Suitable Gradient Research Articles

Some new Liouville-type results for fully nonlinear PDEs on the Heisenberg group

We prove new (sharp) Liouville-type properties via degenerate Hadamard three-sphere theorems for fully nonlinear equations structured over Heisenberg vector fields. As model examples, we cover the case of Pucci’s extremal operators perturbed by suitable semilinear and gradient terms, extending to the Heisenberg setting known contributions valid in the Euclidean framework.

Influence of PECVD-TiO2 film morphology and topography on the spectroscopic ellipsometry data fitting process

TiO2 films of different thickness are deposited on silicon substrate at low temperature and pressure by a Helicon-PECVD reactor. The evolution of film morphology and topography is observed by scanning electron microscopy (SEM) and atomic force microscopy (AFM), meanwhile the spectroscopic ellipsometry (SE) measurements are performed to investigate the film growth mechanism and optical constants. The SEM and AFM observations show that all the films exhibit a columnar structure, moreover all the columns are vertical grown and well-organized when the thickness below [Formula: see text][Formula: see text]80 nm. As the thickness is increased to [Formula: see text][Formula: see text]150 nm, 250 nm and 450 nm, the column size is increased in the top layers, the whole film morphology becomes inhomogeneous, which leads to a decreased density and rougher surface. By fitting the SE measurements, a suitable gradient physical model is found to describe the film morphologies, the model consists of a native SiO2 layer on Si substrate, a mediate layer mixed TiO2 with void whose concentration gradient changed from bottom to top, and a top roughness layer. For thick films ([Formula: see text][Formula: see text]450 nm), the absorption and scattering on the rough surface is considered in order to keep the precision of SE fits. It is found that the optical index is decreased with film thickness, which is related to the evolution of structure in the top layers.

Effect of different freezing modes on the water-heat-vapor behavior in unsaturated coarse-grained filling exposed to freezing and thawing

A series of experiments are carried out for different freezing modes during freezing and thawing to study the water-heat-vapor behavior in the coarse-grained soil (CGS) of high-speed railway (HSR) subgrade in cold regions with an open water supply. The final negative temperature of the freezing mode is kept the same. The total freezing time is 72 h. Three different modes, namely a constant temperature freezing mode, a three-step freezing mode, and a six-step freezing mode, are used. Fluorescein is used as the tracer for the rising height and variation of the liquid water in the external water supply. The external water migrates to the inside of the soil sample when it freezes, and the internal water of the soil sample migrates to the outside when it thaws. The number of steps for the different freezing modes is the key factor affecting the water intake. The amount of water intake affects frost penetration during freezing and thawing. There may be a suitable temperature gradient range for liquid water and vapor coupling migration. In all freezing modes, ice layers appear on the top of the top bath pedestal at the end of freezing. More freezing steps lead to a more uniform water content distribution. Moisture migration in HSR subgrade mainly occurs by vapor migration during long cold winters and winters with slow temperature drops.

Reliable single-phase micro-joints with high melting point for 3D TSV chip stacking

As micro solder-joints downsize to less than 10 μm in 3-dimensional (3D) TSV (Through Silicon Via) chip stacking, rapidly fabricating reliable micro-joints without collapse in chip stacking is regarded as a critical issue. A practicable method with a suitable temperature gradient (TG) and Ni/Sn(10 μm)/Ni interconnection structure was developed compared with conventional transient liquid phase (TLP) bonding. Using this method, the micro-joint fully composed of Ni3Sn4 intermetallic was fabricated within 17 min bonding time. It is nearly three times faster than that under conventional TLP bonding, which may overcome this technology limitation caused by longer bonding times. This fast TG-TLP method provided an asymmetry growth characteristic with thicker Ni3Sn4 at the cold end and thinner Ni3Sn4 at the hot end. The basic micro-joint formation mechanisms were suggested and experimentally verified. Furthermore, the properties of the fabricated Ni3Sn4 micro-joint were evaluated in this study. The results demonstrated its desirable features such as high melting temperature, stable single-phase constitution, stronger mechanical strength and low thermal resistance. Finally, the collapsed micro solder-joint issue was completely solved resulting in higher reliability.

Electric field-driven building blocks for introducing multiple gradients to hydrogels

Gradient biomaterials are considered as preferable matrices for tissue engineering due to better simulation of native tissues. The introduction of gradient cues usually needs special equipment and complex process but is only effective to limited biomaterials. Incorporation of multiple gradients in the hydrogels remains challenges. Here, beta-sheet rich silk nanofibers (BSNF) were used as building blocks to introduce multiple gradients into different hydrogel systems through the joint action of crosslinking and electric field. The blocks migrated to the anode along the electric field and gradually stagnated due to the solution-hydrogel transition of the systems, finally achieving gradient distribution of the blocks in the formed hydrogels. The gradient distribution of the blocks could be tuned easily through changing different factors such as solution viscosity, which resulted in highly tunable gradient of mechanical cues. The blocks were also aligned under the electric field, endowing orientation gradient simultaneously. Different cargos could be loaded on the blocks and form gradient cues through the same crosslinking-electric field strategy. The building blocks could be introduced to various hydrogels such as Gelatin and NIPAM, indicating the universality. Complex niches with multiple gradient cues could be achieved through the strategy. Silk-based hydrogels with suitable mechanical gradients were fabricated to control the osteogenesis and chondrogenesis. Chondrogenic-osteogenic gradient transition was obtained, which stimulated the ectopic osteochondral tissue regeneration in vivo. The versatility and highly controllability of the strategy as well as multifunction of the building blocks reveal the applicability in complex tissue engineering and various interfacial tissues.

The growth and characterization of six inch lithium niobate crystals with high homogeneity

On a self-designed automatic diameter control system, large diameter (6 inch) LiNbO3 crystals without cracks are successfully grown by choosing a suitable temperature gradient, starting composition, and growth parameters with the Czochralski method.

Optimum layout of weep holes in concrete irrigation canals to control uplift pressure and hydraulic gradient

In this study, the effect of weep holes on controlling uplift pressure and hydraulic gradient under concrete canals was investigated in different groundwater levels. For this purpose, three weep holes were embedded in different locations and combinations on the bottom and the sidewall of a laboratory canal. The amounts of seepage discharge were measured from these weep holes in single and combined modes. The corresponding values of seepage discharge, uplift pressure, and exit hydraulic gradient were calculated through simulation with the Seep/W model. The comparison of the observed and the simulated seepage values was indicative of the model’s high accuracy with a mean error of 6.23%. The results showed that uplift pressure values in the single modes of weep holes in three different groundwater levels are similar. Uplift pressure in the binary combinations had a significant reduction compared to the single modes (an average of 73%). The maximum exit hydraulic gradient occurred at the weep hole located at the corner of the canal bottom. In general, the binary combinations of the weep holes were the best choice in terms of the minimum uplift pressure and the suitable exit hydraulic gradient.

Weak Solutions of the Cahn--Hilliard System with Dynamic Boundary Conditions: A Gradient Flow Approach

The Cahn-Hilliard equation is the most common model to describe phase separation processes of a mixture of two components. For a better description of short-range interactions of the material with the solid wall, various dynamic boundary conditions have been considered in recent times. New models with dynamic boundary conditions have been proposed recently by C. Liu and H. Wu [arXiv:1710.08318]. We prove the existence of weak solutions to these new models by interpreting the problem as a suitable gradient flow of a total free energy which contains volume as well as surface contributions. The formulation involves an inner product which couples bulk and surface quantities in an appropriate way. We use an implicit time discretization and show that the obtained approximate solutions converge to a weak solution of the Cahn-Hilliard system. This allows us to substantially improve earlier results which needed strong assumptions on the geometry of the domain. Furthermore, we prove that this weak solution is unique.

On the absolute continuity of random nodal volumes

We study the absolute continuity with respect to the Lebesgue measure of the distribution of the nodal volume associated with a smooth, nondegenerate and stationary Gaussian field $(f(x),{x\in\mathbb{R}^{d}})$. Under mild conditions, we prove that in dimension $d\geq3$, the distribution of the nodal volume has an absolutely continuous component plus a possible singular part. This singular part is actually unavoidable bearing in mind that some Gaussian processes have a positive probability to keep a constant sign on some compact domain. Our strategy mainly consists in proving closed Kac–Rice type formulas allowing one to express the volume of the set $\{f=0\}$ as integrals of explicit functionals of $(f,\nabla f,\operatorname{Hess}(f))$ and next to deduce that the random nodal volume belongs to the domain of a suitable Malliavin gradient. The celebrated Bouleau–Hirsch criterion then gives conditions ensuring the absolute continuity.

Formation of Copolymer-Ag Nanoparticles Composite Micelles in Three-dimensional Co-flow Focusing Microfluidic Device

A novel method was presented to create composite micelles of amphiphilic copolymers and Ag nanoparticles (NPs) in a three-dimensional co-flow focusing microfluidic device (3D CFMD). Self-assembly of the copolymers was initiated by the fast mixing of water and a blend dispersion of hydrophobic Ag NPs and amphiphilic copolymers. At the same time, the hydrophobic Ag NPs enter the core of copolymer micelles, based on the hydrophobic interaction. The copolymer-Ag NPs composite micelles have a core-shell structure with copolymer shell and Ag NPs core. COMSOL Multiphysics is used to simulate the concentration distribution of copolymers and Ag NPs under different flow rates. Co-assembly microfluidic conditions are determined based on simulation results. Under suitable microfluidic conditions, both block copolymers and gradient copolymers can co-assemble with hydrophobic Ag NPs to form composite micelles, respectively. This microfluidic coassembly method will have a good prospect in the preparation of composite micelles of amphiphilic copolymers and metal nanoparticles.

Mechanism of dissipative soliton stabilization by nonlinear gradient terms.

We present a feedback mechanism for dissipative solitons in the cubic complex Ginzburg-Landau (CGL) equation with a nonlinear gradient term. We are making use of a mechanical analog containing contributions from a potential and from a nonlinear viscous term. The feedback mechanism relies on the continuous supply of energy as well as on dissipation of the stable pulse. Our picture is corroborated by the numerical solution of the full equation. A quintic contribution is not necessary for stabilization in the presence of a suitable nonlinear gradient term as we show by using a linear stability analysis for the stationary pulses. We find that the limit of vanishing magnitude of the nonlinear gradient term is singular: For exactly vanishing nonlinear gradient terms stable pulses do not exist. This situation is qualitatively different from that found for the cubic-quintic complex Ginzburg-Landau equation with a nonlinear gradient term: In this case the limit of a vanishing nonlinear gradient contribution is completely smooth. We demonstrate that, for small magnitude of the nonlinear gradient term simple types of scaling behavior are found for the amplitude, the full width at half maximum (FWHM), the velocity, and the effective frequency of the stable pulse as a function of the magnitude of the nonlinear gradient term.

Environmentally Evaluated New HPLC/UV Method for the Simultaneous Determination of Acesulfame-K, Butylated Hydroxytoluene, and Aspartame and Its Degradant in Chewing Gum

Abstract Background: Acesulfame-K (ACE), butylated hydroxytoluene (BHT), and aspartame (ASP) are a common combination of food additives added to chewing gums. The abuse of these additives results in severe adverse health effects; however, they are still extensively used owing to their high performance and low cost. Objective: The development and optimization of a simple, cheap, sensitive, and eco-friendly HPLC/UV method for the simultaneous determination of ASP, ACE, and BHT along with aspartame degradation product phenylalanine (PHEN) in chewing gum. Methods: The method was optimized using a 5 μm C18 column and an eluent consisting of methanol and 0.1 M phosphate buffer (pH 5.0) according to a suitable gradient elution program. Simple sample preparation, consisting of dilution, homogenization, and sonication followed by centrifugation and filtration, was optimized and used for the extraction of chewing gum. The greenness of the method was evaluated. Results: The proposed method exhibited excellent linearity (R2 > 0.9996), low LOQ (0.08–0.95 μg/mL), and recoveries between 85.3 and 98.83% with relative SD (RSD) ≤ 2.7%. High resolution was obtained with <25 min run times with excellent precision (RSD: 0.28–1.33%). This method was successfully applied for the simultaneous determination of ACE, ASP, and BHT in commercial chewing gum; PHEN was not detected. Furthermore, our method is considered to be environmentally acceptable. Conclusions: The results demonstrate that the developed method can be used to detect ACE, BHT, ASP, and PHEN in chewing gum. Highlights: A new sensitive, green HPLC/UV method is developed to be used as a minimal-cost routine analysis procedure for commercial chewing gum.

Breaking Reciprocity with Space-Time-Coding Digital Metasurfaces.

Metasurfaces are artificially engineered ultrathin structures that can finely tailor and control electromagnetic wavefronts. There is currently a strong interest in exploring their capability to lift some fundamental limitations dictated by Lorentz reciprocity, which have strong implications in communication, heat management, and energy harvesting. Time-varying approaches have emerged as attractive alternatives to conventional schemes relying on magnetic or nonlinear materials, but experimental evidence is currently limited to devices such as circulators and antennas. Here, the recently proposed concept of space-time-coding digital metasurfaces is leveraged to break reciprocity. Moreover, it is shown that such nonreciprocal effects can be controlled dynamically. This approach relies on inducing suitable spatiotemporal phase gradients in a programmable way via digital modulation of the metasurface-elements' phase repsonse, which enable anomalous reflections accompanied by frequency conversions. A prototype operating at microwave frequencies is designed and fabricated for proof-of-concept validation. Measured results are in good agreement with theory, hence providing the first experimental evidence of nonreciprocal reflection effects enabled by space-time-modulated digital metasurfaces. The proposed concept and platform set the stage for "on-demand" realization of nonreciprocal effects, in programmable or reconfigurable fashions, which may find several promising applications, including frequency conversion, Doppler frequency illusion, optical isolation, and unidirectional transmission.

Composition Gradients in Sputtered Ti–Au Alloys: Site-Selective Au Decoration of Anodic TiO2 Nanotubes for Photocatalytic H2 Evolution

Au nanoparticles at the TiO$_2$ surface can enhance the photocatalytic H$_2$ generation performances owing to their electron transfer co-catalytic ability. Key to maximize the co-catalytic effect is a fine control over Au nanoparticle size and placement on the photocatalyst, in relation to parameters such as the TiO$_2$ morphology, illumination wavelength and pathway, and light penetration depth in the photocatalyst. Here we present an approach for site-selective intrinsic-decoration of anodic TiO$_2$ nanotubes (TNs) with Au nanoparticles: we produce, by Ti and Au co-sputtering, Ti-Au alloy layers that feature compositional gradients across their thickness; these layers, when anodized under self-ordering electrochemical conditions, can form Au-decorated TNs where the Au nanoparticle density and placement vary according to the Au concentration profile in the metal alloy substrates. Our results suggest that, the Au co-catalyst placement strongly affects the photocatalytic H$_2$ evolution performance of the TNs layers. We demonstrate that, when growing Au-decorated TNs, the use of Ti-Au substrates with a suitable Au compositional gradient can lead to higher H$_2$ evolution rates compared to TNs classically grown with a homogenous co-catalyst decoration. As a side effect, a proper placement of the co-catalyst nanoparticles allows for reducing the amount of noble metal without dumping the H$_2$ evolution activity.

Fluorination-generated uninterrupted gradient-refractive index on commercial flexible substrates for high broadband and omnidirectional transmittance

Abstract Nowadays, flexible substrates, as a part of flexible electronics, receive great attention by its wide application. Particularly, organic light emitting diodes and photovoltaics place high demands on the optical transmittance of flexible substrates. In this paper, direct fluorination is selected to treat commercial poly(ethylene terephthalate) (PET) and polyimide (PI) films. A suitable gradient distribution of fluorine atoms in the fluorinated layer were obtained in the vertical direction of the PET film by optimizing the conditions of direct fluorination. In this way, the refractive index was reduced by the introduction of the fluorine atoms, and the fluorine atoms with gradient distribution on the film's vertical direction led to the gradient decrease of the refractive index. Given this gradient-refractive index, a high broadband and omnidirectional transmittance of >93.0% was achieved by such a non-nanostructured surface over the entire optical wavelength (380–2200 nm), while the transmittance still remains relatively high (>85.0%) when the incident angle is increased from 0° to 60°. Moreover, this cost-effective and easy method presents its universality with the treatment of PI film, which also achieves high broadband and omnidirectional transmittance by direct fluorination.

Connectivity-Preserving Synchronization of Time-Delay Euler-Lagrange Networks With Bounded Actuation.

This paper proposes a strategy to overcome the threats posed to connectivity-preserving synchronization of Euler-Lagrange networks by time-varying delays and bounded actuation. It first introduces a suitable distributed negative gradient plus damping injection controller, based on which it establishes that the local connectivity of time-delay Euler-Lagrange networks can be preserved by appropriately regulating the interagent connections and increasing the damping injection locally. Yet, actuator saturation may impede the proper modulation of the interagent connections and the injection of sufficient damping and, thus, may threaten the maintenance of connectivity. This paper then develops an indirect coupling control framework which integrates the bounded actuation constraints into the control design. The framework endows every agent with a virtual proxy and couples initially adjacent agents through their virtual proxies. The interproxy couplings then tackle the time-varying delays while the agent-proxy couplings account for the saturation of actuators. Lyapunov-Krasovskii analysis proves that the indirect coupling strategy can drive time-delay Euler-Lagrange networks with bounded actuation to connectivity-preserving synchronization by limiting the energy of the agent-proxy and interproxy couplings according to the actuation constraints. Experiments with Geomagic Touch haptic robots validate the proposed designs compared to a conventional proportional plus damping controller.

Environmentally Evaluated New HPLC/UV Method for the Simultaneous Determination of Acesulfame-K, Butylated Hydroxytoluene, and Aspartame and Its Degradant in Chewing Gum.

Background: Acesulfame-K (ACE), butylated hydroxytoluene (BHT), and aspartame (ASP) are a common combination of food additives added to chewing gums. The abuse of these additives results in severe adverse health effects; however, they are still extensively used owing to their high performance and low cost. Objective: The development and optimization of a simple, cheap, sensitive, and eco-friendly HPLC/UV method for the simultaneous determination of ASP, ACE, and BHT along with aspartame degradation product phenylalanine (PHEN) in chewing gum. Methods: The method was optimized using a 5 μm C18 column and an eluent consisting of methanol and 0.1 M phosphate buffer (pH 5.0) according to a suitable gradient elution program. Simple sample preparation, consisting of dilution, homogenization, and sonication followed by centrifugation and filtration, was optimized and used for the extraction of chewing gum. The greenness of the method was evaluated. Results: The proposed method exhibited excellent linearity (R² > 0.9996), low LOQ (0.08-0.95 μg/mL), and recoveries between 85.3 and 98.83% with relative SD (RSD) ≤ 2.7%. High resolution was obtained with <25 min run times with excellent precision (RSD: 0.28-1.33%). This method was successfully applied for the simultaneous determination of ACE, ASP, and BHT in commercial chewing gum; PHEN was not detected. Furthermore, our method is considered to be environmentally acceptable. Conclusions: The results demonstrate that the developed method can be used to detect ACE, BHT, ASP, and PHEN in chewing gum. Highlights: A new sensitive, green HPLC/UV method is developed to be used as a minimal-cost routine analysis procedure for commercial chewing gum.

Determining gradient conditions for peptide purification in RPLC with machine-learning-based retention time predictions

A strategy for determining a suitable solvent gradient in silico in preparative peptide separations is presented. The strategy utilizes a machine-learning–based method, called ELUDE, for peptide retention time predictions based on the amino acid sequences of the peptides. A suitable gradient is calculated according to linear solvent strength theory by predicting the retention times of the peptides being purified at three different gradient slopes. The advantage of this strategy is that fewer experiments are needed to develop a purification method, making it useful for labs conducting many separations but with limited resources for method development.The preparative separation of met-enkephalin and leu-enkephalin was used as model solutes on two stationary phases: XBridge C18 and CSH C18. The ELUDE algorithm contains a support vector regression and is pre-trained, meaning that only 10–50 peptides are needed to calibrate a model for a certain stationary phase and gradient. The calibration is done once and the model can then be used for new peptides similar in size to those in the calibration set. We found that the accuracy of the retention time predictions is good enough to usefully estimate a suitable gradient and that it was possible to compare the selectivity on different stationary phases in silico. The absolute relative errors in retention time for the predicted gradients were 4.2% and 3.7% for met-enkephalin and leu-enkephalin, respectively, on the XBridge C18 column and 2.0% and 2.8% on the CSH C18 column. The predicted retention times were also used as initial values for adsorption isotherm parameter determination, facilitating the numerical calculation of overloaded elution profiles. Changing the trifluoroacetic acid (TFA) concentration from 0.05% to 0.15% in the eluent did not seriously affect the error in the retention time predictions for the XBridge C18 column, an increase of 1.0 min (in retention factor, 1.3). For the CSH C18 column the error was, on average, 2.6 times larger. This indicates that the model needs to be recalibrated when changing the TFA concentration for the CSH column.Studying possible scale-up complications from UHPLC to HPLC such as pressure, viscous heating (i.e., temperature gradients), and stationary-phase properties (e.g., packing heterogeneity and surface chemistry) revealed that all these factors were minor to negligible. The pressure effect had the largest effect on the retention, but increased retention by only 3%. In the presented case, method development can therefore proceed using UHPLC and then be robustly transferred to HPLC.

Determination of Hypericin in Hypericum perforatum (St. John’s Wort) Using Classical C18 and Pentafluorophenyl Stationary Phases: Contribution of Pi–Pi Interactions to High-Performance Liquid Chromatography (HPLC)

Hypericin is one of the most important bioactive substances present in Hypericum perforatum (Saint John’s Wort), which exhibits various biological activities such as inhibition of neuronal processes coupled with transmission of serotonin, dopamine, gamma-amino butyric acid and L-glutamine. This red-colored derivative of anthraquinone contains six benzene cycles and four hydroxy groups that polarize electron density in the conjugated double bond system and enable the molecule to act as a Lewis base in charge-transfer complexes. In this study, four stationary phases modified by the pentafluorophenyl group were selected to investigate the contribution of π-π interactions to the improvement of hypericin separation in comparison to the separation provided with a classical C18 based chromatographic column. In order to develop a suitable gradient chromatographic method for the quantification of hypericin, normal, polar organic and reverse elution modes were evaluated using high-performance liquid chromatography with ultraviolet-visible and mass spectrometry detection. It was disclosed in the analyses that the pentafluorophenyl stationary phase can separate hypericin from hyperforin, which was not possible to achieve with the C18 based stationary phase. The best analytical method found, employing the pentafluorophenyl stationary phase, showed sufficient linearity, accuracy and precision and was used for the determination of hypericin in Saint John’s Wort.

Extending the operational lifetimes of all-direct electron transfer enzymatic biofuel cells by magnetically assembling and exchanging the active biocatalyst layers on stationary electrodes

Enzymatic biofuel cells promise green power generation from a variety of natural resources, yet these systems all suffer from time-dependent degradation effects, in particular progressing inactivation of enzymes, which severely limit the operational lifetimes of such power sources. To extend operational lifetimes, we introduce a method to magnetically exchange exhausted enzymes for fresh ones. To this end, anodic and cathodic enzymes or enzyme cascades are immobilized on carbon coated magnetic nanoparticles. Under the action of suitable magnetic field gradients, these nanoparticles are assembled on the respective stationary electrodes, or released from the electrodes for collection and subsequent exchange. We demonstrate this method on a fructose/oxygen consuming biofuel cell employing fructose dehydrogenase and bilirubin oxidase as well as on anodic and cathodic cascades employing fructose dehydrogenase/invertase and bilirubin oxidase/catalase, respectively. The enzyme-modified nanoparticles support direct electron transfer bioelectrocatalytic currents by wiring the redox active cofactors to the carbonaceous coating and from there to the electrode surfaces. The facile injection, assembly, and removal of enzyme-modified magnetic nanoparticles along with fuel solution provides a promising approach to extend the operational lifetime of enzymatic biofuel cells without the need for exchanging entire systems including chambers and electrodes.