽  
Fiscal Support ◽  
Internal Forces ◽  
Third Dimension ◽  
The 1960S

This study deals with change in organizations. Specifically, the focus is upon Canada's community colleges during a period of economic and socio-political change in the 1980s. Canadian colleges, born and nurtured within an unprecedented era of postsecondary educational expansion in the 1960s, were founded upon ideals of democratization of opportunity, accessibility, adaptability, and comprehensiveness. This study examines if and to what extent the colleges have retained these principles in confronting external and internal forces during the last decade. The theoretical model designed for the study involved a three-dimensional matrix in which theories of adaptation (Cameron, 1984) and power, (Mintzberg, 1979) form two dimensions. The third dimension is created from a variety of optional developmental models specific to the community college as an organization (McCartan, 1983; Cross, 1985; Dennison and Gallagher, 1986). The results of the study revealed that much of the idealism and innovation which guided the colleges in earlier days was still to be found. However, in attempting to deal with increased direction from government, and from reduced fiscal support, the colleges have sought several ways to adjust or adapt. In doing so they have become more enterpreneurial, less community-oriented, and more tightly managed. Diversity, however, was also evident, as adaptive strategies differed widely in various regions across Canada. By applying the matrix designed for the study, it was possible to determine that colleges were managing change by utilizing a variety of techniques. Change in community colleges involves a diversity of methods and produces a diversity of results.

Development for CANDU-6 Moderator Temperature Prediction by Using Porous Media Approach

2012 ◽  
Author(s):  
Jae Ryong Lee ◽  
Han Young Yoon ◽  
Hyoung Tae Kim ◽  
Jae Jun Jeong
Keyword(s):  
Porous Media ◽  
Three Dimensional ◽  
Axial Flow ◽  
Physical Models ◽  
Thermal Hydraulics ◽  
Two Phase ◽  
Grid Systems ◽  
Multi Scale ◽  
The Matrix ◽  
Calculation Results

In this study, a thermal hydraulic behavior of the moderator in the CANDU reactor was numerically investigated by using CUPID code. KAERI has been developing a component-scale thermal hydraulics code, CUPID. The aim of the code is multi-dimensional, multi-physics and multi-scale thermal hydraulics analysis. This code adopts a three-dimensional, transient, two-phase and three-field model, and includes physical models and correlations of the interfacial mass, momentum, and energy transfer for the closure. To avoid the complexity to generate computational geometry around the matrix of 440 Calandria tubes, a porous media approach was applied. Flow resistance inside the porous media zone was derived from the empirical correlation of the frictional pressure loss. In order to consider the turbulent jet inflows from the inlet nozzles, the standard k-ε turbulence model was applied. For the grid dependency test, three different grid systems were tested. The moderator test vessel at Stern Laboratories Inc. (SLI) for the validation is a cylinder with a diameter of 2m and a length of 0.2m (a thin “slice” of CANDU-6 Calandria vessel). Since the axial flow is assumed to be invariant, two-dimensional calculation was performed. Vertical profile of the liquid temperature was compared with other calculation results as well as experimental data.

scholarly journals Three-dimensional geometry and topology effects in viscous streaming

2022 ◽  
Vol 933 ◽  
Author(s):  
Fan Kiat Chan ◽  
Yashraj Bhosale ◽  
Tejaswin Parthasarathy ◽  
Mattia Gazzola
Keyword(s):  
Dynamical Systems ◽  
Bifurcation Theory ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Direct Numerical Simulations ◽  
Flow Topology ◽  
And Topology ◽  
Streaming Flows ◽  
The Impact

Recent studies on viscous streaming flows in two dimensions have elucidated the impact of body curvature variations on resulting flow topology and dynamics, with opportunities for microfluidic applications. Following that, we present here a three-dimensional characterization of streaming flows as functions of changes in body geometry and topology, starting from the well-known case of a sphere to progressively arrive at toroidal shapes. We leverage direct numerical simulations and dynamical systems theory to systematically analyse the reorganization of streaming flows into a dynamically rich set of regimes, the origins of which are explained using bifurcation theory.

Laser Scanning Confocal Microscopy and Three-Dimesnsional Reconstruction of the Mitotic Spindles of Unequally Dividing Embryonic Cells

1990 ◽  
Vol 48 (3) ◽  
pp. 166-167
Author(s):  
J. Holy ◽  
G. Schatten
Keyword(s):  
Confocal Microscopy ◽  
Mitotic Spindle ◽  
Laser Scanning ◽  
Three Dimensional ◽  
Laser Scanning Confocal Microscopy ◽  
Two Dimensions ◽  
Embryonic Cells ◽  
Mitotic Spindles ◽  
Cleavage Division ◽  
Scanning Confocal Microscopy

One of the classic limitations of light microscopy has been the fact that three dimensional biological events could only be visualized in two dimensions. Recently, this shortcoming has been overcome by combining the technologies of laser scanning confocal microscopy (LSCM) and computer processing of microscopical data by volume rendering methods. We have employed these techniques to examine morphogenetic events characterizing early development of sea urchin embryos. Specifically, the fourth cleavage division was examined because it is at this point that the first morphological signs of cell differentiation appear, manifested in the production of macromeres and micromeres by unequally dividing vegetal blastomeres.The mitotic spindle within vegetal blastomeres undergoing unequal cleavage are highly polarized and develop specialized, flattened asters toward the micromere pole. In order to reconstruct the three-dimensional features of these spindles, both isolated spindles and intact, extracted embryos were fluorescently labeled with antibodies directed against either centrosomes or tubulin.

Designing TIMP (tissue inhibitor of metalloproteinases) variants that are selective metalloproteinase inhibitors

2003 ◽  
Vol 70 ◽  
pp. 201-212 ◽  
Author(s):  
Hideaki Nagase ◽  
Keith Brew
Keyword(s):  
Three Dimensional ◽  
Therapeutic Interventions ◽  
Tissue Inhibitors Of Metalloproteinases ◽  
Structural Basis ◽  
Structural Elements ◽  
Ridge Structure ◽  
Extracellular Matrix Components ◽  
Metalloproteinase Inhibitors ◽  
The Matrix ◽  
A Disintegrin And Metalloproteinase

The tissue inhibitors of metalloproteinases (TIMPs) are endogenous inhibitors of the matrix metalloproteinases (MMPs), enzymes that play central roles in the degradation of extracellular matrix components. The balance between MMPs and TIMPs is important in the maintenance of tissues, and its disruption affects tissue homoeostasis. Four related TIMPs (TIMP-1 to TIMP-4) can each form a complex with MMPs in a 1:1 stoichiometry with high affinity, but their inhibitory activities towards different MMPs are not particularly selective. The three-dimensional structures of TIMP-MMP complexes reveal that TIMPs have an extended ridge structure that slots into the active site of MMPs. Mutation of three separate residues in the ridge, at positions 2, 4 and 68 in the amino acid sequence of the N-terminal inhibitory domain of TIMP-1 (N-TIMP-1), separately and in combination has produced N-TIMP-1 variants with higher binding affinity and specificity for individual MMPs. TIMP-3 is unique in that it inhibits not only MMPs, but also several ADAM (a disintegrin and metalloproteinase) and ADAMTS (ADAM with thrombospondin motifs) metalloproteinases. Inhibition of the latter groups of metalloproteinases, as exemplified with ADAMTS-4 (aggrecanase 1), requires additional structural elements in TIMP-3 that have not yet been identified. Knowledge of the structural basis of the inhibitory action of TIMPs will facilitate the design of selective TIMP variants for investigating the biological roles of specific MMPs and for developing therapeutic interventions for MMP-associated diseases.

3D simulation of emulsion flow using the boundary element method on the heterogeneous computational systems

2012 ◽  
Vol 9 (1) ◽  
pp. 142-146
Author(s):  
O.A. Solnyshkina
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Problem Size ◽  
Low Reynolds Numbers ◽  
Infinite Domains ◽  
The Matrix ◽  
Computational Systems ◽  
Element Method

In this work the 3D dynamics of two immiscible liquids in unbounded domain at low Reynolds numbers is considered. The numerical method is based on the boundary element method, which is very efficient for simulation of the three-dimensional problems in infinite domains. To accelerate calculations and increase the problem size, a heterogeneous approach to parallelization of the computations on the central (CPU) and graphics (GPU) processors is applied. To accelerate the iterative solver (GMRES) and overcome the limitations associated with the size of the memory of the computation system, the software component of the matrix-vector product

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

Turbulent three-dimensional dielectric electrohydrodynamic convection between two plates

2012 ◽  
Vol 696 ◽  
pp. 228-262 ◽  
Author(s):  
A. Kourmatzis ◽  
J. S. Shrimpton
Keyword(s):  
Spatial Data ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Energy Budgets ◽  
Turbulent Regime ◽  
Scalar Flux ◽  
Wide Range ◽  
Scalar Variance

AbstractThe fundamental mechanisms responsible for the creation of electrohydrodynamically driven roll structures in free electroconvection between two plates are analysed with reference to traditional Rayleigh–Bénard convection (RBC). Previously available knowledge limited to two dimensions is extended to three-dimensions, and a wide range of electric Reynolds numbers is analysed, extending into a fully inherently three-dimensional turbulent regime. Results reveal that structures appearing in three-dimensional electrohydrodynamics (EHD) are similar to those observed for RBC, and while two-dimensional EHD results bear some similarities with the three-dimensional results there are distinct differences. Analysis of two-point correlations and integral length scales show that full three-dimensional electroconvection is more chaotic than in two dimensions and this is also noted by qualitatively observing the roll structures that arise for both low (${\mathit{Re}}_{E} = 1$) and high electric Reynolds numbers (up to ${\mathit{Re}}_{E} = 120$). Furthermore, calculations of mean profiles and second-order moments along with energy budgets and spectra have examined the validity of neglecting the fluctuating electric field ${ E}_{i}^{\ensuremath{\prime} } $ in the Reynolds-averaged EHD equations and provide insight into the generation and transport mechanisms of turbulent EHD. Spectral and spatial data clearly indicate how fluctuating energy is transferred from electrical to hydrodynamic forms, on moving through the domain away from the charging electrode. It is shown that ${ E}_{i}^{\ensuremath{\prime} } $ is not negligible close to the walls and terms acting as sources and sinks in the turbulent kinetic energy, turbulent scalar flux and turbulent scalar variance equations are examined. Profiles of hydrodynamic terms in the budgets resemble those in the literature for RBC; however there are terms specific to EHD that are significant, indicating that the transfer of energy in EHD is also attributed to further electrodynamic terms and a strong coupling exists between the charge flux and variance, due to the ionic drift term.

Simulation of small-angle scattering curves by numerical Fourier transformation

2007 ◽  
Vol 40 (1) ◽  
pp. 16-25 ◽  
Author(s):  
Klaus Schmidt-Rohr
Keyword(s):  
Form Factor ◽  
Small Angle ◽  
Fourier Transformation ◽  
Three Dimensional ◽  
Power Laws ◽  
Numerical Approach ◽  
Peak Position ◽  
Two Dimensions ◽  
Correlation Peak ◽  
Scattering Intensity

A simple numerical approach for calculating theq-dependence of the scattering intensity in small-angle X-ray or neutron scattering (SAXS/SANS) is discussed. For a user-defined scattering density on a lattice, the scattering intensityI(q) (qis the modulus of the scattering vector) is calculated by three-dimensional (or two-dimensional) numerical Fourier transformation and spherical summation inqspace, with a simple smoothing algorithm. An exact and simple correction for continuous rather than discrete (lattice-point) scattering density is described. Applications to relatively densely packed particles in solids (e.g.nanocomposites) are shown, where correlation effects make single-particle (pure form-factor) calculations invalid. The algorithm can be applied to particles of any shape that can be defined on the chosen cubic lattice and with any size distribution, while those features pose difficulties to a traditional treatment in terms of form and structure factors. For particles of identical but potentially complex shapes, numerical calculation of the form factor is described. Long parallel rods and platelets of various cross-section shapes are particularly convenient to treat, since the calculation is reduced to two dimensions. The method is used to demonstrate that the scattering intensity from `randomly' parallel-packed long cylinders is not described by simple 1/qand 1/q4power laws, but at cylinder volume fractions of more than ∼25% includes a correlation peak. The simulations highlight that the traditional evaluation of the peak position overestimates the cylinder thickness by a factor of ∼1.5. It is also shown that a mix of various relatively densely packed long boards can produceI(q) ≃ 1/q, usually observed for rod-shaped particles, without a correlation peak.

scholarly journals Data-Informed Decomposition for Localized Uncertainty Quantification of Dynamical Systems

Vibration ◽  
2020 ◽  
Vol 4 (1) ◽  
pp. 49-63
Author(s):  
Waad Subber ◽  
Sayan Ghosh ◽  
Piyush Pandita ◽  
Yiming Zhang ◽  
Liping Wang
Keyword(s):  
Dynamical Systems ◽  
Computational Cost ◽  
Three Dimensional ◽  
Region Of Interest ◽  
System Response ◽  
Computational Domain ◽  
User Interest ◽  
Numerical Resolution ◽  
Multi Scale ◽  
Operation Conditions

Industrial dynamical systems often exhibit multi-scale responses due to material heterogeneity and complex operation conditions. The smallest length-scale of the systems dynamics controls the numerical resolution required to resolve the embedded physics. In practice however, high numerical resolution is only required in a confined region of the domain where fast dynamics or localized material variability is exhibited, whereas a coarser discretization can be sufficient in the rest majority of the domain. Partitioning the complex dynamical system into smaller easier-to-solve problems based on the localized dynamics and material variability can reduce the overall computational cost. The region of interest can be specified based on the localized features of the solution, user interest, and correlation length of the material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update the prior knowledge of the localized region of interest using measurements of the system response. Once, the region of interest is identified, the localized uncertainty is propagate forward through the computational domain. We demonstrate our framework using numerical experiments on a three-dimensional elastodynamic problem.

Sign in / Sign up

Export Citation Format

Share Document