Search results for "Linear"
showing 10 items of 7165 documents
A Review of Mathematical and Computational Methods in Cancer Dynamics.
2022
Cancers are complex adaptive diseases regulated by the nonlinear feedback systems between genetic instabilities, environmental signals, cellular protein flows, and gene regulatory networks. Understanding the cybernetics of cancer requires the integration of information dynamics across multidimensional spatiotemporal scales, including genetic, transcriptional, metabolic, proteomic, epigenetic, and multi-cellular networks. However, the time-series analysis of these complex networks remains vastly absent in cancer research. With longitudinal screening and time-series analysis of cellular dynamics, universally observed causal patterns pertaining to dynamical systems, may self-organize in the si…
A note on the uniqueness result for the inverse Henderson problem
2019
The inverse Henderson problem of statistical mechanics is the theoretical foundation for many bottom-up coarse-graining techniques for the numerical simulation of complex soft matter physics. This inverse problem concerns classical particles in continuous space which interact according to a pair potential depending on the distance of the particles. Roughly stated, it asks for the interaction potential given the equilibrium pair correlation function of the system. In 1974, Henderson proved that this potential is uniquely determined in a canonical ensemble and he claimed the same result for the thermodynamical limit of the physical system. Here, we provide a rigorous proof of a slightly more …
CLASSIFICATION THEORY FOR PHASE TRANSITIONS
1993
A refined classification theory for phase transitions in thermodynamics and statistical mechanics in terms of their orders is introduced and analyzed. The refined thermodynamic classification is based on two independent generalizations of Ehrenfests traditional classification scheme. The statistical mechanical classification theory is based on generalized limit theorems for sums of random variables from probability theory and the newly defined block ensemble limit. The block ensemble limit combines thermodynamic and scaling limits and is similar to the finite size scaling limit. The statistical classification scheme allows for the first time a derivation of finite size scaling without reno…
Finite-size scaling in a microcanonical ensemble
1988
The finite-size scaling technique is extended to a microcanonical ensemble. As an application, equilibrium magnetic properties of anL×L square lattice Ising model are computed using the microcanonical ensemble simulation technique of Creutz, and the results are analyzed using the microcanonical ensemble finite-size scaling. The computations were done on the multitransputer system of the Condensed Matter Theory Group at the University of Mainz.
Evaluating the predictive power of sun-induced chlorophyll fluorescence to estimate net photosynthesis of vegetation canopies: A SCOPE modeling study
2016
Abstract Progress in imaging spectroscopy technology and data processing can enable derivation of the complete sun-induced chlorophyll fluorescence (SIF) emission spectrum. This opens up opportunities to fully exploit the use of the SIF spectrum as an indicator of photosynthetic activity. Simulations performed with the coupled fluorescence–photosynthesis model SCOPE were used to determine how strongly canopy-leaving SIF can be related to net photosynthesis of the canopy (NPC) for various canopy configurations. Regression analysis between SIF retrievals and NPC values produced the following general findings: (1) individual SIF bands that were most sensitive to NPC were located around the fir…
Simplified Interception/Evaporation Model
2021
It is known that at the event scale, evaporation losses of rainfall intercepted by canopy are a few millimeters, which is often not much in comparison to other stocks in the water balance. Nevertheless, at yearly scale, the number of times that the canopy is filled by rainfall and then depleted can be so large that the interception flux may become an important fraction of rainfall. Many accurate interception models and models that describe evaporation by wet canopy have been proposed. However, they often require parameters that are difficult to obtain, especially for large-scale applications. In this paper, a simplified interception/evaporation model is proposed, which considers a modified …
Construction sequence analysis of long-span cable-stayed bridges
2018
Abstract In cantilever construction of long-span cable-stayed bridges the stressing sequence of stays is fundamental for establishing the final configuration of the bridge. The structural behaviour of these bridges is usually evaluated through a forward staged construction analysis, in which the values of the prestressing forces to be applied to stays are the main unknowns. A unified procedure for determining the initial cable forces and for analyzing the entire sequence is presented here, considering the geometric nonlinearity of stays through the Dischinger equivalent elastic modulus. The target is the simultaneous determination of the initial cable forces with the simulation of the const…
A continuous decomposition of the Menger curve into pseudo-arcs
2000
It is proved that the Menger universal curve M admits a continuous decomposition into pseudo-arcs with the quotient space homeomorphic to M. Wilson proved [8] Anderson's announcement [1] saying that for any Peano continuum X the Menger universal curve M admits a continuous decomposition into homeomorphic copies of M such that the quotient space is homeomorphic to X. Anderson also announced (unpublished) that the plane admits a continuous decomposition into pseudo-arcs. This result was proved by Lewis and Walsh [4]. In a previous paper [6] the author has proved that each locally planar Peano continuum with no local separating point admits a continuous decomposition into pseudo-arcs. Applying…
Diffusion processes with ultrametric jumps
2007
Abstract In the theory of spin glasses the relaxation processes are modelled by random jumps in ultrametric spaces. One may argue that at the border of glassy and nonglassy phases the processes combining diffusion and jumps may be relevant. Using the Dirichlet form technique we construct a model of diffusion on the real line with jumps on the Cantor set. The jumps preserve the ultrametric feature of a random process on unit ball of 2-adic numbers.
Microbubble PhoXonic resonators: Chaos transition and transfer
2022
We report the activation of optomechanical chaotic oscillations in microbubble resonators (MBRs) through a blue-side excitation of its optical resonances. We confirm the sequence of quasi-periodical oscillation, spectral continuum and aperiodic motion; as well as the transition to chaos without external feedback or modulation of the laser source. In particular, quasi periodic transitions and a spectral continuum are reported for MBRs with diameters up to 600 μm, whereas only an abrupt transition into a spectral con- tinuum is observed for larger microbubbles.