nonlinear growth
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2021 ◽  
Vol 84 (1) ◽  
Author(s):  
Guim Aguadé-Gorgorió ◽  
Stuart Kauffman ◽  
Ricard Solé

AbstractPhenotypic switching in cancer cells has been found to be present across tumor types. Recent studies on Glioblastoma report a remarkably common architecture of four well-defined phenotypes coexisting within high levels of intra-tumor genetic heterogeneity. Similar dynamics have been shown to occur in breast cancer and melanoma and are likely to be found across cancer types. Given the adaptive potential of phenotypic switching (PHS) strategies, understanding how it drives tumor evolution and therapy resistance is a major priority. Here we present a mathematical framework uncovering the ecological dynamics behind PHS. The model is able to reproduce experimental results, and mathematical conditions for cancer progression reveal PHS-specific features of tumors with direct consequences on therapy resistance. In particular, our model reveals a threshold for the resistant-to-sensitive phenotype transition rate, below which any cytotoxic or switch-inhibition therapy is likely to fail. The model is able to capture therapeutic success thresholds for cancers where nonlinear growth dynamics or larger PHS architectures are in place, such as glioblastoma or melanoma. By doing so, the model presents a novel set of conditions for the success of combination therapies able to target replication and phenotypic transitions at once. Following our results, we discuss transition therapy as a novel scheme to target not only combined cytotoxicity but also the rates of phenotypic switching.


2021 ◽  
Vol 105 (1) ◽  
pp. 225-229
Author(s):  
Anna V. Potapenko ◽  
Oleksandr V. Potapenko ◽  
Oleksandr V. Krushevskyi ◽  
Miaomiao Zhou

The paper discusses the electrochemical behavior of a Li-S battery with a new water-soluble binder NV-1A. It is shown that the main contribution is made by the interface, which is formed on the lithium counter electrode. It is noteworthy that the nonlinear growth of the resistance of SEI layer during the discharge process correlates with the change in the resistance of charge transfer through the interface.


Author(s):  
Ningfei Chen ◽  
Shizhao Wei ◽  
Guangyu Wei ◽  
Zhiyong Qiu

Abstract The two-field equations governing fully nonlinear dynamics of the drift wave (DW) and geodesic acoustic mode (GAM) interaction in toroidal geometry are derived in the nonlinear gyrokinetic framework. Two stages with distinctive features are identified and analyzed by both analytical and numerical approaches. In the linear growth stage, the derived set of nonlinear equations can be reduced to the intensively studied parametric decay instability (PDI), accounting for the spontaneous resonant excitation of GAM by DW. The main results of previous works on spontaneous GAM excitation, e.g., the much enhanced GAM group velocity and the nonlinear growth rate of GAM, are reproduced from the numerical solution of the two-field equations. In the fully nonlinear stage, soliton structures are observed to form due to the balancing of the self-trapping effect by the spontaneously excited GAM and kinetic dispersiveness of DW. The soliton structures enhance turbulence spreading from DW linearly unstable to stable region, exhibiting convective propagation instead of typical linear dispersive process, and is thus, expected to induce core-edge interaction and nonlocal transport.


2021 ◽  
pp. 121-158
Author(s):  
Hannu E. J. Koskinen ◽  
Emilia K. J. Kilpua

AbstractHow different wave modes are driven, is a central issue in space plasma physics. A practical problem is that often only indirect evidence of the driver can be identified in observations. The plasma environment is complex and variable and already a small difference in background or initial conditions may lead to widely different observable outcomes. In this chapter we discuss drivers of waves causing acceleration, transport and loss of radiation belt particles, whereas Chap. 10.1007/978-3-030-82167-8_6 discusses these effects in detail. We note that while this division is motivated in a textbook, it is somewhat artificial and the growth of the waves and their consequences often need to be studied together. For example, a whistler-mode wave can grow from thermal fluctuations due to gyro-resonant interactions until a marginally stable state is reached or nonlinear growth takes over. The growing wave starts to interact with different particle populations leading to damping or further growth of the wave. The fluxes of the higher-energy radiation belt particles are, however, small compared to the lower-energy background population, which supports the wave. Thus their effects on the overall wave activity usually remain small, although the waves can have drastic effect on higher-energy populations. Consequently, these two chapters should be studied together.


Author(s):  
Hossein Lotfi ◽  
Mahboub Hosseinpour

By using 2.5-dimensional resistive MHD simulations, dynamics of the plasmoid instability in a Harris current sheet has been studied with taking into account two main controlling parameters: the plasma-β in the range (0 < β < 1) and the amplitude ratio of magnetic guide field to the reconnection plane field in three different cases with zero, uniform, and non-uniform guide field. Varying the plasma-β changes the plasma compressibility which affects significantly on the linear and nonlinear growth rates of the plasmoid instability. For each of three cases, some associated scaling relations between the instability growth rate, the plasma-β and the magnitude of guide field are obtained.


2021 ◽  
Author(s):  
Amanda Diekman ◽  
Heidi E. Williams ◽  
Heidi A. Vuletich ◽  
Joe Vuletich

We delineate a framework for considering the differential implications of understanding human experience when invoking metaphors based on living, biological beings versus metaphors based on machines/technology. We consider the origins and expressions of machine metaphors as culturally dominant in the United States and Western Europe. Machine metaphorical frames differ from living-being metaphorical frames in assumptions about transformation, development, and decline; in expectations about source of motion or change; and in whether environment or season are seen as integral to experience or action. These features then carry consequences for how individuals make sense of their and others’ experiences. In particular, we highlight how understanding based on living, biological beings might result in different meanings attached to the purpose of activity, to pauses in activity or nonlinear growth, in variability across individuals, and in what discomfort signals. We close by considering the implications of these different metaphorical frames for system design, well-being, and group disparities in achievement. This review provides a framework for empirical research that examines the psychological consequences of these different frames.


Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2180
Author(s):  
Rafael Pérez Abreu C. ◽  
Samantha Estrada ◽  
Héctor de-la-Torre-Gutiérrez

Since December 2019, the novel coronavirus (SARS-CoV-2) and its associated illness COVID-19 have rapidly spread worldwide. The Mexican government has implemented public safety measures to minimize the spread of the virus. In this paper, we used statistical models in two stages to estimate the total number of coronavirus (COVID-19) cases per day at the state and national levels in Mexico. In this paper, we propose two types of models. First, a polynomial model of the growth for the first part of the outbreak until the inflection point of the pandemic curve and then a second nonlinear growth model used to estimate the middle and the end of the outbreak. Model selection was performed using Vuong’s test. The proposed models showed overall fit similar to predictive models (e.g., time series and machine learning); however, the interpretation of parameters is simpler for decisionmakers, and the residuals follow the expected distribution when fitting the models without autocorrelation being an issue.


2021 ◽  
Vol 14 (2) ◽  
pp. 100-107
Author(s):  
E. M. Farhadzadeh ◽  
A. Z. Muradalyiev ◽  
S. A. Muradalyiev ◽  
A. A. Nazarov

The organization of operation, maintenance and repair of the basic technological facilities of electric power systems (EPS), which are beyond their designed service life (hereinafter referred to as ageing facilities, or AFs) is one of the problems that determine the energy security of many countries, including economically developed nations. The principal cause of insufficient overall performance of AFs is the traditional focus of the EPS management on economic efficiency and the insufficient attention to reliability and safety of AFs. The tendency to nonlinear growth in the frequency of occurrence of unacceptable consequences in the EPS requires ensuring the operational reliability and safety of AFs. The averaged estimates of reliability and safety used at designing power facilities are not suitable for characterization of overall operational performance. Among the basic and the least investigated (in terms of operational reliability and safety) EPS facilities are overhead power transmission lines (OPL) with a voltage of 110 кV and above. This is for a reason. OPL are electric power facilities with elements distributed along a multi-kilometer line (supports, insulators, wires, accessories, etc.). That is what makes the organization of continuous monitoring of the technical condition of each of these elements, and, consequently, the assessment of operational reliability and safety, so problematic. A method is suggested for assessment of “weak links” among the operated OPL on operative intervals of time along with a method for assessment of the technical condition of OPL at examination of a representative sample.


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