Conforming finite element methods for the clamped plate problem

Finite element methods for solving biharmonic boundary value problems are considered. The particular problem discussed is that of a clamped thin plate. This problem is reformulated in a weak, form in the Sobolev space Techniques for setting up conforming trial Functions are utilized in a Galerkin technique to produce finite element solutions. The shortcomings of various trial function formulations are discussed, and a macro—element approach to local mesh refinement using rectangular elements is given

Superconductivity of various borides: The role of stretched c-parameter

The superconductivity of MgB2, AlB2, NbB2+x, and TaB2+x is intercompared. The stretched c-lattice parameter (c = 3.52 Å) of MgB2 in comparison to NbB2.4 (c = 3.32 Å) and AlB2 (c = 3.25 Å) decides empirically the population of their π and σ bands and as a result their transition temperature Tc values, respectively, at 39 and 9.5 K for the first two and no superconductivity for the later. The nonstoichiometry induces an increase in c parameter with Boron excess both in NbB2+x and TaB2+x. Magnetization (M-T) and resistivity measurements (ρ-T) in case of niobium boride samples show the absence of superconductivity in stoichiometric NbB2 sample (c = 3.26 Å) while a clear diamagnetic signal and a ρ = 0 transition for boron excess NbB2+x samples. On the other hand, superconductivity is not achieved in TaB2+x case. The probable reason behind is the comparatively lesser or insufficient stretching of c parameter

Charge Lattices and Consistency of 6D Supergravity

We extend the known consistency conditions on the low-energy theory of six-dimensional N = 1 supergravity. We review some facts about the theory of two-form gauge fields and conclude that the charge lattice Gamma for such a theory has to be self-dual. The Green-Schwarz anomaly cancellation conditions in the supergravity theory determine a sublattice of Gamma. The condition that this sublattice can be extended to a self-dual lattice Gamma leads to a strong constraint on theories that otherwise appear to be self-consistent.Comment: 15 pages. v2: minor changes; references, additional example added; v3: minor corrections and clarifications added, JHEP versio

¹⁸F-meta-fluorobenzylguanidine (¹⁸F-mFBG) to monitor changes in norepinephrine transporter expression in response to therapeutic intervention in neuroblastoma models

argeted radiotherapy with {13}^1I-mIBG, a substrate of the human norepinephrine transporter (NET-1), shows promising responses in heavily pre-treated neuroblastoma (NB) patients. Combinatorial approaches that enhance {13}^1I-mIBG tumour uptake are of substantial clinical interest but biomarkers of response are needed. Here, we investigate the potential of {18}^F-mFBG, a positron emission tomography (PET) analogue of the {123}^I-mIBG radiotracer, to quantify NET-1 expression levels in mouse models of NB following treatment with AZD2014, a dual mTOR inhibitor. The response to AZD2014 treatment was evaluated in MYCN amplified NB cell lines (Kelly and SK-N-BE(2)C) by Western blot (WB) and immunohistochemistry. PET quantification of {18}^F-mFBG uptake post-treatment in vivo was performed, and data correlated with NET-1 protein levels measured ex vivo. Following 72 h AZD2014 treatment, in vitro WB analysis indicated decreased mTOR signalling and enhanced NET-1 expression in both cell lines, and {18}^F-mFBG revealed a concentration-dependent increase in NET-1 function. AZD2014 treatment failed however to inhibit mTOR signalling in vivo and did not significantly modulate intratumoural NET-1 activity. Image analysis of {18}^F-mFBG PET data showed correlation to tumour NET-1 protein expression, while further studies are needed to elucidate whether NET-1 upregulation induced by blocking mTOR might be a useful adjunct to {131}^I-mIBG therapy

Moduli-Induced Vacuum Destabilisation

We look for ways to destabilise the vacuum. We describe how dense matter environments source a contribution to moduli potentials and analyse the conditions required to initiate either decompactification or a local shift in moduli vevs. We consider astrophysical objects such as neutron stars as well as cosmological and black hole singularities. Regrettably neutron stars cannot destabilise realistic Planck coupled moduli, which would require objects many orders of magnitude denser. However gravitational collapse, either in matter-dominated universes or in black hole formation, inevitably leads to a destabilisation of the compact volume causing a super-inflationary expansion of the extra dimensions.Comment: 21 pages, 12 figure

New Mechanics of Traumatic Brain Injury

The prediction and prevention of traumatic brain injury is a very important aspect of preventive medical science. This paper proposes a new coupled loading-rate hypothesis for the traumatic brain injury (TBI), which states that the main cause of the TBI is an external Euclidean jolt, or SE(3)-jolt, an impulsive loading that strikes the head in several coupled degrees-of-freedom simultaneously. To show this, based on the previously defined covariant force law, we formulate the coupled Newton-Euler dynamics of brain's micro-motions within the cerebrospinal fluid and derive from it the coupled SE(3)-jolt dynamics. The SE(3)-jolt is a cause of the TBI in two forms of brain's rapid discontinuous deformations: translational dislocations and rotational disclinations. Brain's dislocations and disclinations, caused by the SE(3)-jolt, are described using the Cosserat multipolar viscoelastic continuum brain model. Keywords: Traumatic brain injuries, coupled loading-rate hypothesis, Euclidean jolt, coupled Newton-Euler dynamics, brain's dislocations and disclinationsComment: 18 pages, 1 figure, Late

F-Theory and the Mordell-Weil Group of Elliptically-Fibered Calabi-Yau Threefolds

The Mordell-Weil group of an elliptically fibered Calabi-Yau threefold X contains information about the abelian sector of the six-dimensional theory obtained by compactifying F-theory on X. After examining features of the abelian anomaly coefficient matrix and U(1) charge quantization conditions of general F-theory vacua, we study Calabi-Yau threefolds with Mordell-Weil rank-one as a first step towards understanding the features of the Mordell-Weil group of threefolds in more detail. In particular, we generate an interesting class of F-theory models with U(1) gauge symmetry that have matter with both charges 1 and 2. The anomaly equations --- which relate the Neron-Tate height of a section to intersection numbers between the section and fibral rational curves of the manifold --- serve as an important tool in our analysis.Comment: 29 pages + appendices, 5 figures; v2: minor correction

Predicting language diversity with complex network

Evolution and propagation of the world's languages is a complex phenomenon, driven, to a large extent, by social interactions. Multilingual society can be seen as a system of interacting agents, where the interaction leads to a modification of the language spoken by the individuals. Two people can reach the state of full linguistic compatibility due to the positive interactions, like transfer of loanwords. But, on the other hand, if they speak entirely different languages, they will separate from each other. These simple observations make the network science the most suitable framework to describe and analyze dynamics of language change. Although many mechanisms have been explained, we lack a qualitative description of the scaling behavior for different sizes of a population. Here we address the issue of the language diversity in societies of different sizes, and we show that local interactions are crucial to capture characteristics of the empirical data. We propose a model of social interactions, extending the idea from, that explains the growth of the language diversity with the size of a population of country or society. We argue that high clustering and network disintegration are the most important characteristics of models properly describing empirical data. Furthermore, we cancel the contradiction between previous models and the Solomon Islands case. Our results demonstrate the importance of the topology of the network, and the rewiring mechanism in the process of language change

Factorizations of Elements in Noncommutative Rings: A Survey

We survey results on factorizations of non zero-divisors into atoms (irreducible elements) in noncommutative rings. The point of view in this survey is motivated by the commutative theory of non-unique factorizations. Topics covered include unique factorization up to order and similarity, 2-firs, and modular LCM domains, as well as UFRs and UFDs in the sense of Chatters and Jordan and generalizations thereof. We recall arithmetical invariants for the study of non-unique factorizations, and give transfer results for arithmetical invariants in matrix rings, rings of triangular matrices, and classical maximal orders as well as classical hereditary orders in central simple algebras over global fields.Comment: 50 pages, comments welcom

Second-order L2L^2-regularity in nonlinear elliptic problems

A second-order regularity theory is developed for solutions to a class of quasilinear elliptic equations in divergence form, including the $p$-Laplace equation, with merely square-integrable right-hand side. Our results amount to the existence and square integrability of the weak derivatives of the nonlinear expression of the gradient under the divergence operator. This provides a nonlinear counterpart of the classical $L^2$-coercivity theory for linear problems, which is missing in the existing literature. Both local and global estimates are established. The latter apply to solutions to either Dirichlet or Neumann boundary value problems. Minimal regularity on the boundary of the domain is required. If the domain is convex, no regularity of its boundary is needed at all