Asymptotic Speed Research Articles

A Meteor of Apparent Interstellar Origin in the CNEOS Fireball Catalog

The earliest confirmed interstellar object, ‘Oumuamua, was discovered in the solar system by Pan-STARRS in 2017, allowing for a calibration of the abundance of interstellar objects of its size ∼100 m. This was followed by the discovery of Borisov, which allowed for a similar calibration of its size ∼0.4–1 km. One would expect a much higher abundance of significantly smaller interstellar objects, with some of them colliding with Earth frequently enough to be noticeable. Based on the CNEOS catalog of bolide events, we identify the ∼0.45 m meteor detected at 2014 January 8 17:05:34 UTC as originating from an unbound hyperbolic orbit. The U.S. Department of Defense has released an official letter stating that “the velocity estimate reported to NASA is sufficiently accurate to indicate an interstellar trajectory,” which we rely on here as confirmation of the object’s interstellar trajectory. Based on the data provided by CNEOS, we infer that the meteor had an asymptotic speed of v ∞ ∼ 42.1 ± 5.5 km s−1 outside of the solar system. Note that v ∞ here refers to the velocity of the meteor outside the solar system, not the velocity of the meteor outside the atmosphere. Its origin is approximately toward R.A. 49.°4 ± 4.°1 and decl. 11.°2 ± 1.°8, implying that its initial velocity vector was 58 ± 6 km s−1 away from the velocity of the local standard of rest (LSR).

The Radial Evolution of the Solar Wind as Organized by Electron Distribution Parameters

We utilize observations from the Parker Solar Probe (PSP) to study the radial evolution of the solar wind in the inner heliosphere. We analyze electron velocity distribution functions observed by the Solar Wind Electrons, Alphas, and Protons suite to estimate the coronal electron temperature and the local electric potential in the solar wind. From the latter value and the local flow speed, we compute the asymptotic solar wind speed. We group the PSP observations by asymptotic speed, and characterize the radial evolution of the wind speed, electron temperature, and electric potential within each group. In agreement with previous work, we find that the electron temperature (both local and coronal) and the electric potential are anticorrelated with wind speed. This implies that the electron thermal pressure and the associated electric field can provide more net acceleration in the slow wind than in the fast wind. We then utilize the inferred coronal temperature and the extrapolated electric + gravitational potential to show that both electric field driven exospheric models and the equivalent thermally driven hydrodynamic models can explain the entire observed speed of the slowest solar wind streams. On the other hand, neither class of model can explain the observed speed of the faster solar wind streams, which thus require additional acceleration mechanisms.

A delay induced nonlocal free boundary problem

We study the dynamics of a population with an age structure whose population range expands with time, where the adult population is assumed to satisfy a reaction–diffusion equation over a changing interval determined by a Stefan type free boundary condition, while the juvenile population satisfies a reaction–diffusion equation whose evolving domain is determined by the adult population. The interactions between the adult and juvenile populations involve a fixed time-delay, which renders the model nonlocal in nature. After establishing the well-posedness of the model, we obtain a rather complete description of its long-time dynamical behaviour, which is shown to follow a spreading–vanishing dichotomy. When spreading persists, we show that the population range expands with an asymptotic speed, which is uniquely determined by an associated nonlocal elliptic problem over the half line. We hope this work will inspire further research on age-structured population models with an evolving population range.

On the theoretical properties of the exchange algorithm

The exchange algorithm is one of the most popular extensions of the Metropolis–Hastings algorithm to sample from doubly-intractable distributions. However, the theoretical exploration of the exchange algorithm is very limited. For example, natural questions like ‘Does exchange algorithm converge at a geometric rate?’ or ‘Does the exchange algorithm admit a Central Limit Theorem?’ have not been answered yet. In this paper, we study the theoretical properties of the exchange algorithm, in terms of asymptotic variance and convergence speed. We compare the exchange algorithm with the original Metropolis–Hastings algorithm and provide both necessary and sufficient conditions for the geometric ergodicity of the exchange algorithm. Moreover, we prove that our results can be applied to various practical applications such as location models, Gaussian models, Poisson models, and a large class of exponential families, which includes most of the practical applications of the exchange algorithm. A central limit theorem for the exchange algorithm is also established. Our results justify the theoretical usefulness of the exchange algorithm.

Interstellar Probe: Humanity's exploration of the Galaxy Begins

During the course of its evolution, our Sun and its protective magnetic bubble have plowed through dramatically different interstellar environments throughout the galaxy. The vast range of conditions of interstellar plasma, gas, dust and high-energy cosmic rays on this “solar journey” have helped shape the solar system that we live in. Today, our protective bubble, or Heliosphere, is likely about to enter a completely new regime of interstellar space that will, yet again, change the entire heliospheric interaction and how it shields us from the interstellar environment. Interstellar Probe is a mission concept to explore the mechanisms shaping our heliosphere and represents the first step beyond our home, into the interstellar cloud to understand the evolutionary journey of our Sun, Heliosphere and Solar System. The idea of an Interstellar Probe dates back to the 1960's, when also the ideas of a probe to the Sun and its poles were formed. An international team of scientists and a team of engineers at the Johns Hopkins University Applied Physics Laboratory (APL) are funded by NASA to study pragmatic mission concepts that would make a launch in the 2030's a reality. The ground breaking science enabled by such a mission spans not only the discipline of Solar and Space Physics, but also Planetary Sciences and Astrophysics. Detailed analyses including the upcoming SLS Block 2 and powerful stages demonstrate that asymptotic speeds around 7 Astronomical Units (au) per Year are already possible with a Jupiter Gravity Assist. Here, we give an overview of the science discoveries that await along the journey, including the physics of the heliospheric boundary and interstellar medium, the potential for exploration of Kuiper Belt Objects, the circum-solar dust disk and the extra-galactic background light. The scientific rationale, investigations and implementation of an Interstellar Probe are discussed including also example payload, trajectory design and operations.

Detonation modeling with the particles on demand method

A kinetic model based on the particles on demand method is introduced for gas phase detonation hydrodynamics in conjunction with the Lee–Tarver reaction model. The proposed model is realized on two- and three-dimensional lattices and is validated with a set of benchmarks. Quantitative validation is performed with the Chapman–Jouguet theory up to a detonation wave speed of Mach 20 in one dimension. Two-dimensional outward expanding circular detonation is tested for isotropy of the model as well as for the asymptotic detonation wave speed. Mach reflection angles are verified in setups consisting of interacting strong bow shocks emanating from detonation. Spherical detonation is computed to show the viability of the proposed model for three-dimensional simulations.

Propagation Speed of Degenerate Diffusion Equations with Time Delay

We are concerned with a class of degenerate diffusion equations with time delay describing population dynamics with age structure. In our recent study [Nonlinearity, 33 (2020), 4013–4029], we established the existence and uniqueness of critical traveling wave for the time-delayed degenerate diffusion equations, and obtained the reducing mechanism of time delay on critical wave speed. In this paper, we now are able to show the asymptotic spreading speed and its coincidence with the critical wave speed $$c^*(m,r)$$ of sharp wave, and prove that the initial perturbation or the boundary of the compact support of the solution propagates at the critical wave speed $$c^*(m,r)$$ for the time-delayed degenerate diffusion equations. Remarkably, different from the existing studies related to spreading speeds, the time delay and the degenerate diffusion lead to some essential difficulties in the analysis of the spreading speed, because the time delay makes the critical speed of traveling waves slow down in a more complicated fashion such that the critical speed cannot be determined by the characteristic equation, and the degenerate diffusion causes the loss of regularity for the solutions. By a phase transform technique we construct upper and lower solutions with semi-compact supports and then we determine the asymptotic spreading speed. Furthermore, we propose a brand-new sharp-profile-based difference scheme to handle large variation of degenerate diffusion $$(u^m)_{xx}$$ near the sharp edge and carry out some numerical simulations which perfectly confirm our theoretical results.

Reaction–diffusion equations in the half-space

We study reaction–diffusion equations of various types in the half-space. For bistable reactions with Dirichlet boundary conditions, we prove conditional uniqueness: there is a unique nonzero bounded steady state which exceeds the bistable threshold on large balls. Moreover, solutions starting from sufficiently large initial data converge to this steady state as t \to \infty . For compactly supported initial data, the asymptotic speed of this propagation agrees with the unique speed c_* of the one-dimensional traveling wave. We furthermore construct a traveling wave in the half-plane of speed c_* . In parallel, we show analogous results for ignition reactions under both Dirichlet and Robin boundary conditions. Using our ignition construction, we obtain stronger results for monostable reactions with the same boundary conditions. For such reactions, we show in general that there is a unique nonzero bounded steady state. Furthermore, monostable reactions exhibit the hair-trigger effect: every solution with nontrivial initial data converges to this steady state as t \to \infty . Given compactly supported initial data, this disturbance propagates at a speed c_* equal to the minimal speed of one-dimensional traveling waves. We also construct monostable traveling waves in the Dirichlet or Robin half-plane with any speed c \geq c_* .

Propagation dynamics of a nonlocal periodic organism model with non-monotone birth rates

This work is concerned with a nonlocal reaction–diffusion system modeling the propagation dynamics of organisms owning mobile and stationary states in periodic environments. We establish the existence of the asymptotic speed of spreading for the model system with monotone birth function via asymptotic propagation theory of monotone semiflow, and then discuss the case for non-monotone birth function by using the squeezing technique. In terms of the truncated problem on a finite interval, we apply the method of super- and sub-solutions and the fixed point theorem combined with regularity estimation and limit arguments to obtain the existence of time periodic traveling waves for the model system without quasi-monotonicity. The non-existence proof is to use the results of the spreading speed. Finally, as an application, we study the spatial dynamics of the model with the birth rate function of Ricker type and numerically demonstrate analytic results.

Generalized Beta Prime Distribution Applied to Finite Element Error Approximation

In this paper, we propose a new family of probability laws based on the Generalized Beta Prime distribution to evaluate the relative accuracy between two Lagrange finite elements Pk1 and Pk2,(k1<k2). Usually, the relative finite element accuracy is based on the comparison of the asymptotic speed of convergence, when the mesh size h goes to zero. The new probability laws we propose here highlight that there exists, depending on h, cases where the Pk1 finite element is more likely accurate than the Pk2 element. To confirm this assertion, we highlight, using numerical examples, the quality of the fit between the statistical frequencies and the corresponding probabilities, as determined by the probability law. This illustrates that, when h goes away from zero, a finite element Pk1 may produce more precise results than a finite element Pk2, since the probability of the event “Pk1is more accurate thanPk2” becomes greater than 0.5. In these cases, finite element Pk2 is more likely overqualified.

Propagation Phenomena in Periodic Patchy Landscapes with Interface Conditions

This paper is concerned with a model for the dynamics of a single species in a one-dimensional heterogeneous environment. The environment consists of two kinds of patches, which are periodically alternately arranged along the spatial axis. We first establish the well-posedness for the Cauchy problem. Next, we give existence and uniqueness results for the positive steady state and we analyze the long-time behavior of the solutions to the evolution problem. Afterwards, based on dynamical systems methods, we investigate the spreading properties and the existence of pulsating traveling waves in the positive and negative directions. It is shown that the asymptotic spreading speed, \(c^*\), exists and coincides with the minimal wave speed of pulsating traveling waves in positive and negative directions. In particular, we give a variational formula for \(c^*\) by using the principal eigenvalues of certain linear periodic eigenvalue problems.

Propagation phenomena for time-space periodic monotone semiflows and applications to cooperative systems in multi-dimensional media

The current paper is concerned with propagation phenomena for time-space periodic monotone semiflows and applications to time-space periodic cooperative systems in multi-dimensional media. We first establish some abstract theory on spreading speeds and traveling waves for time-space periodic monotone semiflows in the space of vector-valued functions on RN. Among others, we prove the equivalence of spreading speeds adopted by two different approaches, several spreading properties in terms of the spreading speeds, and the existence of periodic traveling waves which extends several known results in various special cases. By applying the abstract theory, we study the spreading speeds and traveling waves of time-space periodic cooperative systems in multi-dimensional media. It is proved that such a system admits a single spreading speed (resp. asymptotic spreading ray speed and asymptotic spreading set) under certain conditions. A set of sufficient conditions are also given for the single spreading speed to be linearly determinate. Furthermore, we show that the spreading speed can be characterized as the minimal wave speed of periodic traveling waves. The obtained results are then applied to the two-species periodic competition system in multi-dimensional media.

A Semi-Lagrangian Computation of Front Speeds of G-equation in ABC and Kolmogorov Flows with Estimation via Ballistic Orbits

The Arnold-Beltrami-Childress (ABC) flow and the Kolmogorov flow are three dimensional periodic divergence free velocity fields that exhibit chaotic streamlines. We are interested in front speed enhancement in G-equation of turbulent combustion by large intensity ABC and Kolmogorov flows. We give a quantitative construction of the ballistic orbits of ABC and Kolmogorov flows, namely those with maximal large time asymptotic speeds in a coordinate direction. Thanks to the optimal control theory of G-equation (a convex but non-coercive Hamilton-Jacobi equation), the ballistic orbits serve as admissible trajectories for front speed estimates. To study the tightness of the estimates, we compute the front speeds of G-equation based on a semi-Lagrangian (SL) scheme with Strang splitting and weighted essentially non-oscillatory (WENO) interpolation. Time step size is chosen so that the Courant number grows sublinearly with the flow intensity. Numerical results show that the front speed growth rate in terms of the flow intensity may approach the analytical bounds from the ballistic orbits.

Long-Run Growth, Speed of Convergence and the Specification of Technology

Abstract This note analyzes the effect that the specification of technology has on the long-run growth rate and the asymptotic speed of convergence in the one-sector endogenous-growth model. We compare three otherwise identical economies – with the same baseline and parameter values – but with different production technologies: CES, VES or Sobelow, respectively. The long-run growth rate and the asymptotic convergence speed under CES production are lower than the corresponding ones under Sobelow production which, in turn, are lower than those under VES production. This is because a higher elasticity of substitution entails a higher easiness to substitute capital for labor which, in the end, results in a higher long-run growth rate.

An Enhanced Sliding Mode Speed Control for Induction Motor Drives

In this paper, an enhanced Integral Sliding Mode Control (ISMC) for mechanical speed of an Induction Motor (IM) is presented and experimentally validated. The design of the proposed controller has been done in the d-q synchronous reference frame and indirect Field Oriented Control (FOC). Global asymptotic speed tracking in the presence of model uncertainties and load torque variations has been guaranteed by using an enhanced ISMC surface. Moreover, this controller provides a faster speed convergence rate compared to the conventional ISMC and the Proportional Integral methods, and it eliminates the steady-state error. Furthermore, the chattering phenomenon is reduced by using a switching sigmoid function. The stability of the proposed controller under parameter uncertainties and load disturbances has been provided by using the Lyapunov stability theory. Finally, the performance of this control method is verified through numerical simulations and experimental tests, getting fast dynamics and good robustness for IM drives.

Propagation Dynamics of a Discrete SIS Model With Time Periodicity

This paper is devoted to the study of the propagation dynamics for a class of spatially discrete multi-type SIS epidemic model with time period. Firstly, the abstract theory of spreading speed and travelling waves for monotonic periodic semiflows is applied to prove the existence of asymptotic spreading speed <i>c</i>_*. Secondly, by using the comparison principle, we obtain that the asymptotic spreading speed coincides with the minimal wave speed of monotone periodic traveling waves.

Gravito-Electrodynamics in Galaxy Rotation Curves. ENG: An Extended Newtonian Gravitation

An extended Newtonian gravitation (ENG) model was developed to explain the rotation curves in galaxies and galaxy clusters. ENG requires the knowledge of a parameter that is a function of the mass of the gravitational source. An approximate eq. for that parameter was obtained (for disk galaxies) that yields asymptotic speeds close to binned measured data. ENG yielded larger circular speeds for galaxy clusters when compared with the MOND results. A classical gravito-electromagnetic model (which neither is based on Einstein GR, nor on gravito-magnetism only) was developed which yielded asymptotic circular speeds very small compared to experimental results. However when ENG was used to develop an extended gravito-electromagnetic model, it yielded results compatible with MOND results for simulated galaxies and larger than MOND results for a simulated galaxy cluster. This model showed measurable increase in the circular speed when compared to ENG alone in the galaxy cluster. The need for modifying the Einstein field equation to address the dark matter problem in the framework of the ENG model was illustrated.

Asymptotic spreading for Fisher-KPP reaction-diffusion equations with heterogeneous shifting diffusivity

&lt;p style='text-indent:20px;'&gt;We determine the asymptotic spreading speed of the solutions of a Fisher-KPP reaction-diffusion equation, starting from compactly supported initial data, when the diffusion coefficient is a fixed bounded monotone profile that is shifted at a given forcing speed and satisfies a general uniform ellipticity condition. Depending on the monotonicity of the profile, we are able to characterize this spreading speed as a function of the forcing speed and the two linear spreading speeds associated to the asymptotic problems at &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$ x = \pm \infty $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;. Most notably, when the profile of the diffusion coefficient is increasing we show that there is an intermediate range for the forcing speed where spreading actually occurs at a speed which is larger than the linear speed associated with the homogeneous state around the position of the front. We complement our study with the construction of strictly monotone traveling front solutions with strong exponential decay near the unstable state when the profile of the diffusion coefficient is decreasing and in the regime where the forcing speed is precisely the selected spreading speed.&lt;/p&gt;

Propagation of stochastic travelling waves of cooperative systems with noise

&lt;p style='text-indent:20px;'&gt;We consider the cooperative system driven by a multiplicative It\^o type white noise. The existence and their approximations of the travelling wave solutions are proven. With a moderately strong noise, the travelling wave solutions are constricted by choosing a suitable marker of wavefront. Moreover, the stochastic Feynman-Kac formula, sup-solution, sub-solution and equilibrium points of the dynamical system corresponding to the stochastic cooperative system are utilized to estimate the asymptotic wave speed, which is closely related to the white noise.&lt;/p&gt;

Propagation dynamics of a nonlocal time-space periodic reaction-diffusion model with delay

&lt;p style='text-indent:20px;'&gt;This paper is concerned with a nonlocal time-space periodic reaction diffusion model with age structure. We first prove the existence and global attractivity of time-space periodic solution for the model. Next, by a family of principal eigenvalues associated with linear operators, we characterize the asymptotic speed of spread of the model in the monotone and non-monotone cases. Furthermore, we introduce a notion of transition semi-waves for the model, and then by constructing appropriate upper and lower solutions, and using the results of the asymptotic speed of spread, we show that transition semi-waves of the model in the non-monotone case exist when their wave speed is above a critical speed, and transition semi-waves do not exist anymore when their wave speed is less than the critical speed. It turns out that the asymptotic speed of spread coincides with the critical wave speed of transition semi-waves in the non-monotone case. In addition, we show that the obtained transition semi-waves are actually transition waves in the monotone case. Finally, numerical simulations for various cases are carried out to support our theoretical results.&lt;/p&gt;