We observe a link between the window size of mass concentration and the rate of explosion of the Strichartz norm by revisiting Bourgain’s mass concentration for the L2-critical nonlinear Schrödinger equations.

This study reports effects of meaning and emotion (taboo vs. neutral words) on an illusory word (IW) phenomenon linked to orthographic repetition blindness (RB). Participants immediately recalled rapid serial visual presentation (RSVP) lists consisting of two critical words (C1 and C2) containing shared letters, followed by a word fragment: for example, lake (C1) brake (C2) ush (fragment). For ...

The goal of this paper is to exhibit a critical mass phenomenon occuring in a model for cell self-organization via chemotaxis. The very well known dichotomy arising in the behavior of the macroscopic Keller-Segel system is derived at the kinetic level, being closer to microscopic features. Indeed, under the assumption of spherical symmetry, we prove that solutions with initial data of large mas...

Here f(u) = λ ( V ∗|u|2 ) u, V (x) = |x|−γ , 0 < γ < d, and ∗ denotes the convolution in Rd. If λ > 0, we call the equation (1.1) defocusing; if λ < 0, we call it focusing. This equation describes the mean-field limit of many-body quantum systems; see, e.g., [6], [7] and [36]. An essential feature of Hartree equation is that the convolution kernel V (x) still retains the fine structure of micro...

We observe the transverse electrokinetic effect (TEK), namely, the generation of a transverse potential difference due to the flow of liquids over a surface on which self-assembled arrays of metallic nanoparticles are immobilized. This paper covers the recent experimental findings and improvements to the theoretical model described in ref 1 [Subramaniam, C.; Pradeep, T.; Chakrabarti, J. Phys. R...

This paper illustrates the phenomenon of the critical speed in the range 100300 km/h. A real explanation and a precise calculation of the critical speed seems to rest an unresolved problem in many cases. Some authors, analogous to “Mach effect”, have attributed this phenomenon to the reaching the Rayleigh wave speed of substructure by trains. But this explanation can’t be thorough in many cases...

A field theory of frictionless grain packings in two dimensions is shown to exhibit a zero-temperature critical point at a nonzero value of the packing fraction. The zero-temperature constraint of force balance plays a crucial role in determining the nature of the transition. Two order parameters, , the deviation of the average number of contacts from the isostatic value, and , the aver...

Critical peak pricing (CPP) is a demand response program that can be used to maximize profits for a load serving entity in a deregulated market environment. Like other such programs, however, CPP is not free from the payback phenomenon: a rise in consumption after a critical event. This payback has a negative effect on profits and thus must be appropriately considered when designing a CPP schem...