اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدBrachistochrones With Loose Ends
72
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The classical problem of the brachistochrone asks for the curve down which a body sliding from rest and accelerated by gravity will slip (without friction) from one point to another in least time. In undergraduate courses on classical mechanics, the solution of this problem is the primary example of the power of the variational calculus. Here we address the generalized brachistochrone problem that asks for the fastest sliding curve between a point and a given curve or between two given curves. The generalized problem can be solved by considering variations with varying endpoints. We will contrast the formal solution with a much simpler solution based on symmetry and kinematic reasoning. Our exposition should encourage teachers to include variational problems with free boundary conditions in their courses and students to try simple, intuitive solutions first.
قيم البحث
اقرأ أيضاً
The winds of cool luminous AGB stars are commonly assumed to be driven by radiative acceleration of dust grains which form in the extended atmospheres produced by pulsation-induced shock waves. The dust particles gain momentum by absorption or scatte
ring of stellar photons, and they drag along the surrounding gas particles through collisions, triggering an outflow. This scenario, here referred to as Pulsation-Enhanced Dust-DRiven Outflow (PEDDRO), has passed a range of critical observational tests as models have developed from empirical and qualitative to increasingly self-consistent and quantitative. A reliable theory of mass loss is an essential piece in the bigger picture of stellar and galactic chemical evolution, and central for determining the contribution of AGB stars to the dust budget of galaxies. In this review, I discuss the current understanding of wind acceleration and indicate areas where further efforts by theorists and observers are needed.
To evaluate the performance of prediction of missing links, the known data are randomly divided into two parts, the training set and the probe set. We argue that this straightforward and standard method may lead to terrible bias, since in real biolog
ical and information networks, missing links are more likely to be links connecting low-degree nodes. We therefore study how to uncover missing links with low-degree nodes, namely links in the probe set are of lower degree products than a random sampling. Experimental analysis on ten local similarity indices and four disparate real networks reveals a surprising result that the Leicht-Holme-Newman index [E. A. Leicht, P. Holme, and M. E. J. Newman, Phys. Rev. E 73, 026120 (2006)] performs the best, although it was known to be one of the worst indices if the probe set is a random sampling of all links. We further propose an parameter-dependent index, which considerably improves the prediction accuracy. Finally, we show the relevance of the proposed index on three real sampling methods.
Transforming an initial quantum state into a target state through the fastest possible route---a quantum brachistochrone---is a fundamental challenge for many technologies based on quantum mechanics. Here, we demonstrate fast coherent transport of an
atomic wave packet over a distance of 15 times its size---a paradigmatic case of quantum processes where the target state cannot be reached through a local transformation. Our measurements of the transport fidelity reveal the existence of a minimum duration---a quantum speed limit---for the coherent splitting and recombination of matter waves. We obtain physical insight into this limit by relying on a geometric interpretation of quantum state dynamics. These results shed light upon a fundamental limit of quantum state dynamics and are expected to find relevant applications in quantum sensing and quantum computing.
This article introduces the notion of a loose family of Engel structures and shows that two such families are Engel homotopic if and only if they are formally homotopic. This implies a complete h-principle when some auxiliary data is fixed. As a coro
llary, we show that Lorentz and orientable Cartan prolongations are classified up to homotopy by their formal data.
Let G and F be finitely generated groups with infinitely many ends and let A and B be graph of groups decompositions of F and G such that all edge groups are finite and all vertex groups have at most one end. We show that G and F are quasi-isometric
if and only if every one-ended vertex group of A is quasi-isometric to some one-ended vertex group of B and every one-ended vertex group of B is quasi-isometric to some one-ended vertex group of A. From our proof it also follows that if G is any finitely generated group, of order at least three, the groups: G*G, G*Z,G*G*G and G* Z/2Z are all quasi-isometric.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
