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

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: $${\cal E}(u)=\beta||u(0,\cdot)||^2_{H^{1/2}([0,h])}+ \int_{0}^{L} dx \int_0^h dy \big(|u_x|^2 + \epsilon |u_{yy}| \big)$$ where $u:[0,L]\times[0,h]\to R$ is periodic in $y$ and $u_y=\pm 1$ almost everywhere. Conti proved that if $\beta\gtrsim\epsilon L/h^2$ then the minimal specific energy scales like $\sim \min\{(\epsilon\beta/L)^{1/2}, (\epsilon/L)^{2/3}\}$, as $(\epsilon/L)\to 0$. In the regime $(\epsilon\beta/L)^{1/2}\ll (\epsilon/L)^{2/3}$, 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

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

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

purpleSTARS: A creative intervention into AI's Algorithms through co-production of a live ‘AI, sense of self’ portrait

We propose an exploration into the intersection of artificial intelligence (AI), sensory art, and portraiture, with a focus on inclusive research and sensory art co-production. AI algorithms often lack the nuanced understanding of diverse human experiences, particularly those of marginalised communities. We aim to challenge and reshape these algorithms to be more inclusive by engaging with them, so AI becomes more reflective of diversity, and becomes less biased. We plan to co-create a series of experimental AI generated portraits that reflect on our sensory Sense of Self, highlighting our sense of touch, smell, taste which AI cannot (yet) reproduce as well as our senses of sound and sight. Objectives: 1. Empowerment Through Artistic Expression: Provide individuals with learning disabilities and differences with a platform for creative expression and agency through inclusive research and co-production. 2. Critique and Intervention: Encourage critical reflection on the biases and limitations of AI algorithms and explore how sensory art can intervene to address these issues. 3. Co-Production and Collaboration: Facilitate collaborative processes between individuals with lived experience of learning disabilities, and conference participants to feed AI algorithms with diverse, sensory experiences and personal narratives. 4. Knowledge Sharing and Community Building: Foster an inclusive dialogue among diverse people to share insights and best practices for inclusive AI design. The session: Conference participants will be invited to co-create ‘AI, sense of self’ portraits in groups with purpleSTARS. The space will be set up similar to a traditional life drawing room but with a 360 camera at the centre instead of a life model. Easels/stands will face into the camera with screens to display AI generated imagery. Traditional art and sensory materials, highlighting touch, smell and taste will also be available circling the camera. The portraits will be captured by the 360 camera where everyone and everything is included. We hope the session will foster collaborations for future inclusive research in AI design, with a focus on centring the voices and experiences of people with learning disabilities and differences, fostering more ethical, inclusive, and human-centred AI systems

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 $\ell^1$-anisotropic Rudin-Osher-Fatemi model in $\mathbb{R}^2$ 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 $\mathbb{R}^n$. The core of our proof consists in showing that averaging operators associated to certain rectilinear grids map subgradients of the $\ell^1$-anisotropic total variation seminorm to subgradients