On Singularity Formation of a Nonlinear Nonlocal System

We investigate the singularity formation of a nonlinear nonlocal system. This nonlocal system is a simplified one-dimensional system of the 3D model that was recently proposed by Hou and Lei in [13] for axisymmetric 3D incompressible Navier-Stokes equations with swirl. The main difference between the 3D model of Hou and Lei and the reformulated 3D Navier-Stokes equations is that the convection term is neglected in the 3D model. In the nonlocal system we consider in this paper, we replace the Riesz operator in the 3D model by the Hilbert transform. One of the main results of this paper is that we prove rigorously the finite time singularity formation of the nonlocal system for a large class of smooth initial data with finite energy. We also prove the global regularity for a class of smooth initial data. Numerical results will be presented to demonstrate the asymptotically self-similar blow-up of the solution. The blowup rate of the self-similar singularity of the nonlocal system is similar to that of the 3D model.Comment: 28 pages, 9 figure

Pressure moderation and effective pressure in Navier-Stokes flows

We study the Cauchy problem of the Navier–Stokes equations by both semi-analytic and classical energy methods. The former approach provides a physical picture of how viscous effects may or may not be able to suppress singularity development. In the latter approach, we examine the pressure term that drives the dynamics of the velocity norms ||u||Lq , for q ≥ 3. A key idea behind this investigation is due to the fact that the pressure p in this term is determined upto a function of both space and |u|, say Ƥ(x, |u|), which may assume relatively broad forms. This allows us to use Ƥ as a pressure moderator in the evolution equation for ||u||Lq , whereby optimal regularity criteria can be sought by varying Ƥ within its admissible classes. New regularity criteria are derived with and without making use of the moderator. The results obtained in the absence of the moderator feature some improvement over existing criteria in the literature. Several criteria are derived in terms of the moderated (effective) pressure p+Ƥ. A simple moderation scheme and the plausibility of the present approach to the problem of Navier–Stokes regularity are discussed.PostprintPeer reviewe

A genetic mouse model with postnatal Nf1 and p53 loss recapitulates the histology and transcriptome of human malignant peripheral nerve sheath tumor

BACKGROUND: Malignant peripheral nerve sheath tumors (MPNST) are aggressive sarcomas. Somatic inactivation of METHODS: We combined 2 genetically modified alleles, an RESULTS: Postnatal CONCLUSIONS: The NP-Plp model recapitulates human MPNST genetically, histologically, and molecularly

Radiative Corrections to the Casimir Energy

The lowest radiative correction to the Casimir energy density between two parallel plates is calculated using effective field theory. Since the correlators of the electromagnetic field diverge near the plates, the regularized energy density is also divergent. However, the regularized integral of the energy density is finite and varies with the plate separation L as 1/L^7. This apparently paradoxical situation is analyzed in an equivalent, but more transparent theory of a massless scalar field in 1+1 dimensions confined to a line element of length L and satisfying Dirichlet boundary conditions.Comment: 7 pages, Late

Comparison of arch form between ethnic Malays and Malaysian Aborigines in Peninsular Malaysia

Objective: To determine and compare the frequency distribution of various arch shapes in ethnic Malays and Malaysian Aborigines in Peninsular Malaysia and to investigate the morphological differences of arch form between these two ethnic groups. Methods: We examined 120 ethnic Malay study models (60 maxillary, 60 mandibular) and 129 Malaysian Aboriginal study models (66 maxillary, 63 mandibular). We marked 18 buccal tips and incisor line angles on each model, and digitized them using 2-dimensional coordinate system. Dental arches were classified as square, ovoid, or tapered by printing the scanned images and superimposing Orthoform arch templates on them. Results: The most common maxillary arch shape in both ethnic groups was ovoid, as was the most common mandibular arch shape among ethnic Malay females. The rarest arch shape was square. Chi-square tests, indicated that only the distribution of the mandibular arch shape was significantly different between groups (p = 0.040). However, when compared using independent t-tests, there was no difference in the mean value of arch width between groups. Arch shape distribution was not different between genders of either ethnic group, except for the mandibular arch of ethnic Malays. Conclusions: Ethnic Malays and Malaysian Aborigines have similar dental arch dimensions and shapes. Korean J Orthod 2012;42(1):47-54. This record was migrated from the OpenDepot repository service in June, 2017 before shutting down

Membraneless organelles formed by liquid-liquid phase separation increase bacterial fitness

Liquid-liquid phase separation is emerging as a crucial phenomenon in several fundamental cell processes. A range of eukaryotic systems exhibit liquid condensates. However, their function in bacteria, which in general lack membrane-bound compartments, remains less clear. Here, we used high-resolution optical microscopy to observe single bacterial aggresomes, nanostructured intracellular assemblies of proteins, to undercover their role in cell stress. We find that proteins inside aggresomes are mobile and undergo dynamic turnover, consistent with a liquid state. Our observations are in quantitative agreement with phase-separated liquid droplet formation driven by interacting proteins under thermal equilibrium that nucleate following diffusive collisions in the cytoplasm. We have discovered aggresomes in multiple species of bacteria, and show that these emergent, metastable liquid-structured protein assemblies increase bacterial fitness by enabling cells to tolerate environmental stresses

User Oriented Resource Management with Virtualization: A Hierarchical Game Approach

The explosive advancements in mobile Internet and Internet of Things challenge the network capacity and architecture. The ossification of wireless networks hinders the further evolution towards the fifth generation of mobile communication systems. Ultra-dense small cell networks are considered as a feasible way to meet high-capacity demands. Meanwhile, ultradense small cell network virtualization also exploits an insightful perspective for the evolution because of