364 research outputs found
Domain structure of bulk ferromagnetic crystals in applied fields near saturation
We investigate the ground state of a uniaxial ferromagnetic plate with
perpendicular easy axis and subject to an applied magnetic field normal to the
plate. Our interest is the asymptotic behavior of the energy in macroscopically
large samples near the saturation field. We establish the scaling of the
critical value of the applied field strength below saturation at which the
ground state changes from the uniform to a branched domain magnetization
pattern and the leading order scaling behavior of the minimal energy.
Furthermore, we derive a reduced sharp-interface energy giving the precise
asymptotic behavior of the minimal energy in macroscopically large plates under
a physically reasonable assumption of small deviations of the magnetization
from the easy axis away from domain walls. On the basis of the reduced energy,
and by a formal asymptotic analysis near the transition, we derive the precise
asymptotic values of the critical field strength at which non-trivial
minimizers (either local or global) emerge. The non-trivial minimal energy
scaling is achieved by magnetization patterns consisting of long slender
needle-like domains of magnetization opposing the applied fieldComment: 38 pages, 7 figures, submitted to J. Nonlin. Sci
Structured Deformations of Continua: Theory and Applications
The scope of this contribution is to present an overview of the theory of
structured deformations of continua, together with some applications.
Structured deformations aim at being a unified theory in which elastic and
plastic behaviours, as well as fractures and defects can be described in a
single setting. Since its introduction in the scientific community of rational
mechanicists (Del Piero-Owen, ARMA 1993), the theory has been put in the
framework of variational calculus (Choksi-Fonseca, ARMA 1997), thus allowing
for solution of problems via energy minimization. Some background, three
problems and a discussion on future directions are presented.Comment: 11 pages, 1 figure, 1 diagram. Submitted to the Proceedings volume of
the conference CoMFoS1
Digital Financial Inclusion in a Cashless Society
Quarriers commissioned the Rix Inclusive Research team to carry out an evaluation study to explore how people with learning disabilities manage and use their money, what works and what is difficult. This report details the activities undertaken by the research team as part of this phase. It provides an account of the aims and objectives, methodology, points of discussion, conclusion, and recommendations for Phase 2 of the project, which will consider possible practical solutions to support people with learning disabilities to move from cash to cashless (digital) payments, and towards digital finance overall, in order to fully participate in the cashless society
Striped periodic minimizers of a two-dimensional model for martensitic phase transitions
In this paper we consider a simplified two-dimensional scalar model for the
formation of mesoscopic domain patterns in martensitic shape-memory alloys at
the interface between a region occupied by the parent (austenite) phase and a
region occupied by the product (martensite) phase, which can occur in two
variants (twins). The model, first proposed by Kohn and Mueller, is defined by
the following functional: where
is periodic in and almost everywhere.
Conti proved that if then the minimal specific
energy scales like ,
as . In the regime , we improve Conti's results, by computing exactly the
minimal energy and by proving that minimizers are periodic one-dimensional
sawtooth functions.Comment: 29 pages, 3 figure
The existence of an inverse limit of inverse system of measure spaces - a purely measurable case
The existence of an inverse limit of an inverse system of (probability) measure spaces has been investigated since the very beginning of the birth of the modern probability theory. Results from Kolmogorov
[10], Bochner [2], Choksi [5], Metivier [14], Bourbaki [3] among others have paved the way of the deep understanding of the problem under consideration. All the above results, however, call for some topological concepts, or at least ones which are closely related topological ones. In this paper we investigate purely measurable inverse systems of (probability) measure spaces, and give a sucient condition for the existence of a unique inverse limit. An example for the considered purely measurable inverse systems of (probability) measure spaces is also given
Froth-like minimizers of a non local free energy functional with competing interactions
We investigate the ground and low energy states of a one dimensional non
local free energy functional describing at a mean field level a spin system
with both ferromagnetic and antiferromagnetic interactions. In particular, the
antiferromagnetic interaction is assumed to have a range much larger than the
ferromagnetic one. The competition between these two effects is expected to
lead to the spontaneous emergence of a regular alternation of long intervals on
which the spin profile is magnetized either up or down, with an oscillation
scale intermediate between the range of the ferromagnetic and that of the
antiferromagnetic interaction. In this sense, the optimal or quasi-optimal
profiles are "froth-like": if seen on the scale of the antiferromagnetic
potential they look neutral, but if seen at the microscope they actually
consist of big bubbles of two different phases alternating among each other. In
this paper we prove the validity of this picture, we compute the oscillation
scale of the quasi-optimal profiles and we quantify their distance in norm from
a reference periodic profile. The proof consists of two main steps: we first
coarse grain the system on a scale intermediate between the range of the
ferromagnetic potential and the expected optimal oscillation scale; in this way
we reduce the original functional to an effective "sharp interface" one. Next,
we study the latter by reflection positivity methods, which require as a key
ingredient the exact locality of the short range term. Our proof has the
conceptual interest of combining coarse graining with reflection positivity
methods, an idea that is presumably useful in much more general contexts than
the one studied here.Comment: 38 pages, 2 figure
Phase 2 Study of Pemetrexed Plus Carboplatin, or Pemetrexed Plus Cisplatin with Concurrent Radiation Therapy Followed by Pemetrexed Consolidation in Patients with Favorable-Prognosis Inoperable Stage IIIA/B Non–Small-Cell Lung Cancer
IntroductionThere is no consensus chemotherapy regimen with concurrent radiotherapy (RT) for inoperable stage IIIA/B non–small-cell lung cancer. This trial evaluated pemetrexed with carboplatin (PCb) or cisplatin (PC) with concurrent RT followed by consolidation pemetrexed.MethodsIn this open-label, noncomparative phase II trial, patients with inoperable stage IIIA/B non–small-cell lung cancer (initially all histologies, later restricted to nonsquamous) were randomized (1:1) to PCb or PC with concurrent RT (64–68 Gy over days 1–45). Consolidation pemetrexed monotherapy was administered every 21 days for three cycles. Primary endpoint was 2-year overall survival (OS) rate.ResultsFrom June 2007 to November 2009, 98 patients were enrolled (PCb: 46; PC: 52). The 2-year OS rate was PCb: 45.4% (95% confidence interval [CI], 29.5–60.0%); PC: 58.4% (95% CI, 42.6–71.3%), and in nonsquamous patients was PCb: 48.0% (95% CI, 29.0–64.8%); PC: 55.8% (95% CI, 38.0–70.3%). Median time to disease progression was PCb: 8.8 months (95% CI, 6.0–12.6 months); PC: 13.1 months (95% CI, 8.3–not evaluable [NE]). Median OS (months) was PCb: 18.7 (95% CI, 12.9–NE); PC: 27.0 (95% CI, 23.2–NE). The objective response rates (ORRs) were PCb: 52.2%; PC: 46.2%. Grade 4 treatment-related toxicities (% PCb/% PC) were: anemia, 0/1.9; neutropenia, 6.5/3.8; thrombocytopenia, 4.3/1.9; and esophagitis, 0/1.9. Most patients completed scheduled chemotherapy and RT during induction and consolidation phases. No drug-related deaths were reported during chemoradiotherapy.ConclusionsBecause of study design, efficacy comparisons cannot be made. However, both combinations with concurrent RT were active and well tolerated
Preservation of Piecewise Constancy under TV Regularization with Rectilinear Anisotropy
A recent result by Lasica, Moll and Mucha about the -anisotropic
Rudin-Osher-Fatemi model in asserts that the solution is
piecewise constant on a rectilinear grid, if the datum is. By means of a new
proof we extend this result to . The core of our proof consists
in showing that averaging operators associated to certain rectilinear grids map
subgradients of the -anisotropic total variation seminorm to
subgradients
The Glial Regenerative Response to Central Nervous System Injury Is Enabled by Pros-Notch and Pros-NFκB Feedback
Organisms are structurally robust, as cells accommodate changes preserving structural integrity and function. The molecular mechanisms underlying structural robustness and plasticity are poorly understood, but can be investigated by probing how cells respond to injury. Injury to the CNS induces proliferation of enwrapping glia, leading to axonal re-enwrapment and partial functional recovery. This glial regenerative response is found across species, and may reflect a common underlying genetic mechanism. Here, we show that injury to the Drosophila larval CNS induces glial proliferation, and we uncover a gene network controlling this response. It consists of the mutual maintenance between the cell cycle inhibitor Prospero (Pros) and the cell cycle activators Notch and NFκB. Together they maintain glia in the brink of dividing, they enable glial proliferation following injury, and subsequently they exert negative feedback on cell division restoring cell cycle arrest. Pros also promotes glial differentiation, resolving vacuolization, enabling debris clearance and axonal enwrapment. Disruption of this gene network prevents repair and induces tumourigenesis. Using wound area measurements across genotypes and time-lapse recordings we show that when glial proliferation and glial differentiation are abolished, both the size of the glial wound and neuropile vacuolization increase. When glial proliferation and differentiation are enabled, glial wound size decreases and injury-induced apoptosis and vacuolization are prevented. The uncovered gene network promotes regeneration of the glial lesion and neuropile repair. In the unharmed animal, it is most likely a homeostatic mechanism for structural robustness. This gene network may be of relevance to mammalian glia to promote repair upon CNS injury or disease
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