scholarly journals Steady-State-Preserving Simulation of Genetic Regulatory Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-16
Author(s):  
Ruqiang Zhang ◽  
Julius Osato Ehigie ◽  
Xilin Hou ◽  
Xiong You ◽  
Chunlu Yuan

A novel family of exponential Runge-Kutta (expRK) methods are designed incorporating the stable steady-state structure of genetic regulatory systems. A natural and convenient approach to constructing new expRK methods on the base of traditional RK methods is provided. In the numerical integration of the one-gene, two-gene, and p53-mdm2 regulatory systems, the new expRK methods are shown to be more accurate than their prototype RK methods. Moreover, for nonstiff genetic regulatory systems, the expRK methods are more efficient than some traditional exponential RK integrators in the scientific literature.

2018 ◽  
Vol 787 ◽  
pp. 113-122
Author(s):  
Jian Wei Zhang ◽  
Hai Jun Chen ◽  
Sheng Jun Wang ◽  
Yuan Ren

Exciton-polariton condensate is a new kind of system exhibiting spontaneous coherence, which is a new quantum dissipation system. Numerical simulation and analytical methods can be used to study the static and dynamical properties of exciton-polariton condensate. In this paper, A modified Lagrangian method is developed for exciton-polariton system to find the steady-state structure and regimes among the parameters of the system, and two new forms of trial wave function are proposed. The modified Lagrangian method is successfully applied to the exciton-polariton system described by the open-dissipative Gross-Pitaevskii equation for the first time. Furthermore, static version of the modified Lagrangian method provides stationary shape of the steady-state structure, while the time-dependent version can be used to study small amplitude oscillations around stationary states. On the one hand, comparison of the profiles for steady-state structure, predicted by the modified Lagrangian and those found from numerical solution of the open-dissipative Gross-Pitaevskii(dGP) equation shows good agreement, thereby proving the accuracy of the trial wave function and validating the proposed approach. Particularly, this new method promotes the deeper cognition and understanding for the dissipative exciton-polariton system and is helpful to explore the mechanism of the gain and dissipation effect on the steady-state structure of the system.


Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 174
Author(s):  
Janez Urevc ◽  
Miroslav Halilovič

In this paper, a new class of Runge–Kutta-type collocation methods for the numerical integration of ordinary differential equations (ODEs) is presented. Its derivation is based on the integral form of the differential equation. The approach enables enhancing the accuracy of the established collocation Runge–Kutta methods while retaining the same number of stages. We demonstrate that, with the proposed approach, the Gauss–Legendre and Lobatto IIIA methods can be derived and that their accuracy can be improved for the same number of method coefficients. We expressed the methods in the form of tables similar to Butcher tableaus. The performance of the new methods is investigated on some well-known stiff, oscillatory, and nonlinear ODEs from the literature.


2012 ◽  
Vol 6 (3) ◽  
pp. 573-588 ◽  
Author(s):  
F. Pattyn ◽  
C. Schoof ◽  
L. Perichon ◽  
R. C. A. Hindmarsh ◽  
E. Bueler ◽  
...  

Abstract. Predictions of marine ice-sheet behaviour require models that are able to robustly simulate grounding line migration. We present results of an intercomparison exercise for marine ice-sheet models. Verification is effected by comparison with approximate analytical solutions for flux across the grounding line using simplified geometrical configurations (no lateral variations, no effects of lateral buttressing). Unique steady state grounding line positions exist for ice sheets on a downward sloping bed, while hysteresis occurs across an overdeepened bed, and stable steady state grounding line positions only occur on the downward-sloping sections. Models based on the shallow ice approximation, which does not resolve extensional stresses, do not reproduce the approximate analytical results unless appropriate parameterizations for ice flux are imposed at the grounding line. For extensional-stress resolving "shelfy stream" models, differences between model results were mainly due to the choice of spatial discretization. Moving grid methods were found to be the most accurate at capturing grounding line evolution, since they track the grounding line explicitly. Adaptive mesh refinement can further improve accuracy, including fixed grid models that generally perform poorly at coarse resolution. Fixed grid models, with nested grid representations of the grounding line, are able to generate accurate steady state positions, but can be inaccurate over transients. Only one full-Stokes model was included in the intercomparison, and consequently the accuracy of shelfy stream models as approximations of full-Stokes models remains to be determined in detail, especially during transients.


2003 ◽  
Vol 14 (08) ◽  
pp. 1087-1105 ◽  
Author(s):  
ZHONGCHENG WANG ◽  
YONGMING DAI

A new twelfth-order four-step formula containing fourth derivatives for the numerical integration of the one-dimensional Schrödinger equation has been developed. It was found that by adding multi-derivative terms, the stability of a linear multi-step method can be improved and the interval of periodicity of this new method is larger than that of the Numerov's method. The numerical test shows that the new method is superior to the previous lower orders in both accuracy and efficiency and it is specially applied to the problem when an increasing accuracy is requested.


2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Cao Taiqiang ◽  
Chen Zhangyong ◽  
Wang Jun ◽  
Sun Zhang ◽  
Luo Qian ◽  
...  

In order to implement a high-efficiency bridgeless power factor correction converter, a new topology and operation principles of continuous conduction mode (CCM) and DC steady-state character of the converter are analyzed, which show that the converter not only has bipolar-gain characteristic but also has the same characteristic as the traditional Boost converter, while the voltage transfer ratio is not related with the resonant branch parameters and switching frequency. Based on the above topology, a novel bridgeless Bipolar-Gain Pseudo-Boost PFC converter is proposed. With this converter, the diode rectifier bridge of traditional AC-DC converter is eliminated, and zero-current switching of fast recovery diode is achieved. Thus, the efficiency is improved. Next, we also propose the one-cycle control policy of this converter. Finally, experiments are provided to verify the accuracy and feasibility of the proposed converter.


2002 ◽  
Vol 124 (4) ◽  
pp. 537-544 ◽  
Author(s):  
Gong Cheng ◽  
Jean W. Zu

In this paper, a mass-spring-friction oscillator subjected to two harmonic disturbing forces with different frequencies is studied for the first time. The friction in the system has combined Coulomb dry friction and viscous damping. Two kinds of steady-state vibrations of the system—non-stop and one-stop motions—are considered. The existence conditions for each steady-state motion are provided. Using analytical analysis, the steady-state responses are derived for the two-frequency oscillating system undergoing both the non-stop and one-stop motions. The focus of the paper is to study the influence of the Coulomb dry friction in combination with the two frequency excitations on the dynamic behavior of the system. From the numerical simulations, it is found that near the resonance, the dynamic response due to the two-frequency excitation demonstrates characteristics significantly different from those due to a single frequency excitation. Furthermore, the one-stop motion demonstrates peculiar characteristics, different from those in the non-stop motion.


2021 ◽  
Author(s):  
Xueyun Wang ◽  
Xueqiao Xu ◽  
Philip B Snyder ◽  
Zeyu Li

Abstract The BOUT++ six-field turbulence code is used to simulate the ITER 11.5MA hybrid scenario and a brief comparison is made among ITER baseline, hybrid and steady-state operation (SSO) scenarios. Peeling-ballooning instabilities with different toroidal mode numbers dominate in different scenarios and consequently yield different types of ELMs. The energy loss fractions (ΔWped/Wped) caused by unmitigated ELMs in the baseline and hybrid scenarios are large (~2%) while the one in the SSO scenario is dramatically smaller (~1%), which are consistent with the features of type-I ELMs and grassy ELMs respectively. The intra ELM divertor heat flux width in the three scenarios given by the simulations is larger than the estimations for inter ELM phase based on Goldston’s heuristic drift model. The toroidal gap edge melting limit of tungsten monoblocks of divertor targets imposes constraints on ELM energy loss, giving that the ELM energy loss fraction should be smaller than 0.4%, 1.0%, and 1.2% for ITER baseline, hybrid and SSO scenarios, correspondingly. The simulation shows that only the SSO scenario with grassy ELMs may satisfy the constraint.


Author(s):  
Natalia G. Krivulya ◽  

Animated documentary is becoming one of the fastest growing phenomena of modern screen art in the post-truth era. The review and analysis of scientific works devoted to animated documentary is seen as relevant both for the further development of scientific thought and the search for new research strategies that expand the problem field, and for the practical sphere. The research was conducted on the basis of a review and analysis of scientific literature (monographs and articles in international journals included in electronic research system international databases Scopus, Web of Science, eLibrary.ru) in English, Spanish and Russian for the period 1997-2019. The novelty of the review article is not only an attempt to present a systematic view of animated documentary as a phenomenon of screen art, but also to identify and systematize the areas in which scientific discussions are conducted. It introduces the reader to theoretical views on the terminology, Genesis, specifics, nature, and classification systems of documentary animation. Animated documentary appeared when the cinema was just taking first steps but its development began in the 1980s. At this time, animation begins to take an interest in reality, inner peace, and socially taboo topics. Since the 1990s, the foundations of animated documentary are laid, narrative strategies are developed, and a new language are actively sought. Interest in animated documentary from the scientific community arose only in the 2000s. On the one hand, it has been manifested by the increasing role of documentation in the art, which has taken on an attraction character since the advent of digital technology; on the other hand, and as a consequence of the convergence of screen arts and the emergence of hybridization trends. The academic community has focused around developing definitions and understanding what can be attributed to the field of documentary animation. By 2010, the scientific literature focused on issues related to the specifics of animated documentary, ways of presenting reality, and indexing. By the mid-2010s, animation is becoming the subject of interdisciplinary study. At this time, there are develop tools for analyzing works of animated documentaries, and its genre system begins to build. One of the main features of animated documentaries is hybridity. Its dual nature is born of fluctuations between the certainty of facts and artistic embodiment. The problems of authenticity and representation of reality become one of the most controversial topics in an animated film. The work provides an overview of theoretical studies on the genesis, history and particularities of animadoc. The theoretical texts identify three approaches that form the main directions in the analysis of animated documentary. The first group of researchers analyzes this phenomenon and its nature based on the theories of documentaries and the transformation with the advent of digital technologies, of the concepts of reality, authenticity and fact (document). The second group of authors considers animation as a phenomenon of modern animation that arose as a result of technological renewal and changes in its role as a socio-cultural practice. A third group of scientists believes that animadoc is a post-postmodern phenomenon that arose as a means of presenting a world in which there is mobility of borders and cyberspace becomes a new reality. The review allows us to conclude that animated documentary is a manifestation of a new mode of postphotographic vision of a reflexive nature, in which the imagination that refracts images of reality becomes of primary importance. Despite the interest in it from the academic community and the emergence of theoretical works, the study of this phenomenon is only at the initial stage. Despite the interest in it from the academic community, there is a small number of deep theoretical works caused by the hybrid nature of the phenomenon itself, the imperfection of working models and methods for analyzing representational strategies, and the problems of forming a conceptual apparatus.


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