scholarly journals Global, non-scattering solutions to the energy critical Yang–Mills problem

2021 ◽  
Vol 18 (01) ◽  
pp. 29-141
Author(s):  
Mohandas Pillai
Keyword(s):  
A Priori ◽  
Finite Energy ◽  
Necessary Condition ◽  
Length Scale ◽  
Wave Maps ◽  
Interesting Point ◽  
Yang Mills ◽  
Fixed Solution ◽  
Radiation Profile ◽  
Better Than

We consider the Yang–Mills problem on [Formula: see text] with gauge group [Formula: see text]. In an appropriate equivariant reduction, this Yang–Mills problem reduces to a single scalar semilinear wave equation. This semilinear equation admits a one-parameter family of solitons, each of which is a re-scaling of a fixed solution. In this work, we construct a class of solutions, each of which consists of a soliton whose length scale is asymptotically constant, coupled to large radiation, plus corrections which slowly decay to zero in the energy norm. Our class of solutions includes ones for which the radiation component is only “logarithmically” better than energy class. As such, the solutions are not constructed by a priori assuming the length scale to be constant. Instead, we use an approach similar to a previous work of the author regarding wave maps. In the setup of this work, the soliton length scale asymptoting to a constant is a necessary condition for the radiation profile to have finite energy. An interesting point of our construction is that, for each radiation profile, there exist one-parameter families of solutions consisting of the radiation profile coupled to a soliton, which has any asymptotic value of the length scale.

From Isovist to Spatial Perception: Wayfinding in Historic Quarter

2016 ◽  
Vol 1 (3) ◽  
Author(s):  
Chih-Hung Chen ◽  
Ting-Ju Lin ◽  
Chih-Yu Chen
Keyword(s):  
Social Interactions ◽  
Spatial Perception ◽  
Publishing House ◽  
A Priori ◽  
Relative Area ◽  
Social Stimuli ◽  
Historical District ◽  
International Publishing ◽  
A Priori Analysis ◽  
Better Than

Based on the assumption that human behaviours are mainly affected by physical and animate environments, this empirical research takes the changeful and complex historical district in Tainan to observe wayfinding behaviours. An a priori analysis of the isovist fields is conducted to identify spatial characteristics. Three measures, the relative area, convexity, and circularity, are applied to scrutinize the possible stopping points, change of speed, and route choices. Accordingly, an experiment is carried out to observe spatial behaviours and different influences of social stimuli. Results show that social interactions afford groups and pairs to perform better than individual observers in wayfinding.© 2016. The Authors. Published for AMER ABRA by e-International Publishing House, Ltd., UK. Peer–review under responsibility of AMER (Association of Malaysian Environment-Behaviour Researchers), ABRA (Association of Behavioural Researchers on Asians) and cE-Bs (Centre for Environment-Behaviour Studies, Faculty of Architecture, Planning & Surveying, Universiti Teknologi MARA, MalaysiaKeywords: wayfinding; isovist; spatial perception and social stimuli; historic quarter

scholarly journals Sensorimotor priors in nonstationary environments

2013 ◽  
Vol 109 (5) ◽  
pp. 1259-1267 ◽  
Author(s):  
Devika Narain ◽  
Robert J. van Beers ◽  
Jeroen B. J. Smeets ◽  
Eli Brenner
Keyword(s):  
Environmental Variables ◽  
A Priori ◽  
Past Research ◽  
Systematic Change ◽  
Recent Experience ◽  
Environmental Variance ◽  
Adaptive Models ◽  
Priori Information ◽  
Human Nervous System ◽  
Better Than

In the course of its interaction with the world, the human nervous system must constantly estimate various variables in the surrounding environment. Past research indicates that environmental variables may be represented as probabilistic distributions of a priori information (priors). Priors for environmental variables that do not change much over time have been widely studied. Little is known, however, about how priors develop in environments with nonstationary statistics. We examine whether humans change their reliance on the prior based on recent changes in environmental variance. Through experimentation, we obtain an online estimate of the human sensorimotor prior (prediction) and then compare it to similar online predictions made by various nonadaptive and adaptive models. Simulations show that models that rapidly adapt to nonstationary components in the environments predict the stimuli better than models that do not take the changing statistics of the environment into consideration. We found that adaptive models best predict participants' responses in most cases. However, we find no support for the idea that this is a consequence of increased reliance on recent experience just after the occurrence of a systematic change in the environment.

FINITE ENERGY ONE-HALF MONOPOLE SOLUTIONS

2012 ◽  
Vol 27 (40) ◽  
pp. 1250233 ◽  
Author(s):  
ROSY TEH ◽  
BAN-LOONG NG ◽  
KHAI-MING WONG
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Magnetic Flux ◽  
Topological Charge ◽  
Magnetic Monopole ◽  
Magnetic Charge ◽  
Finite Energy ◽  
Spatial Infinity ◽  
Yang Mills ◽  
The Magnetic Field

We present finite energy SU(2) Yang–Mills–Higgs particles of one-half topological charge. The magnetic fields of these solutions at spatial infinity correspond to the magnetic field of a positive one-half magnetic monopole at the origin and a semi-infinite Dirac string on one-half of the z-axis carrying a magnetic flux of [Formula: see text] going into the origin. Hence the net magnetic charge is zero. The gauge potentials are singular along one-half of the z-axis, elsewhere they are regular.

scholarly journals Comparative Study of the Grid-Scale and Subgrid-Scale Velocity Fields - A Priori Test

1970 ◽  
Vol 30 ◽  
pp. 19-31
Author(s):  
M Ashraf Uddin ◽  
M Matiar Rahman ◽  
M Saiful Islam Mallik
Keyword(s):  
Isotropic Turbulence ◽  
A Priori ◽  
Velocity Fields ◽  
Subgrid Scale ◽  
Homogeneous Isotropic Turbulence ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Spatial Spectra ◽  
Sharp Cutoff ◽  
Better Than

Generation of grid-scale (GS) and subgrid-scale (SGS) velocity fields is performed by direct filtering of DNS (Direct Numerical Simulation) data at a low Reynolds number in homogeneous isotropic turbulence in order to assess the spectral accuracy as well as the performance of filter functions for LES (Large Eddy Simulation). The filtering is performed using three classical filter functions: Gaussian, Tophat and Sharp cutoff filters and in all three cases the results are compared with three different filter widths for LES. Comparing the distributions of GS and SGS velocities, and the decay of turbulence with those from DNS fields through out the whole calculation we have found that among the three filter functions, the performance of Sharp cutoff filter is better than that of the other two filter functions in terms of both spatial spectra and the distribution of velocities. Furthermore, it is shown that the accuracy of the filtering approach does not depend only on the filter functions but also on the filter widths for LES. GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 30 (2010) 19-31   DOI: http://dx.doi.org/10.3329/ganit.v30i0.8499

Finite Energy Solutions of the Yang-Mills Equations in ℝ 3+1

1995 ◽  
Vol 142 (1) ◽  
pp. 39 ◽  
Author(s):  
S. Klainerman ◽  
M. Machedon
Keyword(s):  
Finite Energy ◽  
Yang Mills

Do Theodicists Mean What They Say?

Philosophy ◽  
1974 ◽  
Vol 49 (190) ◽  
pp. 357-374
Author(s):  
Clement Dore
Keyword(s):  
Necessary Condition ◽  
Better Than

Many theodicists have maintained that God is justified in permitting suffering on the ground that His doing so is a necessary condition of the realization of certain intrinsically valuable ends which the suffering serves and whose value outweighs the suffering which occasions them. Examples of ends which are frequently cited in this connection are freely chosen actions in accordance with stringent obligations to be charitable and steadfast. To say that the value of these ends outweighs the suffering which gives rise to them is to say that the existence both of these ends and of suffering is better than the non-existence of both. (Of course, the best thing of all on the view of the theodicists under discussion would be for these ends to exist and for the suffering not to exist, but they point out that it is logically impossible for there to be desirable responses to suffering in the absence of suffering.)

scholarly journals The risks of mixing dependency lengths from sequences of different length

Glottotheory ◽  
2014 ◽  
Vol 5 (2) ◽  
Author(s):  
Ramon Ferrer-i-Cancho ◽  
Haitao Liu
Keyword(s):  
Null Hypothesis ◽  
Empirical Distribution ◽  
A Priori ◽  
Sentence Length ◽  
The Other ◽  
Language Research ◽  
Varying Length ◽  
Syntactic Dependency ◽  
Better Than

AbstractMixing dependency lengths from sequences of different length is a common practice in language research. However, the empirical distribution of dependency lengths of sentences of the same length differs from that of sentences of varying length. The distribution of dependency lengths depends on sentence length for real sentences and also under the null hypothesis that dependencies connect vertices located in random positions of the sequence. This suggests that certain results, such as the distribution of syntactic dependency lengths mixing dependencies from sentences of varying length, could be a mere consequence of that mixing. Furthermore, differences in the global averages of dependency length (mixing lengths from sentences of varying length) for two different languages do not simply imply a priori that one language optimizes dependency lengths better than the other because those differences could be due to differences in the distribution of sentence lengths and other factors.

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