Desired Gradient Research Articles

Using Micrometer Scale X-Ray CT and Pore Network Modeling to Assess High-Energy Bi-Layer Li-Ion Battery Cathode Structures

The optimization of cathode pore space is pivotal for enhancing the rate capability of lithium-ion battery electrodes. Previous studies on simulated cathodes have highlighted the importance of achieving an optimal porosity gradient, with a gradual increase from the current collector side to the separator side to accommodate the growing demand for ion transport in that direction [1]–[3]. In this research, we address this requirement by introducing and investigating bi-layer NCM 811 cathodes. These cathodes consist of a slurry-coated dense bottom layer and a spray-coated highly porous top layer with varying relative thickness to approximate the desired porosity gradient. Employing Micrometer-scale X-ray CT characterization and pore network modeling, we evaluate the structural features, demonstrating the effectiveness of the design, and quantify essential parameters such as porosity and tortuosity. Furthermore, the cathodes are integrated into lithium anode half-cells and subjected to electrochemical cycling at different rates to assess ion transport and rate capability. Our findings reveal that to achieve the highest discharge spatial energy density above 1C for cathodes approximately 100μm thick, the compressed bottom layer with 30% porosity should have a thickness of 60μm, while the highly porous top layer with around 47% porosity should be 40μm thick.Reference:[1] A. Shodiev et al., “Deconvoluting the benefits of porosity distribution in layered electrodes on the electrochemical performance of Li-ion batteries,” Energy Storage Mater., vol. 47, pp. 462–471, May 2022, doi: 10.1016/j.ensm.2022.01.058.[2] X. Lu et al., “3D microstructure design of lithium-ion battery electrodes assisted by X-ray nano-computed tomography and modelling,” Nat. Commun., vol. 11, no. 1, p. 2079, Apr. 2020, doi: 10.1038/s41467-020-15811-x.[3] K. Song, C. Zhang, N. Hu, X. Wu, and L. Zhang, “High performance thick cathodes enabled by gradient porosity,” Electrochimica Acta, vol. 377, p. 138105, May 2021, doi: 10.1016/j.electacta.2021.138105.

The Combined Effect of Spin-Transfer Torque and Voltage-Controlled Strain Gradient on Magnetic Domain-Wall Dynamics: Toward Tunable Spintronic Neuron

Magnetic domain wall (DW), as one of the promising information carriers in spintronic devices, have been widely investigated owing to its nonlinear dynamics and tunable properties. Here, we theoretically and numerically demonstrate the DW dynamics driven by the synergistic interaction between current-induced spin-transfer torque (STT) and voltage-controlled strain gradient (VCSG) in multiferroic heterostructures. Through electromechanical and micromagnetic simulations, we show that a desirable strain gradient can be created and it further modulates the equilibrium position and velocity of the current-driven DW motion. Meanwhile, an analytical Thiele’s model is developed to describe the steady motion of DW and the analytical results are quite consistent with the simulation data. Finally, we find that this combination effect can be leveraged to design DW-based biological neurons where the synergistic interaction between STT and VCSG-driven DW motion as integrating and leaking motivates mimicking leaky-integrate-and-fire (LIF) and self-reset function. Importantly, the firing response of the LIF neuron can be efficiently modulated, facilitating the exploration of tunable activation function generators, which can further help improve the computational capability of the neuromorphic system.

V-doped MoS2 nanozymes providing reactive oxygen species and depleting glutathione for photothermally-enhanced nanocatalytic therapy.

Introduction: The tumor microenvironment and multidrug resistance of tumor cells seriously impair the activity of the nanozymes. Methods: Herein, a polyethylene glycol (PEG)-modified vanadium-doped molybdenum disulfide (V-MoS2@PEG) nanozymes were constructed to enhance anti-tumor activity through multi-enzymatic catalysis and photothermal effect with simultaneous reactive oxygen species replenishment and glutathione depletion. Results and discussion: V-MoS2@PEG nanosheets exerted peroxidase activity by causing molybdenum ion (Mo4+) to react with hydrogen peroxide to form toxic hydroxyl radicals (·OH). Meanwhile, the V-doping can deplete glutathione avoiding ·OH consumption. In addition, the high heat generated by V-MoS2@PEG nanozymes under near-infrared laser irradiation brought about a desirable local temperature gradient, which produced an enhanced catalytic effect by promoting band bending. Furthermore, the photothermally inspired polarized charge increased the permeability of the tumor cell membrane and promoted further aggregation of the nanozymes, which realized the combination of photothermal therapy with multi-enzymatic catalysis, solved the problem of multi-enzyme catalysis, and improved the anti-tumor efficiency.

Study on Lattice Radiotherapy Treatments (LRT) for Head and Neck Bulky Tumors

Lattice radiotherapy (LRT) exploits various effects of radiation, such as the bystander effect and the abscopal effect, and consists on the administration of high dose fraction in small areas with large tumor masses, helping to solve the problem of treating bulky disease, especially if it is located in a critical anatomical area. The optimization of LRT treatment plans is challenging due to the difficulty to generate spots of high dose within the tumor with consequent high gradient. This study compares the plan dosimetry and delivery time of two delivery techniques VMAT and CyberKnife for LRT treatments of bulky head and neck lesions. Six patients with giant head and neck tumors who received LRT at our institution were included in this study. Target and OARs were contoured following international guidelines; to allow easy identification of the desired high gradient zones, an artificial geometrical lattice structure with spherical vertices was arranged inside the target volume (GTV), and the vertices of the lattice representing the high dose boost volumes (GTVboost) were delineated. The GTVboost and GTV were prescribed to receive 12 Gy and 3 Gy, respectively in a single fraction. Separate VMAT and CyberKnife LRT plans were optimized for each patient with lattice vertex of 0.5 diameter and center-to-center distances of 1.5 cm (LRT1.5) and 3 cm (LRT3). The dose heterogeneity was measured as the peak-to-valley dose ratio (PVDR), with the traditional definition being replaced by the D10/D90 ratio, where D10 and D90 represent the doses covering 10% and 90% of the GTV, respectively. For each plan generated, the treatment delivery time, the monitor units (MU), and the PVDR were assessed. Pre-treatment plan verifications were performed with ArcCheck array and Gafchromics film for VMAT and CyberKnife, respectively, using gamma analysis criteria of 3%-3mm. The mean PVDR obtained for VMAT LRT plans were 2.0 and 2.6 for LRT1.5 and LRT3, respectively, and 3.2 and 4.7, respectively for CyberKnife LRT plans. For each pre-treatment plan dose verification, the gamma passing rate (GPR) was higher than 95.0 %; CyberKnife delivery time and MU were more than 10 times higher than that of VMAT, nevertheless, VMAT had a lower PVDR. The detailed results are shown in the table below. CyberKnife LRT has a strong ability to place the peak dose within the target, generating a higher peak-to-valley dose ratio, however its use is partially invalidated by the long beam delivery times and the resulting high MU number; the use of the VMAT LRT technique allows clinically adequate dosimetry with acceptable delivery times.

Design and evaluation of a thermal precipitation aerosol electrometer (TPAE)

Abstract. A new aerosol electrometer (AE), the thermal precipitation aerosol electrometer (TPAE), was designed for use with particles of sizes less than 300 nm, and its performance was experimentally evaluated. The TPAE combines the thermal precipitator with a microcurrent measurement circuit board (i.e., pre-amplifier) for measuring the current carried by collected particles. The thermal precipitator is in the disk-to-disk configuration. Heating paste and air cooling were adopted to establish the desired temperature gradient in the precipitation chamber. At a sample flow rate of 0.3 L min−1 and a temperature gradient of 264 K cm−1, the precipitation efficiency of 70 nm particles reaches ∼100 %. The measurement range of the designed aerosol electrometer is ±5×105 fA, and the accuracy is ±2 fA (2500 to 6.25×107 cm−3 using a flow rate of 0.3 L min−1 and assuming that only singly charged particles exist in the sample). During the evaluation process, the electrical performance of the TPAE was first tested using sodium chloride (NaCl) and soot particles previously classified by a differential mobility analyzer (DMA) and compared to the reference. The precipitation performance of the TPAE was then characterized as functions of the temperature gradient, sampling flow rate and particle size. It was shown that the particle collection efficiency of the built-in thermal precipitator is inversely proportional to the sampling flow rate and proportional to the temperature gradient. The effect of particle size on the particle collection efficiency was minor for NaCl particles of sizes between 23 and 200 nm. Unlike that which was observed for the NaCl particles, a slightly positive correlation between the collection efficiency and the mobility size for soot particles (in the size range of 30–160 nm) was observed. This observation might be due to the existence of soot agglomerates. Compared to existing electrometers, the TPAE does not require the use of high-efficiency filters and includes the additional feature of the “soft” collection of particles for offline particle characterization as well as aerosol current measurement.

Applying position and time dependent nusselt number and friction factor into 1D model to improve regenerator design for solid-state caloric cooling cycles

Active caloric regenerative cycles have recently attracted much attention as a promising cooling technology that can potentially replace the vapor compression cycle based on its high efficiency and eco-friendly characteristics. The use of modeling is necessary in optimizing the active caloric regenerative cycle due to the system’s complex structure and numerous parameters that need to be taken into account. The cycle uses oscillatory flow to efficiently exchange heat between the caloric material and the heat transfer fluid and to generate a desired temperature gradient in the regenerator. When the oscillatory flow is used, hydrodynamically and thermally developing regions occur all over the regenerator when the direction of the fluid flow changes.To the best of the authors’ knowledge, no previous research has considered the oscillatory developing regions in a 1D model. Therefore, this study incorporated the developing regions generated by the oscillatory flow as well as the entrance developing regions into a regenerator model for the first time. Based on the modeling results, the influence of the oscillatory developing regions and the average Nusselt number increase with higher cycle frequency. Additionally, the new 1D model produces average Nusselt number similar to the 2D model with a maximum error of 4 %. Considering that the 2D model requires very high computational cost to solve the transient condition of the caloric cycle, the advanced 1D model can accurately assess the performance of the caloric cycle and provide a detailed analysis of heat transfer phenomena and fluid dynamics in the regenerator at modest computational cost.The parallel plate type, optimized using the new model, has a hydraulic diameter of 0.1 mm. However, maintaining such a small space between the plates can be challenging from an application standpoint. Therefore, this study proposes the use of a wide rectangular microchannel matrix as the regenerator. The rectangular microchannel matrix, with an aspect ratio of 30, produces a coefficient of performance of 5.65, which is comparable to the parallel plate matrix. Consequently, the wide rectangular microchannel matrix can achieve both high Nusselt number and structural stability simultaneously.

Numerical predictions and experimental validation on the effect of material properties in filament material extrusion

The numerical prediction of dimensional accuracy and mechanical performance of 3D-printed structures can eliminate or reduce the need to perform trial-and-error experimentation to achieve the desired part quality quickly and at a reduced cost. Therefore, this study focuses on experimental and numerical investigations of the effect of material properties on dimensional control of the material extrusion additive manufacturing process. A thermomechanical model is utilized, validated, and used to predict the part deflections, warpages, and residual stresses in 3D-printed components for two different materials (i.e., polyamide-6 (PA6) and acrylonitrile butadiene styrene (ABS)). In addition, numerical simulations for mechanical testing were performed and validated through experimental investigations. The numerical model considered the effect of material on final product quality and was in close agreement with experimental results. It was concluded that the materials with a lower thermal expansion coefficient (CTE) would provide better dimensional accuracy of 3D-printed parts. In addition, the lower thermal conductivity and temperature variations within the 3D-printed part will further produce precise parts. The controlled ambient environment using a closed chamber can also assist in maintaining desired thermal gradient and avoid non-uniform cooling during the process. Finally, the numerical model accurately predicted the mechanical behavior of 3D-printed samples as validated via experimentation.

ADEV: Sound Automatic Differentiation of Expected Values of Probabilistic Programs

Optimizing the expected values of probabilistic processes is a central problem in computer science and its applications, arising in fields ranging from artificial intelligence to operations research to statistical computing. Unfortunately, automatic differentiation techniques developed for deterministic programs do not in general compute the correct gradients needed for widely used solutions based on gradient-based optimization. In this paper, we present ADEV, an extension to forward-mode AD that correctly differentiates the expectations of probabilistic processes represented as programs that make random choices. Our algorithm is a source-to-source program transformation on an expressive, higher-order language for probabilistic computation, with both discrete and continuous probability distributions. The result of our transformation is a new probabilistic program, whose expected return value is the derivative of the original program’s expectation. This output program can be run to generate unbiased Monte Carlo estimates of the desired gradient, that can be used within the inner loop of stochastic gradient descent. We prove ADEV correct using logical relations over the denotations of the source and target probabilistic programs. Because it modularly extends forward-mode AD, our algorithm lends itself to a concise implementation strategy, which we exploit to develop a prototype in just a few dozen lines of Haskell (https://github.com/probcomp/adev).

Functionally Graded Multilayer Composites Based on Poly(D,L lactide)/Bioactive Fillers Fabricated by a 3D Direct Pellet Printing Multi-Extrusion Process

The aim of the present work was to investigate a 3D manufacturing process dealing with 3D Direct Pellet multi-Extrusion (DPPmE). Throughout this paper, various functionally graded materials (FGM) were obtained with tailored properties for bone regeneration. Therefore, an experimental investigation was performed to gain a better understanding of the structure-processing-properties relationships. A poly(D,l-lactic acid) (PDLLA) matrix and bioglass (BG) or hydroxyapatite (HA) bioactive fillers were chosen to obtain hybrid FGM in comparison to composite references. Different compositions and shape factors (from microspheres to fibers) of these bioactive fillers were used to control the PDLLA matrix degradation. Then, different strategies of DPPmE were used to tailor and tune the desired gradient of properties. Interestingly, good interfaces and adhesion properties were obtained. Subsequently, rheological, size-exclusion chromatography, and porosity measurements corroborated the present findings. Besides, tensile as well as thermomechanical properties showed the advantages of the DPPmE process to fabricate FGM composites with tailored architectures.

Lithography-based additive manufacturing of porosity graded alumina

• In recent years, alumina ceramics exhibiting gradient in porosity, i.e., porosity graded alumina ceramics (PGACs), with a controlled amount of both open/closed or macro/micro pores is of high interest for several applications such as thick barrier coating, cores for precision casting, biocompatible implants, membranes/filters, and fabrication of functionally graded metals through infiltration. • Lithography-based Ceramic Manufacturing (LCM) offers high quality and near-net manufacturing of complex ceramic components with high resolution. • Two-vat system in the newly developed multi-material LCM printer setup enables not only assigning one material to any desired layer but also use of different materials in each layer by assigning the respective materials to selected pixels of the layer image. • This article introduces methodologies for the fabrication of porosity gradient alumina with continuous and discrete porosity transitions zones by combining sacrificial templating and LCM. With the developments in manufacturing technologies, interest on porosity graded alumina ceramics has increased for applications such as thick barrier coating, cores for precision casting and biocompatible implants. Lithography-based Ceramic Manufacturing (LCM) offers high quality and near-net manufacturing of complex ceramic components with high resolution. Multi-material LCM printing setup can overcome the main problems of conventional manufacturing techniques for fabrication of porosity graded alumina with desired microstructure and gradient architecture (i.e., gradient direction, fraction, type). Two-vat system in the newly developed multi-material LCM printer setup enables not only assigning one material to any desired layer but also use of different materials in each layer by assigning the respective materials to selected pixels of the layer image. This article introduces methodologies for the fabrication of porosity graded alumina ceramics (PGACs) with continuous and discrete porosity transitions zones by combining sacrificial templating and LCM. It is illustrated how the properties of the slurry and the desired gradient architecture play an important role for the selection of suitable method.

Fast NURBS-based parametric modeling of human calves with high-accuracy for personalized design of graduated compression stockings

Background and objectivesAccurate human body models are increasingly demanded by high-quality human-centered ergonomic applications, especially the design and manufacturing of compressive functional apparels. However, existing parametric models in related works are not capable to accurately describe detailed local shape features of human. MethodsIn this work, a high-accuracy parametric modeling approach for human limb was proposed. 3D Scans of human calves were studied. Key data points of the scanned human calves were identified according to human anatomy, forming a quasi-triangular mesh of feature points. Then, non-uniform rational B-splines (NURBS) method was implemented. Control points were calculated from the key data points, with which the human calf shapes can be reconstructed by the smooth NURBS surface, giving rise to a new parametric model of human calves. Error between the scanned and reconstructed calf shapes were analyzed to verify the effectiveness of this model. ResultsError analysis showed that, this proposed method delivers a high-efficiency and high-accuracy parametric shape modeling approach with averaged error observed as only 0.37% for all the 260 subjects, much less compared to previous relative works (around 5%). For tentative application, customized medical compression stockings were designed based on this model and proved as valid to exert desired gradient compression on the according calf mannequin. ConclusionsBy introducing the non-uniform rational B-splines method, a parametric model capable of characterizing human limbs with high-accuracy was proposed. Using very small amount of data, this model is expected to highly facilitate remote customized design and provide 3D shape references for design of compressive garments. Moreover, the proposed methods can inspire developments of other mixed modeling methods for high-accuracy applications.

Predicting physiologically-relevant oxygen concentrations in precision-cut liver slices using mathematical modelling.

Precision cut liver slices represent an encouraging ex vivo method to understand the pathogenesis of liver disease alongside drug induced liver injury. Despite being more physiologically relevant compared to in vitro models, precision cut liver slices are limited by the availability of healthy human tissue and experimental variability. Internal oxygen concentration and media composition govern the longevity and viability of the slices during the culture period and as such, a variety of approaches have been taken to maximise the appropriateness of the internal oxygen concentrations across the slice. The aim of this study was to predict whether it is possible to generate a physiologically relevant oxygen gradient of 35-65mmHg across a precision cut liver slice using mathematical modelling. Simulations explore how the internal oxygen concentration changes as a function of the diameter of the slice, the position inside the well and the external incubator oxygen concentration. The model predicts that the desired oxygen gradient may be achieved using a 5mm diameter slice at atmospheric oxygen concentrations, provided that the slice is positioned at a certain height within the well of a 12-well plate.

Retroreflector With Polarization Isolation Based on Nonreciprocal Metasurface

This letter proposes a nonreciprocal metasurface retroreflector, which introduces isolation between two orthogonal polarizations. The proposed metasurface is based on the transistor-loaded nonreciprocity mechanism and receiving-reradiating structure. Benefitting from this design, the nonreciprocal polarization response introduced by the backloaded transistor amplifier can provide isolation between the two orthogonal polarizations. Besides, the unit cross-polarized reflection phase can be designed arbitrarily to realize desired phase gradient. As a result, the metasurface converts vertically polarized waves to horizontally polarized waves with amplification and retroreflects at a specific incident angle. Meanwhile, absorption occurs when horizontally polarized waves are incident at the same angle. A prototype is fabricated and measured. The measured results prove that the proposed metasurface can realize retroreflection at a 30° incident angle with cross-polarization isolation of 29.42 dB at 5.44 GHz. The proposed metasurface is expected to expand applications of planar retroreflectors.

On the gradient tracking problem for a bilinear reaction–diffusion equation excited by distributed bounded controls

This paper addresses a gradient tracking problem of a bilinear reaction–diffusion equation evolving in a spatial domain . Such an equation is excited with distributed and bounded controls. The problem is formulated by the minimisation of a functional constituted of the deviation between the desired gradient and the current one all over a time interval and the energy term. Then we prove the existence of an optimal control that we characterise by an optimality system. Moreover, we discuss two sets of particular controls: the set of time dependent controls and the space dependent ones. A computational approach and illustrative simulations are also given.

Wall Pressure Spectra and Convection: Two-Dimensional Analysis Under Mean Pressure Gradients

Wall pressure fluctuations beneath turbulent boundary layers subjected to a pressure gradient are studied in a subsonic channel flow, up to , where the test section’s ceiling is adjusted to create the desired pressure gradients with the Clauser parameter ranging from to 0.8. A rotating antenna of 63 nonuniformly distributed remote microphones enables a fine spatial resolution, down to 1 mm. The focus is put on the convective velocity, coherence scales, and two-dimensional wavenumber–frequency spectra. The convective velocity is increased by adverse pressure gradients, with values up to 14% higher than without gradient, which goes against the trend reported in previous studies. Both anisotropy and wall friction are increased by a favorable pressure gradient. In the subconvective region of the wavenumber–frequency spectra, classical models fail to match the data in terms of both levels and decay rates. Finally, the aspect ratio of these spectra’s convective ridges is increased from adverse to zero, and then favorable pressure gradients. These results are discussed in light of the literature on coherent motion in boundary layers and how it is affected by pressure gradients. Mechanisms that could explain the observed pressure gradients’ effects are finally proposed.

Full‐Polarization Frequency Controlled Multimode Spoof Surface Plasmon Polaritons Excitation via Anisotropic Metastructure

AbstractSurface plasmon polaritons (SPPs) have great applications in imaging, sensing, waveguide, and communication. Especially in the trending of electromagnetic (EM) metastructure field, researchers used the phase gradient design to achieve the efficient surface wave propagating performance ranging from GHz to THz. However, due to the intrinsic coupling interference from the current structure design, the phase and amplitude of different polarization are hard to freely manipulate simultaneously, making the design of multifunctional channels SPPs still a challenging project. Here, an anisotropic structure is proposed to realize independent control of both polarization and amplitude along different component of the wavefront. By analyzing the polarization dependent mechanism, the hexagon and half‐hexagon meta‐atom are introduced to the coupler structure to tailor the desired phase gradient along different directions under different polarized EM waves. Then the dispersion of coupler is further coupled with the propagating patch metasurface by optimization algorithm. As a result, the multifunctional SPP is achieved, and the multimode excitation can be generated under both linear and circular polarized incidence. Both simulation and experiment validate the effectiveness and wideband of spoof SPPs excitation performance, verifying that this method reduces the excitation condition of surface wave and improves the multiplexing effect of propagation channel.

Gradient optimal control problem of the bilinear reaction-diffusion equation using distributed bounded controls

This paper addresses a gradient tracking problem of a bilinear reaction-diffusion equation evolving in a spatial domain Ω ⊂ Rn,n ≤ 3. Such an equation is excited with distributed and bounded controls. The problem is formulated by the minimization of a functional constituted of the deviation between the desired gradient and the current one all over a time interval and the energy term. Then we prove the existence of an optimal control that we characterize by an optimality system. Moreover, we discuss two sets of particular controls: the set of time dependent controls, and the space dependent ones. A computational approach and illustrative simulations are also given.

Rational route to fabrication of uni-dimensional surface gradients presenting stochastic and periodic arrangement of nanoparticles

Nanostructure gradients exhibiting graded variation in a nanostructure geometric variable carry high promise as tool for parallel and high-throughput optimization of a range of on-chip devices and functional interfaces. The capabilities to fabricate nanostructure gradients, with desired size and slope, while preserving scalability and operational flexibility is however limited. In this direction, we demonstrate a simple and flexible approach to prepare nanostructure gradients, subjecting a functionalized chip for the adsorption of nanoparticles or ions from aqueous media, with varying durations of exposure along the length of the chip. The configuration is similar to dip-coating, however, with the solution front moving relative to a stationary substrate. The flow rate, dimension of the chamber, and the functional layers are shown as simple handles to achieve the desired gradient morphology. Gradients with stochastic as well as periodic organization of nanoparticle assemblies are demonstrated through the choice of different functional layers underneath the nanoparticle layer, viz. aminosilane monolayers, cross-linked plasma polymer and copolymer templates. The approach paves way to rationally designed gradients, benefitting from the significant flexibility in the choice of operational conditions, without specific constraints on the size of the substrates that can be used.

Optimization of solvent swelling for efficient organic solar cells via sequential deposition

Compared to bulk heterojunction (BHJ) organic solar cells (OSCs) prepared by the blend casting in “one step process”, sequential deposition (SD) processed OSCs can realize an ideal profile of vertical component distribution due to the swelling of polymer films. Herein, we did trials on several kinds of second solvents for swelling the polymer layer, and investigated the packing structure and morphology of the swollen films and the performance of the resulting devices. We found that an optimized morphology can be achieved by solvent swelling while using orthodichlorobenzene ( o -DCB) as the second layer processing-solvent, with polymer donor PffBT-3 as bottom layer, PC 71 BM as top layer and bicontinuous networks in the middle. Such solvent swelling process also makes the SD method exempt from thermal annealing treatment. The device based on SD yields a power conversion efficiency (PCE) up to 8.7% without any post-treatment, outperforming those from the devices based on SD using other solvents and that (7.06%) from BHJ device, respectively. We also extended the use of this approach to all-polymer blend system, and successfully improved the efficiency from 4.72% (chloroform) to 9.35% ( o -DCB), which is among the highest PCEs in all-polymer-based OSCs fabricated with SD method. The results demonstrate that the swelling of the polymer by the second layer solvent is a necessity for SD, paving the way towards additive-free high-performance OSCs. Solvent-swelling effect of the sequential deposition process is crucial for achieving desirable gradient separation along the vertical direction for efficient organic solar cells.

Regional boundary controllability of the gradient of semi-linear parabolic systems

The purpose of this paper is to explore the concept of regional gradient-controllability for semi linear parabolic distributed systems. We are interested in transferring the state gradient of the system to a desired gradient given on the subregion ω or Γ of the whole domain Ω. We give a definition and delineate some properties of this concept, and we show that under some hypothesis, that the approximate regional controllability for the associated linear system holds, we determine the control ensuring the transfer of the system. The approach developed is based on an extension of the method H.U.M and the Schauder fixed point theorem. The developed method lead to an algorithms for constructing the control ensuring the transfer of the system from a desired gradient and we finish by numerical simulation.