Field patterns: a new type of wave with infinitely degenerate band structure

Field pattern materials (FP-materials) are space-time composites with PT-symmetry in which the one-dimensional- spatial distribution of the constituents changes in time in such a special manner to give rise to a new type of waves, which we call field pattern waves (FP-waves) [G. W. Milton and O. Mattei, Proc. R. Soc. A 473, 20160819 (2017), O. Mattei and G. W. Milton, arXiv:1705.00539 (2017)]. Specifically, due to the special periodic space-time geometry of these materials, when an instantaneous disturbance propagates through the system, the branching of the characteristic lines at the space-time interfaces between phases does not lead to a chaotic cascade of disturbances but concentrates on an orderly pattern of disturbances: this is the field pattern. By applying Bloch-Floquet theory we find that the dispersion diagrams associated with these FP-materials are infinitely degenerate: associated with each point on the dispersion diagram is an infinite space of Bloch functions, a basis for which are generalized functions each concentrated on a field pattern, paramaterized by a variable that we call the launch parameter. The dynamics separates into independent dynamics on the different field patterns, each with the same dispersion relation.Comment: 8 pages, 4 figure

On the forces that cable webs under tension can support and how to design cable webs to channel stresses

In many applications of Structural Engineering the following question arises: given a set of forces $\mathbf{f}_1,\mathbf{f}_2,\dots,\mathbf{f}_N$ applied at prescribed points $\mathbf{x}_1,\mathbf{x}_2,\dots,\mathbf{x}_N$, under what constraints on the forces does there exist a truss structure (or wire web) with all elements under tension that supports these forces? Here we provide answer to such a question for any configuration of the terminal points $\mathbf{x}_1,\mathbf{x}_2,\dots,\mathbf{x}_N$ in the two- and three-dimensional case. Specifically, the existence of a web is guaranteed by a necessary and sufficient condition on the loading which corresponds to a finite dimensional linear programming problem. In two-dimensions we show that any such web can be replaced by one in which there are at most $P$ elementary loops, where elementary means the loop cannot be subdivided into subloops, and where $P$ is the number of forces $\mathbf{f}_1,\mathbf{f}_2,\dots,\mathbf{f}_N$ applied at points strictly within the convex hull of $\mathbf{x}_1,\mathbf{x}_2,\dots,\mathbf{x}_N$. In three-dimensions we show that, by slightly perturbing $\mathbf{f}_1,\mathbf{f}_2,\dots,\mathbf{f}_N$, there exists a uniloadable web supporting this loading. Uniloadable means it supports this loading and all positive multiples of it, but not any other loading. Uniloadable webs provide a mechanism for distributing stress in desired ways.Comment: 18 pages, 8 figure

An extremal problem arising in the dynamics of two-phase materials that directly reveals information about the internal geometry

In two phase materials, each phase having a non-local response in time, it has been found that for some driving fields the response somehow untangles at specific times, and allows one to directly infer useful information about the geometry of the material, such as the volume fractions of the phases. Motivated by this, and to obtain an algorithm for designing appropriate driving fields, we find approximate, measure independent, linear relations between the values that Markov functions take at a given set of possibly complex points, not belonging to the interval [-1,1] where the measure is supported. The problem is reduced to simply one of polynomial approximation of a given function on the interval [-1,1] and to simplify the analysis Chebyshev approximation is used. This allows one to obtain explicit estimates of the error of the approximation, in terms of the number of points and the minimum distance of the points to the interval [-1,1]. Assuming this minimum distance is bounded below by a number greater than 1/2, the error converges exponentially to zero as the number of points is increased. Approximate linear relations are also obtained that incorporate a set of moments of the measure. In the context of the motivating problem, the analysis also yields bounds on the response at any particular time for any driving field, and allows one to estimate the response at a given frequency using an appropriately designed driving field that effectively is turned on only for a fixed interval of time. The approximation extends directly to Markov-type functions with a positive semidefinite operator valued measure, and this has applications to determining the shape of an inclusion in a body from boundary flux measurements at a specific time, when the time-dependent boundary potentials are suitably tailored.Comment: 36 pages, 7 figure

The obstacle problem in masonry structures and cable nets

We consider the problem of finding a net that supports prescribed forces applied at prescribed points, yet avoids certain obstacles, with all the elements of the net under compression (strut net) or under tension (cable web). In the case of masonry structures, for instance, this consists in finding a strut net that supports the forces, is contained within the physical structure, and avoids regions that may be not accessible due, for instance, to the presence of holes. We solve such a problem in the two-dimensional case, where the prescribed forces are applied at the vertices of a convex polygon, and we treat the cases of both single and multiple obstacles. By approximating the obstacles by polygonal regions, the task reduces to identifying the feasible domain in a linear programming problem. For a single obstacle we show how the region $\Gamma$ available to the obstacle can be enlarged as much as possible in the sense that there is no other strut net, having a region $\Gamma_1$ available to the obstacle with $\Gamma_1 \subset\Gamma$. The case where some of the forces are reactive, unprescribed but reacting to the other prescribed forces, is also treated. It again reduces to identifying the feasible domain in a linear programming problem. Finally, one may allow a subset of the reactive forces to each act not at a prescribed point, but rather at any point on a prescribed line segment. Then the task reduces to identifying the feasible domain in a quadratic programming problem.Comment: 22 pages, 12 figures, 3 supplemental video

Off-label long acting injectable antipsychotics in real-world clinical practice: a cross-sectional analysis of prescriptive patterns from the STAR Network DEPOT study

Introduction Information on the off-label use of Long-Acting Injectable (LAI) antipsychotics in the real world is lacking. In this study, we aimed to identify the sociodemographic and clinical features of patients treated with on- vs off-label LAIs and predictors of off-label First- or Second-Generation Antipsychotic (FGA vs. SGA) LAI choice in everyday clinical practice. Method In a naturalistic national cohort of 449 patients who initiated LAI treatment in the STAR Network Depot Study, two groups were identified based on off- or on-label prescriptions. A multivariate logistic regression analysis was used to test several clinically relevant variables and identify those associated with the choice of FGA vs SGA prescription in the off-label group. Results SGA LAIs were more commonly prescribed in everyday practice, without significant differences in their on- and off-label use. Approximately 1 in 4 patients received an off-label prescription. In the off-label group, the most frequent diagnoses were bipolar disorder (67.5%) or any personality disorder (23.7%). FGA vs SGA LAI choice was significantly associated with BPRS thought disorder (OR = 1.22, CI95% 1.04 to 1.43, p = 0.015) and hostility/suspiciousness (OR = 0.83, CI95% 0.71 to 0.97, p = 0.017) dimensions. The likelihood of receiving an SGA LAI grew steadily with the increase of the BPRS thought disturbance score. Conversely, a preference towards prescribing an FGA was observed with higher scores at the BPRS hostility/suspiciousness subscale. Conclusion Our study is the first to identify predictors of FGA vs SGA choice in patients treated with off-label LAI antipsychotics. Demographic characteristics, i.e. age, sex, and substance/alcohol use co-morbidities did not appear to influence the choice towards FGAs or SGAs. Despite a lack of evidence, clinicians tend to favour FGA over SGA LAIs in bipolar or personality disorder patients with relevant hostility. Further research is needed to evaluate treatment adherence and clinical effectiveness of these prescriptive patterns

The Role of Attitudes Toward Medication and Treatment Adherence in the Clinical Response to LAIs: Findings From the STAR Network Depot Study

Background: Long-acting injectable (LAI) antipsychotics are efficacious in managing psychotic symptoms in people affected by severe mental disorders, such as schizophrenia and bipolar disorder. The present study aimed to investigate whether attitude toward treatment and treatment adherence represent predictors of symptoms changes over time. Methods: The STAR Network \u201cDepot Study\u201d was a naturalistic, multicenter, observational, prospective study that enrolled people initiating a LAI without restrictions on diagnosis, clinical severity or setting. Participants from 32 Italian centers were assessed at three time points: baseline, 6-month, and 12-month follow-up. Psychopathological symptoms, attitude toward medication and treatment adherence were measured using the Brief Psychiatric Rating Scale (BPRS), the Drug Attitude Inventory (DAI-10) and the Kemp's 7-point scale, respectively. Linear mixed-effects models were used to evaluate whether attitude toward medication and treatment adherence independently predicted symptoms changes over time. Analyses were conducted on the overall sample and then stratified according to the baseline severity (BPRS < 41 or BPRS 65 41). Results: We included 461 participants of which 276 were males. The majority of participants had received a primary diagnosis of a schizophrenia spectrum disorder (71.80%) and initiated a treatment with a second-generation LAI (69.63%). BPRS, DAI-10, and Kemp's scale scores improved over time. Six linear regressions\u2014conducted considering the outcome and predictors at baseline, 6-month, and 12-month follow-up independently\u2014showed that both DAI-10 and Kemp's scale negatively associated with BPRS scores at the three considered time points. Linear mixed-effects models conducted on the overall sample did not show any significant association between attitude toward medication or treatment adherence and changes in psychiatric symptoms over time. However, after stratification according to baseline severity, we found that both DAI-10 and Kemp's scale negatively predicted changes in BPRS scores at 12-month follow-up regardless of baseline severity. The association at 6-month follow-up was confirmed only in the group with moderate or severe symptoms at baseline. Conclusion: Our findings corroborate the importance of improving the quality of relationship between clinicians and patients. Shared decision making and thorough discussions about benefits and side effects may improve the outcome in patients with severe mental disorders

Determination of the size of an inclusion from one boundary measurement at a specific moment of time

In this talk we will show an application of the theory of Herglotz-Nevannlina functions for the linear viscoelastic problem, the dielectric problem and the conductivity problem in the time domain. Specifically, by using the analyticity of the Dirichlet-to-Neumann map which relates the applied field on the boundary to the corresponding measured field on the boundary one can determine bounds on the response of the body for any moment of time. Such bounds are tighter the more information regarding the body is incorporated. By tailoring the time-dependent applied field so that the bounds incorporating the volume of the inclusion are extremely tight at specific moments of time, one can then use them in an inverse fashion to determine the size of the inclusion.Non UBCUnreviewedAuthor affiliation: University of UtahPostdoctora

A structural model for plane sandwich beams including transverse core deformability and arbitrary boundary conditions

In order to model the effect of arbitrary boundary conditions on plane linear elastic sandwich beams, we develop a structural theory relying on a zigzag warping: each layer, of arbitrary thickness and modulus, is described by the Timoshenko kinematics and, for the core, we further consider the transverse strain, which measures the normal deformability along the core thickness. This structural model, dependent on six functions of the beam axis coordinate, builds on the theory put forward by Dusan Krajcinovic in the early Seventies. By following a variational approach, we obtain and discuss the (Euler-Lagrange) balance equations and the (natural) boundary conditions governing the model. In sandwich beams having a soft core, this model can describe relevant features of the stress state due to "severe boundary conditions", including, for instance, loading on a specific skin coupled with constraints realised, at certain cross-sections, on the opposite skin only. In this work we focus on the flexure accompanied with non-uniform shear. In particular, we consider the cases of cantilever and propped-cantilever beams subject to uniform load. We provide accurate shear stress estimates by post-processing, through a Jourawski-like approach, the longitudinal normal stress predicted by the beam model. We demonstrate the capability of the proposed model by comparison of its results, obtained by using the Rayleigh-Ritz method, with those ofThe predictions of the present beam model are shown to be useful at fully clamped cross-sections, where displacement-based FE results are unreliable. continuum plane stress Finite Element (FE) simulations