scholarly journals Fractal initial conditions and natural parameter values in hybrid inflation

2009 ◽  
Vol 80 (12) ◽  
Author(s):  
Sébastien Clesse ◽  
Christophe Ringeval ◽  
Jonathan Rocher
Keyword(s):  
Initial Conditions ◽  
Natural Parameter ◽  
Hybrid Inflation ◽  
Parameter Values

scholarly journals Harmonic hybrid inflation

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Federico Carta ◽  
Nicole Righi ◽  
Yvette Welling ◽  
Alexander Westphal
Keyword(s):  
Domain Wall ◽  
Symmetry Breaking ◽  
Initial Conditions ◽  
Scalar Potential ◽  
Field Range ◽  
Slow Roll ◽  
Minimal Form ◽  
Wide Range ◽  
Hybrid Inflation ◽  
Type Iib String Theory

Abstract We present a mechanism for realizing hybrid inflation using two axion fields with a purely non-perturbatively generated scalar potential. The structure of the scalar potential is highly constrained by the discrete shift symmetries of the axions. We show that harmonic hybrid inflation generates observationally viable slow-roll inflation for a wide range of initial conditions. This is possible while accommodating certain UV arguments favoring constraints f ≲ MP and ∆ϕ60 ≲ MP on the axion periodicity and slow-roll field range, respectively. We discuss controlled ℤ2-symmetry breaking of the adjacent axion vacua as a means of avoiding cosmological domain wall problems. Including a minimal form of ℤ2-symmetry breaking into the minimally tuned setup leads to a prediction of primordial tensor modes with the tensor-to-scalar ratio in the range 10−4 ≲ r ≲ 0.01, directly accessible to upcoming CMB observations. Finally, we outline several avenues towards realizing harmonic hybrid inflation in type IIB string theory.

scholarly journals Initial conditions for smooth hybrid inflation

1996 ◽  
Vol 54 (2) ◽  
pp. 1369-1373 ◽  
Author(s):  
G. Lazarides ◽  
C. Panagiotakopoulos ◽  
N. D. Vlachos
Keyword(s):  
Initial Conditions ◽  
Hybrid Inflation

scholarly journals Predicting Experimental Sepsis Survival with a Mathematical Model of Acute Inflammation

2021 ◽  
Vol 1 ◽  
Author(s):  
Jared Barber ◽  
Amy Carpenter ◽  
Allison Torsey ◽  
Tyler Borgard ◽  
Rami A. Namas ◽  
...  
Keyword(s):  
Immune Response ◽  
Growth Rate ◽  
Inflammatory Response ◽  
Inflammatory Responses ◽  
Initial Conditions ◽  
Mortality Data ◽  
Experimental Sepsis ◽  
Initial Inoculum ◽  
Molecular Pattern ◽  
Parameter Values

Sepsis is characterized by an overactive, dysregulated inflammatory response that drives organ dysfunction and often results in death. Mathematical modeling has emerged as an essential tool for understanding the underlying complex biological processes. A system of four ordinary differential equations (ODEs) was developed to simulate the dynamics of bacteria, the pro- and anti-inflammatory responses, and tissue damage (whose molecular correlate is damage-associated molecular pattern [DAMP] molecules and which integrates inputs from the other variables, feeds back to drive further inflammation, and serves as a proxy for whole-organism health status). The ODE model was calibrated to experimental data from E. coli infection in genetically identical rats and was validated with mortality data for these animals. The model demonstrated recovery, aseptic death, or septic death outcomes for a simulated infection while varying the initial inoculum, pathogen growth rate, strength of the local immune response, and activation of the pro-inflammatory response in the system. In general, more septic outcomes were encountered when the initial inoculum of bacteria was increased, the pathogen growth rate was increased, or the host immune response was decreased. The model demonstrated that small changes in parameter values, such as those governing the pathogen or the immune response, could explain the experimentally observed variability in mortality rates among septic rats. A local sensitivity analysis was conducted to understand the magnitude of such parameter effects on system dynamics. Despite successful predictions of mortality, simulated trajectories of bacteria, inflammatory responses, and damage were closely clustered during the initial stages of infection, suggesting that uncertainty in initial conditions could lead to difficulty in predicting outcomes of sepsis by using inflammation biomarker levels.

Dynamic bifurcations in non-stationary systems: transitions with an unpredictable outcome

1995 ◽  
Vol 451 (1942) ◽  
pp. 471-485 ◽  
Keyword(s):  
Critical Parameter ◽  
Initial Conditions ◽  
Basins Of Attraction ◽  
Important Concept ◽  
New Form ◽  
Parameter Values ◽  
Dynamic Bifurcations

In nonlinear non-stationary systems, dynamic bifurcations result in a transition to a qualitatively new state. In this paper we examine how the dynamics of transition of such systems may be assessed using the concept of transient basins of attraction. We delineate the phenomenon of indeterminate dynamic bifurcations, where it is shown that the response, after the system passes through critical parameter values, may be extremely sensitive to the choice of initial conditions or parameter states. This new form of unpredictability in systems whose parameters vary with time, is clearly an important concept to be assimilated in the theory of non-stationary dynamics.

FLUCTUATIONS IN THE STATE OF CHAOS-CHAOS INTERMITTENCY OF CHUA’S CIRCUIT

1995 ◽  
Vol 05 (01) ◽  
pp. 271-273
Author(s):  
M. KOCH ◽  
R. TETZLAFF ◽  
D. WOLF
Keyword(s):  
Power Spectrum ◽  
Initial Conditions ◽  
Piecewise Linear ◽  
The State ◽  
Circuit Parameter ◽  
Chua’S Circuit ◽  
External Excitation ◽  
Chua's Circuit ◽  
Parameter Values

We studied the power spectrum of the normalized voltage across the capacitor parallel to a piecewise-linear resistor of Chua’s circuit in the “chaos-chaos intermittency” state [Anishchenko et al., 1992]. The investigations included various initial conditions and circuit parameter values without and with external excitation. In all cases we found spectra showing a 1/ω2-decay over more than four decades.

scholarly journals Topographically forced long waves on a sheared coastal current. Part 2. Finite amplitude waves

1997 ◽  
Vol 343 ◽  
pp. 153-168 ◽  
Author(s):  
S. R. CLARKE ◽  
E. R. JOHNSON
Keyword(s):  
Wave Equation ◽  
Initial Conditions ◽  
Finite Amplitude ◽  
Coastal Current ◽  
Constant Vorticity ◽  
Long Wave ◽  
Long Time ◽  
Wave Limit ◽  
Parameter Values ◽  
Upstream Flow

This paper analyses the finite-amplitude flow of a constant-vorticity current past coastal topography in the long-wave limit. A forced finite-amplitude long-wave equation is derived to describe the evolution of the vorticity interface. An analysis of this equation shows that three distinct near-critical regimes occur. In the first the upstream flow is restricted, with overturning of the vorticity interface for sufficiently large topography. In the second quasi-steady nonlinear waves form downstream of the topography with weak upstream influence. In the third regime the upstream rotational fluid is partially blocked. Blocking and overturning are enhanced at headlands with steep rear faces and decreased at headlands with steep forward faces. For certain parameter values both overturning and partially blocked solutions are possible and the long-time evolution is critically dependent on the initial conditions. The reduction of the problem to a one-dimensional nonlinear wave equation allows solutions to be followed to much longer times and parameter space to be explored more finely than in the related pioneering contour-dynamical integrations of Stern (1991).

Inviscid quasi-geostrophic flow over topography: testing statistical mechanical theory

1996 ◽  
Vol 309 ◽  
pp. 85-91 ◽  
Author(s):  
William J. Merryfield ◽  
Greg Holloway
Keyword(s):  
Numerical Simulations ◽  
Large Range ◽  
Initial Conditions ◽  
Steady Flows ◽  
Mechanical Theory ◽  
Geostrophic Flow ◽  
Mechanical Description ◽  
Flow Over Topography ◽  
Statistical Mechanical ◽  
Parameter Values

Numerical simulations are employed in a detailed test of the statistical mechanical description of topographic turbulence. Predictions of steady flows correlated with topography are given particular attention. Agreement between numerical and statistical mechanical results is demonstrated for a large range of parameter values, and over an ensemble of random choices of topography and initial conditions.

scholarly journals Stability, Bifurcation, Chaos : Discrete Prey Predator Model with Step Size

2019 ◽  
Vol 9 (1) ◽  
pp. 3382-3387 ◽  
Keyword(s):  
Chaotic Behavior ◽  
Initial Conditions ◽  
Equilibrium States ◽  
Phase Portraits ◽  
Step Size ◽  
Dynamical Nature ◽  
Predator Model ◽  
The Stability ◽  
Parameter Values ◽  
Bifurcation Chaos

In this work titled Stability, Bifurcation, Chaos: Discrete prey predator model with step size, by Forward Euler Scheme method the discrete form is obtained. Equilibrium states are calculated and the stability of the equilibrium states and dynamical nature of the model are examined in the closed first quadrant 2 R with the help of variation matrix. It is observed that the system is sensitive to the initial conditions and also to parameter values. The dynamical nature of the model is investigated with the assistance of Lyapunov Exponent, bifurcation diagrams, phase portraits and chaotic behavior of the system is identified. Numerical simulations validate the theoretical observations.

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