Singular Sturm–Liouville Theory on Manifolds

AbstractIn this paper we investigate Schrödinger operators L=−Δg+a(x) on a compact Riemannian manifold (M, g), where the potential function a(x) is assumed to be continuous, but not necessarily bounded, outside of some closed set Σ⊂M of measure zero. Under certain geometric hypotheses on Σ and growth conditions on a(x) as x→Σ, we prove that the Dirichlet extension of L is bounded from below with discrete spectrum; in many cases, a(x) is allowed to approach −∞ as x→Σ. We also consider conditions on Σ and a(x) under which the Sturm–Liouville theory of L is “singular” in that no boundary conditions are needed to specify the eigenvalues and eigenfunctions of L; in particular, this occurs when the domain of L does not depend on boundary conditions, for example, when L is essentially self-adjoint or more generally “essentially Dirichlet” (a new property that we define). The behavior of L on weighted Sobolev spaces is also discussed. In most of the paper we assume that Σ is a k-dimensional submanifold without boundary, but in the last few sections we generalize our results to stratified sets

Soft Robotics for Chemists

Soft robots: A methodology based on embedded pneumatic networks (PneuNets) is described that enables large-amplitude actuations in soft elastomers by pressurizing embedded channels. Examples include a structure that can change its curvature from convex to concave, and devices that act as compliant grippers for handling fragile objects (e.g., a chicken egg).Chemistry and Chemical Biolog

Predictive Modeling of Fast-Curing Thermosets in Nozzle-Based Extrusion

This work presents an approach to modeling the dynamic spreading and curing behavior of thermosets in nozzle-based extrusions. Thermosets cover a wide range of materials, some of which permit low-temperature processing with subsequent high-temperature and high-strength working properties. Extruding thermosets may overcome the limited working temperatures and strengths of conventional thermoplastic materials used in additive manufacturing. This project aims to produce technology for the fabrication of thermoset-based structures leveraging advances made in nozzle-based extrusion, such as fused deposition modeling (FDM), material jetting, and direct writing. Understanding the synergistic interactions between spreading and fast curing of extruded thermosetting materials will provide essential insights for applications that require accurate dimensional controls, such as additive manufacturing [1], [2] and centrifugal coating/forming [3]. Two types of thermally curing thermosets -- one being a soft silicone (Ecoflex 0050) and the other being a toughened epoxy (G/Flex) -- served as the test materials in this work to obtain models for cure kinetics and viscosity. The developed models align with extensive measurements made with differential scanning calorimetry (DSC) and rheology. DSC monitors the change in the heat of reaction, which reflects the rate and degree of cure at different crosslinking stages. Rheology measures the change in complex viscosity, shear moduli, yield stress, and other properties dictated by chemical composition. By combining DSC and rheological measurements, it is possible to establish a set of models profiling the cure kinetics and chemorheology without prior knowledge of chemical composition, which is usually necessary for sophisticated mechanistic modeling. In this work, we conducted both isothermal and dynamic measurements with both DSC and rheology. With the developed models, numerical simulations yielded predictions of diameter and height of droplets, along with width and height of extruded lines cured at varied temperatures. Experimental results carried out on a goniometric platform and a nozzle-based 3D printer showed agreement with the numerical simulations. Finally, this presentation will show how the models are adaptable to the planning of tool paths and designs in additive manufacturing

White light emission from blends of blue-emitting organic molecules: A general route to the white organic light-emitting diode?

We show that all possible binary combinations of molecules from four different families of organics - a diamine derivative, N,N′-bis(3methylphenyl)-N,N′-diphenylbenzidine, an oxidiazole derivative, 2-(4-biphenylyl)-5-(4-tert-butylphenyl)-1,3,4-oxadiazole, a substituted thiophene dioxide, 2,5-bis(trimethylsilyl thiophene)-1,1-dioxide, and poly(9-vinylcarbazole) - produce white or near-white emission. We suggest that this is due to exciplex formation, and that this is likely to be a general phenomenon for blends of blue-emitting aromatic organics. This implies that films of spin-coated blends of blue-emitting organics represent a general, simple, and cheap route to white-emitting organic light-emitting diodes

FLEXBLE ROBOTIC ACTUATORS

Some embodiments of the disclosed subject matter includes a laminated robotic actuator. The laminated robotic actuator includes a strain-limiting layer comprising a flexible, non extensible material in the form of a sheet or thin film, a flexible inflatable layer in the form of a thin film or sheet in facing relationship with the Strain-limiting layer, wherein the inflatable layer is selectively adhered to the strain-limiting layer, and wherein a portion of an un-adhered region between the strain-limiting layer and the inflatable layer defines a pressurizable channel, and at least one fluid inlet in fluid communication with the pressurizable channel. The first flexible non-extensible material has a stiffness that is greater than the stiffness of the second flexible elastomeric material and the flexible elastomer is non-extensible under actuation conditions

A Facile Graphene Conductive Polymer Paper Based Biosensor for Dopamine, TNF-α, and IL-6 Detection

Paper-based biosensors are a potential paradigm of sensitivity achieved via microporous spreading/microfluidics, simplicity, and affordability. In this paper, we develop decorated paper with graphene and conductive polymer (herein referred to as graphene conductive polymer paper-based sensor or GCPPS) for sensitive detection of biomolecules. Planetary mixing resulted in uniformly dispersed graphene and conductive polymer ink, which was applied to laser-cut Whatman filter paper substrates. Scanning electron microscopy and Raman spectroscopy showed strong attachment of conductive polymer-functionalized graphene to cellulose fibers. The GCPPS detected dopamine and cytokines, such as tumor necrosis factor-alpha (TNF-α), and interleukin 6 (IL-6) in the ranges of 12.5–400 µM, 0.005–50 ng/mL, and 2 pg/mL–2 µg/mL, respectively, using a minute sample volume of 2 µL. The electrodes showed lower detection limits (LODs) of 3.4 µM, 5.97 pg/mL, and 9.55 pg/mL for dopamine, TNF-α, and IL-6 respectively, which are promising for rapid and easy analysis for biomarkers detection. Additionally, these paper-based biosensors were highly selective (no serpin A1 detection with IL-6 antibody) and were able to detect IL-6 antigen in human serum with high sensitivity and hence, the portable, adaptable, point-of-care, quick, minute sample requirement offered by our fabricated biosensor is advantageous to healthcare applications

Using Explosions to Power a Soft Robot

This manuscript describes the use of explosions to power a soft robot—one composed solely of organic elastomers (e.g., silicones). The robot has three pneumatic actuators (pneu-nets) in a tripedal configuration. Explosion of a stoichiometric mixture of methane and oxygen within the microchannels making up the actuators produced hot gas that rapidly inflated the pneu-nets, and caused the robot to launch itself vertically from a flat surface (e.g., to jump). A soft flap embedded in the pneu-net acted as the valve of a passive exhaust system, and allowed multiple sequential actuations. The flame and temperature increase from the explosions are short-lived, and do not noticeably damage the robots over dozens of actuation cycles.Chemistry and Chemical Biolog

Impact of safety-related dose reductions or discontinuations on sustained virologic response in HCV-infected patients: Results from the GUARD-C Cohort

BACKGROUND: Despite the introduction of direct-acting antiviral agents for chronic hepatitis C virus (HCV) infection, peginterferon alfa/ribavirin remains relevant in many resource-constrained settings. The non-randomized GUARD-C cohort investigated baseline predictors of safety-related dose reductions or discontinuations (sr-RD) and their impact on sustained virologic response (SVR) in patients receiving peginterferon alfa/ribavirin in routine practice. METHODS: A total of 3181 HCV-mono-infected treatment-naive patients were assigned to 24 or 48 weeks of peginterferon alfa/ribavirin by their physician. Patients were categorized by time-to-first sr-RD (Week 4/12). Detailed analyses of the impact of sr-RD on SVR24 (HCV RNA <50 IU/mL) were conducted in 951 Caucasian, noncirrhotic genotype (G)1 patients assigned to peginterferon alfa-2a/ribavirin for 48 weeks. The probability of SVR24 was identified by a baseline scoring system (range: 0-9 points) on which scores of 5 to 9 and <5 represent high and low probability of SVR24, respectively. RESULTS: SVR24 rates were 46.1% (754/1634), 77.1% (279/362), 68.0% (514/756), and 51.3% (203/396), respectively, in G1, 2, 3, and 4 patients. Overall, 16.9% and 21.8% patients experienced 651 sr-RD for peginterferon alfa and ribavirin, respectively. Among Caucasian noncirrhotic G1 patients: female sex, lower body mass index, pre-existing cardiovascular/pulmonary disease, and low hematological indices were prognostic factors of sr-RD; SVR24 was lower in patients with 651 vs. no sr-RD by Week 4 (37.9% vs. 54.4%; P = 0.0046) and Week 12 (41.7% vs. 55.3%; P = 0.0016); sr-RD by Week 4/12 significantly reduced SVR24 in patients with scores <5 but not 655. CONCLUSIONS: In conclusion, sr-RD to peginterferon alfa-2a/ribavirin significantly impacts on SVR24 rates in treatment-naive G1 noncirrhotic Caucasian patients. Baseline characteristics can help select patients with a high probability of SVR24 and a low probability of sr-RD with peginterferon alfa-2a/ribavirin

Analyses of cerebral microdialysis in patients with traumatic brain injury: relations to intracranial pressure, cerebral perfusion pressure and catheter placement

<p>Abstract</p> <p>Background</p> <p>Cerebral microdialysis (MD) is used to monitor local brain chemistry of patients with traumatic brain injury (TBI). Despite an extensive literature on cerebral MD in the clinical setting, it remains unclear how individual levels of real-time MD data are to be interpreted. Intracranial pressure (ICP) and cerebral perfusion pressure (CPP) are important continuous brain monitors in neurointensive care. They are used as surrogate monitors of cerebral blood flow and have an established relation to outcome. The purpose of this study was to investigate the relations between MD parameters and ICP and/or CPP in patients with TBI.</p> <p>Methods</p> <p>Cerebral MD, ICP and CPP were monitored in 90 patients with TBI. Data were extensively analyzed, using over 7,350 samples of complete (hourly) MD data sets (glucose, lactate, pyruvate and glycerol) to seek representations of ICP, CPP and MD that were best correlated. MD catheter positions were located on computed tomography scans as pericontusional or nonpericontusional. MD markers were analyzed for correlations to ICP and CPP using time series regression analysis, mixed effects models and nonlinear (artificial neural networks) computer-based pattern recognition methods.</p> <p>Results</p> <p>Despite much data indicating highly perturbed metabolism, MD shows weak correlations to ICP and CPP. In contrast, the autocorrelation of MD is high for all markers, even at up to 30 future hours. Consequently, subject identity alone explains 52% to 75% of MD marker variance. This indicates that the dominant metabolic processes monitored with MD are long-term, spanning days or longer. In comparison, short-term (differenced or Δ) changes of MD vs. CPP are significantly correlated in pericontusional locations, but with less than 1% explained variance. Moreover, CPP and ICP were significantly related to outcome based on Glasgow Outcome Scale scores, while no significant relations were found between outcome and MD.</p> <p>Conclusions</p> <p>The multitude of highly perturbed local chemistry seen with MD in patients with TBI predominately represents long-term metabolic patterns and is weakly correlated to ICP and CPP. This suggests that disturbances other than pressure and/or flow have a dominant influence on MD levels in patients with TBI.</p