Stable blow-up dynamics in the -critical and -supercritical generalized Hartree equation

We study stable blow-up dynamics in the generalized Hartree equation with radial symmetry, which is a Schrödinger-type equation with a nonlocal, convolution-type nonlinearity: First, we consider the -critical case in dimensions and obtain that a generic blow-up has a self-similar structure and exhibits not only the square root blowup rate , but also the log-log correction (via asymptotic analysis and functional fitting), thus, behaving similarly to the stable blow-up regime in the -critical nonlinear Schrödinger equation. In this setting, we also study blow-up profiles and show that generic blow-up solutions converge to the rescaled , a ground state solution of the elliptic equation . We also consider the -supercritical case in dimensions . We derive the profile equation for the self-similar blow-up and establish the existence and local uniqueness of its solutions. As in the NLS -supercritical regime, the profile equation exhibits branches of nonoscillating, polynomially decaying (multi-bump) solutions. A numerical scheme of putting constraints into solving the corresponding ordinary differential equation is applied during the process of finding the multi-bump solutions. Direct numerical simulation of solutions to the generalized Hartree equation by the dynamic rescaling method indicates that the is the profile for the stable blow-up. In this supercritical case, we obtain the blow-up rate without any correction. This blow-up happens at the focusing level , and thus, numerically observable (unlike the -critical case). In summary, we find that the results are similar to the behavior of stable self-similar blowup solutions in the corresponding settings for the nonlinear Schrödinger equation. Consequently, one may expect that the form of the nonlinearity in the Schrödinger-type equations is not essential in the stable formation of singularities.     

Nonexistence of global solutions of wave equations with weak time-dependent damping and combined nonlinearity

In our previous two works, we studied the blow-up and lifespan estimates for damped wave equations with a power nonlinearity of the solution or its derivative, with scattering damping independently. In this work, we are devoted to establishing a similar result for a combined nonlinearity. Comparing to the result of wave equation without damping, one can say that the scattering damping has no influence.     

Local atomic and electronic structure in the LiVPO4(F,O) tavorite-type materials from solid-state NMR combined with DFT calculations

⁷Li, ³¹P, and ¹⁹F solid-state nuclear magnetic resonance (NMR) spectroscopy was used to investigate the local arrangement of oxygen and fluorine in LiVPO₄F_1-yO_y materials, interesting as positive electrode materials for Li-ion batteries. From the evolution of the 1D spectra versus y, 2D ⁷Li radiofrequency-driven recoupling (RFDR) experiments combined, and a tentative signal assignment based on density functional theory (DFT) calculations, it appears that F and O are not randomly dispersed on the bridging X position between two X–VO₄–X octahedra (X = O or F) but tend to segregate at a local scale. Using DFT calculations, we analyzed the impact of the different local environments on the local electronic structure. Depending on the nature of the VO₄X₂ environments, vanadium ions are either in the +III or in the +IV oxidation state and can exhibit different distributions of their unpaired electron(s) on the d orbitals. Based on those different local electronic structures and on the computed Fermi contact shifts, we discuss the impact on the spin transfer mechanism on adjacent nuclei and propose tentative signal assignments. The O/F clustering tendency is discussed in relation with the formation of short V^IVO vanadyl bonds with a very specific electronic structure and possible cooperative effect along the chain.     

MODELING CONTACTS OF IONIC POLYMER METAL COMPOSITES BASED TACTILE SENSORS

We report the first attempt to model the contacts of an ionic polymer metal composite（IPMC） based tactile sensor. The tactile sensor comprises an IPMC actuator, an IPMC sensor and the target to be detected. The system makes use of multiple contacts to work： the actuator comes into contact with the sensor and pushes the movement of sensor; the contact between the sensor and the object detects the existence and the stiffness of the target. We integrate modeling of various physical processes involved in IPMC devices to form a simulation scheme. An iteration and optimization strategy is also described to correlate the experimental and simulation results of an IPMC bending actuator to identify the two key parameters used in electromechanical transduction. Modeling the multiple contacts will aid the design and optimization of such IPMC based soft robotics.     

Numerical analysis of stress distribution in the upper arm tissues under an inflatable cuff: Implications for noninvasive blood pressure measurement

An inflatable cuff wrapped around the upper arm is widely used in noninvasive blood pressure measurement. However, the mechanical interaction between cuff and arm tissues, a factor that potentially affects the accuracy of noninvasive blood pressure measurement, remains rarely addressed. In the present study, finite element (FE) mod-els were constructed to quantify intra-arm stresses generated by cuff compression, aiming to provide some theoretical evi-dence for identifying factors of importance for blood pressure measurement or explaining clinical observations. Obtained results showed that the simulated tissue stresses were highly sensitive to the distribution of cuff pressure on the arm sur-face and the contact condition between muscle and bone. In contrast, the magnitude of cuff pressure and small variations in elastic properties of arm soft tissues had little influence on the efficiency of pressure transmission in arm tissues. In par-ticular, it was found that a thickened subcutaneous fat layer in obese subjects significantly reduced the effective pres-sure transmitted to the brachial artery, which may explain why blood pressure overestimation occurs more frequently in obese subjects in noninvasive blood pressure measurement.     

Novel Azobenzene-Functionalized Polyelectrolytes of Different Substituted Head Groups 2: Control of Surface Wetting in Self-Assembled Multilayer Films

A novel set of light-responsive polyelectrolytes has been developed and studied, to control and tune surface wettability by introducing various types of substituted R head-groups of azo polyelectrolytes in self-assembled multilayer (SAMU) films. As part of a larger project to develop polymer surfaces where one can exert precise control over properties important to proteins and cells in contact, photo-reversibly, we describe here how one can tune quite reliably the contact angle of a biocompatible SAMU, containing a photo-reversible azo chromophore for eventual directed cell growth. The azo polyelectrolytes described here have different substituted R head-group pairs of shorter-ionized hydrophilic COOH and SO₃H, shorter non-ionized hydrophobic H and OC₂H₅, and larger non-ionized hydrophobic octyl C₈H₁₇ and C₈F₁₇, and were employed as polyanions to fabricate the SAMU onto silicon substrates by using the counter-charge polycation PDAC. The prepared SAMU films were primarily characterized by measurement of their contact angles with water. The surface wetting properties of the thin films were found to be dependent on the type of substituted R-groups of the azo polyelectrolytes through their degree of ionization, size, hydrophobicity/hydrophilicity, solubility, conformation, and inter-polymeric association and intra-polymeric aggregation. All these factors appeared to be inter-related, and influenced variations in hydrophobic/hydrophilic character to different extents of aggregates/non-aggregates in solution because of solvation effects of the azo polyanions, and were thus manifested when adsorbed as thin films via the SAMU deposition process. For example, one interesting observation is significantly higher contact angles of 79° for SAMU films of larger octyl R groups of PAPEA-C₈F₁₇ and PAPEA-C₈H₁₇ than for others with contact angles of 64° observed for non-polar R-groups of OC₂H₅ and H. Furthermore, lower contact angle values of 59° for SAMU films with polar R-groups of COOH and SO₃H relative to that of non-polar R-groups are in accordance with their expected order of the hydrophilicity or hydrophobicity. It is possible that the large octyl groups are more effective in shielding the ionic functional groups on the substrate surface, and contributed less to the water drop-molecule interactions with ionic groups of the PDAC and/or AA groups. In addition, higher hydrophobicity of the SAMU films may be due to the incorporation of bulky and hydrophobic groups in these polyelectrolytes, which can produce aggregates on the surfaces of the SAMU films. Through understanding and controlling the complex aggregation behavior of the different substituted R-groups of these azo polyelectrolytes, and hence their adsorption on substrates, it appears possible to finely tune the surface energy of these biocompatible films over a wide range, enhance the photo-switching capabilities of the SAMU films, and tailor other surface properties for the development and application of new devices in diverse areas of microfluidics, specialty coatings, sensors, and biomedical sciences.     

A new nonlinear optical silicate carbonate K2Ca[Si2O5](CO3) with a hybrid structure of kalsilite and soda-like layered fragments

Single crystals of a new silicate carbonate, K₂Ca[Si₂O₅](CO₃), have been synthesized in a multi-components hydrothermal solution with a pH value close to neutral and a high concentration of a carbonate mineralizer. The new compound has an axial structure (s.g. P6₃22) with unit cell parameters a = 5.04789 (15), c = 17.8668 (6) Å. Pseudosymmetry of the structure corresponds to s.g. P6₃/mmc which is broken only by one oxygen position. The structure consists of two layered fragments: one of the type of the mineral kalsilite (KAlSiO₄) and the other of the high-temperature soda-like α-Na₂CO₃, Ca substituting for Na. The electro-neutral layer K₂[Si₂O₅] (denoted K) as well as the layer Ca(CO₃) (denoted S) may separately correspond to individual structures. In K₂Ca[Si₂O₅](CO₃) the S-K layers are connected together via Ca-O interactions between Ca atoms from the carbonate layer and apical O atoms from the silicate one, and also via K-O interlayer interactions. A hypothetical acentric structure, sp.gr. P-62c, is predicted on the basis of the order-disorder theory. It presents another symmetrical option for the arrangement of K-layers relative to S-layers. The K,Ca-silicate-carbonate powder produces a moderate SHG signal that is two times larger that of the α-quartz powder standard and close to other silicates with acentric structures and low electronic polarizability.     

First mushroom-shaped adhesive microstructure: A review

This letter reviews the adhesive and frictional properties of the first mushroom-shaped adhesive microstructure (MSAMS), which has come a long way from inspiration by the attachment devices evolved in beetles to a large-scale industrial production. It was shown to have an that about twice higher pull-off force compared to a smooth control made from the same material measured on smooth substrates. Pull-off forces measured underwater are even higher than those in air. Moreover, it retained adhesive performance over thousands of attachment cycles and initial adhesive capability could be recovered by washing after being contaminated. In shearing, MSAMS exhibits reduced and stabilized friction in comparison with a smooth control, which demonstrated pronounced stick-slip motion, and shows zero pull-off force in a sheared state, allowing the adhesion to be switched on and off. The presence of a fluid in the contact zone showed adhesion enhancement on both smooth and rough substrates. All these features lead us to conclude that MSAMS may have practical potential in a variety of applications.     

The contact Yamabe flow on K-contact manifolds

We use the contact Yamabe flow to find solutions of the contact Yamabe problem on K-contact manifolds.