Global Behavior Of Finite Energy Solutions To The dd-Dimensional Focusing Nonlinear Schr\"odinger Equation

We study the global behavior of finite energy solutions to the $d$-dimensional focusing nonlinear Schr\"odinger equation (NLS), $i \partial_t u+\Delta u+ |u|^{p-1}u=0,$ with initial data $u_0\in H^1,\; x \in R^n$. The nonlinearity power $p$ and the dimension $d$ are such that the scaling index $s=\frac{d}2-\frac2{p-1}$ is between 0 and 1, thus, the NLS is mass-supercritical $(s>0)$ and energy-subcritical $(s<1).$ For solutions with \ME[u_0]<1 (\ME[u_0] stands for an invariant and conserved quantity in terms of the mass and energy of $u_0$), a sharp threshold for scattering and blowup is given. Namely, if the renormalized gradient \g_u of a solution $u$ to NLS is initially less than 1, i.e., \g_u(0)<1, then the solution exists globally in time and scatters in $H^1$ (approaches some linear Schr\"odinger evolution as $t\to\pm\infty$); if the renormalized gradient \g_u(0)>1, then the solution exhibits a blowup behavior, that is, either a finite time blowup occurs, or there is a divergence of $H^1$ norm in infinite time. This work generalizes the results for the 3d cubic NLS obtained in a series of papers by Holmer-Roudenko and Duyckaerts-Holmer-Roudenko with the key ingredients, the concentration compactness and localized variance, developed in the context of the energy-critical NLS and Nonlinear Wave equations by Kenig and Merle.Comment: 57 pages, 4 figures and updated reference

Helium- and Lithium-like ionic sequences: Critical charges

In non-relativistic quantum mechanics we study the Coulomb systems of infinitely massive center of charge Z and two-three electrons: $(Z,e,e)$ and $(Z,e,e,e)$. It is shown that in both cases the total energy curve in $Z$ is smooth, without any visible irregularities. Thus, for both systems the physical integer charges $Z=1,2,...$ do not play a distinguished role as would be associated with charge quantization. By definition, a critical charge $Z_{cr}$ is a charge which separates a domain of the existence of bound states from a domain of unbound ones (continuum). For both systems the critical charges are found, $Z_{cr,2e}=0.91085$ and $Z_{cr,3e}=2.009$, respectively. Based on numerical analysis, the Puiseux expansion in fractional powers of $(Z-Z_{cr})$ is constructed for both systems. Our results indicate the existence of a square-root branch point singularity at $Z_{cr}$ with exponent 3/2. A connection between the critical charge and the radius of convergence of 1/Z-expansion is briefly discussed.Comment: 10 pages, LaTeX, typos corrected, Fig.1 added, a Note Added with calculated critical charge for $2^1S$ state for $(Z,e,e)$ system, $Z_{cr,2e}^{(2^1S)}\ =\ 1.02

Molecular Interactions of Polydimethylsiloxane and Ni-Mn-Ga

With the recent advent of magnetic shape memory alloys (MSMA), such as martensitic Ni-Mn-Ga, researchers focused studies about these materials on properties such as magnetic-field-induced deformation. Currently, some of the properties of interest include, but are not limited to: twin boundary deformation, strain, stress, magnetic and thermal activation, operating temperatures, magnetic permeability, and electric resistivity. Given some of these properties, materials such as Ni-Mn-Ga have been used as actuators, channels, and membranes in pumps. While these pumps are currently at the stage of sub-microliter medical application, they have also been shown to possess great accuracy in delivery as well as strength in pumping against relatively high back pressures. In this system, given the small size of the pump, a typical O-ring cannot provide the same effective seal as it would in a regular impeller pump. However, using a Polydimethylsiloxane (PDMS) gel has proven to be a useful sealant for these MSMA pumps. The interaction of the sealant against the Ni-Mn-Ga itself, in particular adhesion and detachment, take on a critical role in the pumping process. That is to say that as the channel , created by the twin boundary shift, moves, the PDMS must adhere to the alloy up to a specific limit and then detach. This adhesion-detachment must be controlled and repeatable. This simulation study aims to quantify the interaction of PDMS and Ni-Mn-Ga, as it pertains to the adhesivity of the former to the latter, in order to better determine how best to cure PDMS for optimal adhesion and separation. In order to study these PDMS-MSMA surfaces, GPUs in the XK nodes of the Blue Waters Supercomputer, at the University of Illinois, Urbana-Champaign, were used in conjunction with the HOOMD-blue particle simulation kit to render them and study the molecular dynamics between these two materials. The PDMS models for this simulation were based on a united atom (UA), Lennard-Jones potential modified from previous studies(1) , utilizing 20-mer chains. While the Ni-Mn-Ga surface was based on an M1 matrix developed at Boise State. The MSMA surface his modeled as a rigid lattice structure without twin boundary movement, the motion is instead replaced by simulating a pulling force on the PDMS surface up to where it detaches from the MSM surface. By utilizing these constraints we can begin to study the effects that the curing time of PDMS has on this interaction with Ni-Mn-Ga, how the MSMA’s lattice structure reacts in this scenario, and how best to continue incorporating further constraints into these simulation studies, such as simulated twin boundary movement

Active Exterior Cloaking

A new method of cloaking is presented. For two-dimensional quasistatics it is proven how a single active exterior cloaking device can be used to shield an object from surrounding fields, yet produce very small scattered fields. The problem is reduced to finding a polynomial which is approximately one within one disk and zero within a second disk, and such a polynomial is constructed. For the two-dimensional Helmholtz equation, it is numerically shown that three active exterior devices placed around the object suffice to produce very good cloaking.Comment: 4 pages, 3 figures, submitted to Physical Review Letter

Leveling the Viewing Field: The Impact of Target Prevalence on Searcher\u27s Functional Viewing Field

It is well known that target prevalence impacts various cognitive processes. In visual search, rare search targets are more difficult to detect than common targets. The present research investigated novel questions about target prevalence, focusing on observers’ functional viewing field (FVF) during passive search tasks. The FVF is the area in a display where attention is focused and item processing is enhanced. According the FVF framework (Hulleman & Olivers, 2017), the size of the FVF is modulated by the ease of target detections, such that visual search involving difficult target detection reduces the FVF. Although this would suggest that low target prevalence searches should be conducted with a “narrow” FVF, recent evidence from eye-movement analyses (Papesh & Guevara Pinto, 2019) seems to indicate the opposite: Relative to high-prevalence conditions, low-prevalence search yields a wider FVF. It is possible that this effect is due to expectations of target frequency learned during high target prevalence conditions. Three experiments were conducted to test hypotheses regarding the interaction of target prevalence and target expectations in modulating the FVF. Using a dual-task paradigm, where observers passively searched for targets at center of the display while simultaneously processing probes in their periphery, Experiment 1 examined the effects of target prevalence on the FVF size. Experiment 2 manipulated observers’ trial-by-trial expectations about target presence, revealing the consequences of expectations for the FVF in isolation from effects of target prevalence. Lastly, Experiment 3 directly contrasted prevalence and expectations within the same experimental design. The results showed that the size of FVF is modulated by direct experiences (i.e., target prevalence) and externally generated expectations (i.e., trial-by-trial cues), but the interaction between the two remains unclear. The implications of these findings expand our theoretical understanding of how target prevalence influence search behaviors, particularly those that extend beyond search miss rates

Constructing the Search Template: Episodic and Semantic Influences on Categorical Template Formation

Search efficiency is usually improved by presenting observers with highly detailed target cues (e.g., pictures). However, in the absence of accurate target cues, observers must rely only on categorical information to find targets. Models of visual search suggest that guidance in a categorical search results from matching categorically-diagnostic target features in the search display to a top-down attentional set (i.e., the search template), but the mechanisms by which such attentional set is constructed have not been specified. The present investigation examined the influences of both semantic and episodic memory on search template formation. More precisely, the present study tested whether observers incorporated a recent experience with a target-category exemplar into their search template, instead of relying on long-term learned regularities about object categories (Experiment 1) or on the semantic context of the search display (Experiment 2). In both experiments participants completed a categorical search task (75% of trials) in conjunction with a dot-probe response task (25% of trials). The dot-probe response task assessed the contents of the search template by capturing spatial attention if the dot-probe was presented at an inconsistent location relative to objects matching the search template. In Experiment 1 it was shown that observers include recently encoded objects into their search templates, when given the opportunity to do so. Experiment 2, however, showed that observers rely on context semantics to construct categorical search templates, and they continue to do so in the presence of repeated target cues related to different contexts. These results suggest that observers can, and will, rely on episodic representations to construct categorical search templates when such representations are available, but only if no external cues (i.e., scene semantics) are present to identify criterial target feature

Participatory co-design of science communication strategies for public engagement in the US and Ecuador around health behaviour change

Science communication research and practice currently promote strategies oriented towards creating audience engagement around scientific content. Consequently, science communication needs to continually explore new methodologies that enable audiences’ participation in order to meet their interests and needs. The present study combines qualitative and participatory action research (PAR) methods guided by decolonial epistemologies to develop a co-designed project with public health, nutrition and sports science researchers to recruit young audiences from Albuquerque, New Mexico, USA, and from Cuenca, Ecuador. The main goal of this study was to create strategies to motivate young audiences’ engagement and interest in adopting healthy habits. This article focuses on the study’s research design in order to provide guidelines and procedural recommendations for facilitating a co-design approach for developing science communication initiatives targeting children and teenagers in Ecuador and the United States. As we demonstrate, the PAR approach for co-design leads to useful outcomes: (1) the incorporation of decolonial theory guidelines in participatory research; and (2) the development of science communication strategies that combine online and offline activities to put in dialogue scientists and their audiences, ultimately resulting in mutual learning, thus allowing scholars and practitioners to explore in practical terms how to co-design improved strategies