Cylindrical Phase Research Articles

Controllability and Optimal Fast Operation of Nonlinear Systems

A new method for solving the problem of controllability and optimal transient behavior of nonlinear systems subject to boundary conditions and constraints on control values was proposed. Unlike existing methods, this new approach is based on constructing a general solution of the integral equation for a linear controlled system, followed by transforming the original problem into a special initial optimal control problem. We propose a new method for studying the global asymptotic stability of dynamical systems with a cylindrical phase space with a countable equilibrium position based on a non-singular transformation of the equation of motion and estimation of improper integrals along the solution of the system. Conditions for global asymptotic stability were obtained without involving any periodic Lyapunov function, as well as the frequency theorem. The effectiveness of the proposed method is shown with an example.

Design of a metalens for beam collimation and angular amplification in optical phased array devices

We present an analytical design for increasing the beam sharpness (collimation) and field of view (FOV) of an optical phased array (OPA) device. In this work, a cylindrical metalens is used for collimation, while a set of metalens, with both concave and convex phase profiles, are incorporated to increase the FOV. Following the generalized vector law of reflection or refraction, the trajectories of the reflected or transmitted rays corresponding to the phase profile of phase gradient metasurfaces/metalens are obtained. Through the ray tracing method, the elliptical beam from the OPA device with a vertical beam (fast axis) width of 21 mm was collimated to a sharp spherical beam of width 1.5 mm by a metalens with a cylindrical phase profile. In addition, the incorporation of angular amplifier metalens with a 64-channel OPA device has shown an increased in FOV by almost threefold i.e., from 15 o to 41.96 o . Our results suggest that the use of metasurfaces/metalens can enhance the quality of output beam and provide significant advantages for compact on-chip integration with OPA devices in solid-state LiDAR applications.

A Computational Study on Utilizing Phase Change Material With a Condenser to Improve air Conditioning System Performance

ABSTRACTThe efficacy of employing multiple cylindrical phase change materials (PCM) to enhance the performance of an air conditioning (AC) unit is examined in this study. The objective of the present study is to examine the effects of combining an AC unit with a cylindrical PCM container configuration on the PCM discharge process and the performance of the AC system. The procedure involves the connection of a heat exchanger with a cold energy storage PCM to the condenser of the AC. During the daytime, the warm surrounding air is cooled and then transmitted to the AC unit's condenser. Four different turbulence models, that is, the SST , standard , Realizable and RNG have been considered for the present computational study. The investigation has been performed for different air flow rates, that is, 33.6, 42, and 49 for a constant inlet air temperature of 308.15 K. The present outcomes indicate that as the flow rate rises, the air temperature inside the domain increases and the solid PCM starts melting. It is noted that complete discharging time for multi‐cylindrical PCM reduces as the air flow rate rises which are around 13.36, 11.03, and 9.94 h for airflow rates of 33.6, 42, and 49 , respectively. The maximum achieved increase in the COP is around 94.49%, 88.68%, and 87.57% at airflow rates of 33.6, 42, and 49 L/s, respectively, for the multi‐cylindrical PCM throughout the summer. It is found that for the same temperature, as the airflow rate rises, the consumed power saving rises.

Evaluation of melting front kinetics in cylindrical phase change materials module using infrared thermography and digital imaging

An experimental study examined buoyancy-driven convection in the unconstrained melting of PCM within a cylindrical module. Melting progress and PCM fraction were analyzed using IRT and digital imaging. Initial symmetric melting led to accelerated phase change at the bottom and a rippled PCM surface. Thermal stratification in the lower module was evident, with molten liquid displacing colder fluid. Observations underestimated bottom PCM waviness and melting. As the melt zone expanded, buoyancy-driven convection intensified, speeding up melting at the top while the bottom relied more on conduction. The study details transient front positions, temperature profiles, solid PCM amounts, and melting times. Unstable fluid layers near the bottom caused waviness due to chaotic fluctuations. Nucleation rates critically impacted PCM crystallization kinetics and properties.

3D transient numerical analysis of PCM dendritic cylindrical heat sinks designed by constructal theory

The phase change material (PCM) heat sink represents an important cooling tool for many applications. The presence of a heat sink in devices requires additional space to occupy it. This led to modeling this space to obtain the highest thermal performance with the smallest size. Among the modern modeling methods is constructal theory. This work presents a numerical modeling of the performance of cylindrical phase change material heat sinks with branched heat transfer fluid tubes in the manner of arterial and venous according to constructal theory. The aim of numerical simulations is to demonstrate the effect of growth in design by increasing the number of branches on thermal performance and melting time and the extent to which this is reflected in pressure drops. Several branching configurations are studied for comparison purpose. The governing continuity, momentum and energy equations were solved using the computational fluid dynamics method. Three-dimensional transient simulations of the melting process of phase change materials were performed using an enthalpy and porosity model. Four combinations of constructal dendritic tubes were considered. The results show that the proposed dendritic PCM heat sink significantly reduces the melting time of PCM compared to the traditional heat sink consisting of a shell and single tube up to 69.1 %. The drop in heat transfer fluid temperature at the outlet decreased by up to 51.7 %. The results proved also the heat transfer enhancement is governed with pressure drop increase because of changing branches configuration. Finally, this paper demonstrated the ability of constructal theory to provide promising solutions for cylindrical heat sinks of phase change materials in various applications.

Machine learning predictions and optimization for thermal energy storage in cylindrical encapsulated phase change material

Machine learning predictions and optimization for thermal energy storage in cylindrical encapsulated phase change material

Patterning and epitaxy of large-area arrays of nanoscale complex oxide epitaxial heterostructures

A combination of block copolymer (BCP) lithography and solid-phase epitaxy can be employed to form large areas, on the order of square centimeters, of a high density of epitaxial crystalline complex oxide nanostructures. We have used BCP lithography with a poly(styrene-block-methyl methacrylate) (PS-b-PMMA) copolymer to template a nanohole array either directly on an (001)-oriented SrTiO3 (STO) single crystal substrate or on a 20 nm-thick Si3N4 layer deposited on the STO substrate. BCPs with the selected compositions assembled in a cylindrical phase with 16 nm diameter PMMA cylinders and a cylinder-to-cylinder spacing of 32 nm. The substrate was modified with an energetically non-preferential polymer layer to allow for the vertical alignment of the cylinders. The PMMA cylinders were removed using a subtractive process, leaving an array of cylindrical holes. For BCPs assembled on Si3N4/STO, the pattern was transferred to the Si3N4 layer using reactive ion etching, exposing the underlying STO substrate in the nanoholes. An amorphous LaAlO3 (LAO) layer was deposited on the patterned Si3N4/STO at room temperature. The amorphous LAO epitaxially crystallized within the nanoscale-patterned holes with fully relaxed lattice parameters through solid phase epitaxy, resulting in the formation of nanoscale LAO/STO epitaxial heterostructures.

On the motion stabilization of a three-link robotic manipulator with incomplete measurement

Abstract. This paper considers a mathematical model of a manipulator which consists of a vertical column, two links, connected to it in series, and a gripper with a load. The column resting on a fixed base can rotate around its vertical axis. The links are connected by cylindrical hinges allowing them to rotate in the same vertical plane. The column and the links are modeled as rigid bodies with the links having unequal principal moments of inertia. The position of the manipulator in space is determined by three rotation angles of the column and the links. The manipulator can have several types of steady-state program movements. When gravitational torques are compensated by control torques applied in the cylindrical hinges, the manipulator has a program equilibrium position. The manipulator can also have a program motion when the column rotates at a given constant angular velocity, and the links have given relative equilibrium positions in their plane. The stabilization problem of manipulator motion is investigated by means of control torques with feedback when only the rotation angles of the column and links are measured. The problem posed is solved in the form of a nonlinear proportional-integral controller taking into account the cylindrical phase space of the manipulator's mathematical model. The solution includes construction of a Lyapunov functional with a semi-definite derivative and application of the corresponding theorems on the asymptotic stability of non-autonomous functional differential retarded-type equations. The obtained conditions for the program motion stabilization are robust with respect to the mass-inertial parameters of the manipulator. The numerical simulation results demonstrate global attraction to its given position in cylindrical phase space.

Experimental and numerical study of cylindrical encapsulated phase change material in packed bed thermal energy storage with expansion and shrinkage effects

Packed bed latent heat thermal energy storage (PBTES) is a promising technology for storing thermal energy with a relatively compact size and smaller temperature variation during phase change. In this study, a lab-scale low-cost PBTES with cylindrical shape encapsulation of phase change material (PCM) is designed and fabricated for evaluating the charging-alone and discharging-alone thermal performance for medium-temperature range (200–350 °C) latent heat storage applications. Air is used as a heat transfer fluid (HTF), and solar salt is employed as a PCM. A new numerical model incorporating shrinkage and expansion of PCM during phase change is developed by considering the packed bed as the porous medium and the melt fraction-based density variation of PCM to model the transport and solid-liquid phase change phenomena in the PBTES. The numerical model is validated with the in-house experimental results. The maximum thermal charging efficiency is found to be 67.1 % for the mass flow rate of 4.3 g/s and a maximum charging inlet air temperature of 360.9 °C. The maximum discharging efficiency of 86.1 % is obtained for the mass flow rate of 4.3 g/s and discharging inlet air temperature of 35 °C. It is found that the expansion and shrinkage effects are prominent during the phase change of PCM during the charging and discharging operations of the PBTES.

Phase Behavior and Conformational Asymmetry near the Comb-to-Bottlebrush Transition in Linear-Brush Block Copolymers.

This study explores how conformational asymmetry influences the bulk phase behavior of linear-brush block copolymers. We synthesized 60 diblock copolymers composed of poly(trifluoroethyl methacrylate) as the linear block and poly[oligo(ethylene glycol) methyl ether methacrylate] as the brush block, varying the molecular weight, composition, and side-chain length to introduce different degrees of conformational asymmetry. Using small-angle X-ray scattering, we determined the morphology and phase diagrams for three different side-chain length systems, mainly observing lamellar and cylindrical phases. Increasing the side-chain length of the brush block from three to nine ethylene oxide units introduces sufficient asymmetry between the blocks to alter the phase behavior, shifting the lamellar-to-cylindrical transitions toward lower brush block compositions and transitioning the brush block from the dense comb-like regime to the bottlebrush regime. Coarse-grained simulations support our experimental observations and provide a mapping between the composition and conformational asymmetry. A comparison of our findings to strong stretching theory across multiple phase boundary predictions confirms the transition between the dense comb-like regime and the bottlebrush regime.

Reaction-induced morphological transitions in a blend of diblock copolymers and reactive monomers: dissipative particle dynamics simulation.

The dissipative particle dynamics (DPD) method is applied to the morphological transitions of microphase-separated domains in a mixture of symmetric AB-diblock copolymers and reactive C-monomers, where polymerization and cross-linking reactions take place among C-monomers. The initial structure for the DPD simulation is an equilibrated cylindrical domain structure prepared by the density-biased Monte Carlo method with density profiles obtained from the self-consistent field theory. By introducing a cross-linking reaction among reactive C-monomers, we confirmed that the DPD simulation reproduces the morphological transitions observed in experiments, where the domain morphology changes due to segregation between A-blocks of diblock copolymers and cross-linking networks of C-monomers. When the cross-linking reaction of C-monomers is sufficiently fast compared to the deformation of the domains, the initial cylindrical domains are preserved, while the distance between the domains increases. On the other hand, when the formation of the cross-linking network is slow, the domains can deform and reconnect with each other in the developing cross-linking network. In this case, we observe morphological transitions from the initial domain morphology with a large-curvature interface to another domain morphology with a smaller-curvature interface, such as the transition from the cylindrical phase to the lamellar phase. We calculated the spatial correlations in the microphase-separated domains and found that such correlations are affected by the speed of the formation of the cross-linking network depending on whether the bridging between microphase-separated domains occurs in a nucleation and growth process or in a spinodal decomposition process.

Stabilizing undulated lamellae by diblock copolymers confined in alternately adsorbed thin films

The self-assembly behavior of AB diblock copolymer confined in staggering alternately adsorbed thin films is studied using the self-consistent field theory (SCFT) and dissipative particle dynamics (DPD), focusing on the emergence and stability of the undulated lamella (UL) phase. Phase diagrams for the volume fraction of blocks, period of the adsorbed pattern and thickness of the confinement are constructed. Our results indicate that the UL phase can be stable in the case with a large period of adsorbed pattern, and is more favorable in the asymmetrical diblock copolymer with volume fraction around f = 0.40, which becomes cylindrical phases (C) with too small f and transforms into tilted lamellae (TL) on the contrary. Furthermore, the number of layers in the UL phases can be regulated by adjusting the period of the adsorbed pattern and the confinement degree of the thin film. In addition, the formation of the UL is verified by DPD simulations. The study demonstrates that the specially confined diblock copolymers provide an efficient route to regulate the stability of the complex UL phases.

High-Density Packing of Spherical Microdomains from A(AB3)3 Dendron-like Miktoarm Star Copolymer.

An A(AB3)3 dendron-like miktoarm star copolymer consisting of polystyrene (PS, A) and poly(2-vinylpyridine) (P2VP, B) was synthesized using a series of anionic polymerization, atom-transfer radical polymerization (ATRP), and click reaction. The morphology of A(AB3)3 changed greatly depending on the volume fraction of A and the chain asymmetry. Interestingly, a body-centered cubic spherical phase was found even at fA = 0.51 because the chain architecture of A(AB3)3 stabilizes the large interfacial curvature toward A domains. On the other hand, when the length difference between the end and middle A blocks decreased, a hexagonally packed cylindrical phase was formed at fA = 0.50. This is attributed to the fact that the middle A chains are arranged in a more relaxed way, resulting in a milder interfacial curvature toward A domains. The experimental observations are well-consistent with the predictions based on self-consistent-field theory.

High-axial-resolution speckle-free holographic reconstruction via cylindrical quadratic phase method and temporal focusing.

Holographic techniques enable precise laser manipulation, but suffer from two considerable limitations: speckle and deterioration of axial distribution. Here, we propose a cylindrical quadratic phase (CQP) method with temporal focusing (TF) to generate speckle-free holographic illumination with high axial resolution. TF-CQP utilizes a superposed cylindrical phase as the initial guess to iteratively optimize phase hologram, realizing speckle-free holographic reconstruction on the target focal plane and eliminating secondary focus on the defocused planes. TF-CQP further disperses defocused beams symmetrically by a blazed grating, placed conjugate to the focal plane, which enhances axial confinement. Simulation and experimental results show that TF-CQP reconstructs speckle-free illumination with arbitrary shapes and <10 µm axial resolution. Compared to TF-GS (Gerchberg-Saxton algorithm), widely used in holographic optogenetics, TF-CQP shows increased uniformity of 200% and improved modulation efficiency of 32.33% for parallel holographic illumination, as well as a 10% increment in axial resolution.

Synthesis and Structural Insight into poly(dimethylsiloxane)-b-poly(2-vinylpyridine) Copolymers.

In this study, the use of anionic polymerization for the synthesis of living poly(dimethylsiloxane) or PDMS-Li+, as well as poly(2-vinylpyridine) or P2VP-Li+ homopolymers, and the subsequent use of chlorosilane chemistry in order for the two blocks to be covalently joined leading to PDMS-b-P2VP copolymers is proposed. High vacuum manipulations enabled the synthesis of well-defined materials with different molecular weights (Μ¯n, from 9.8 to 36.0 kg/mol) and volume fraction ratios (φ, from 0.15 to 0.67). The Μ¯n values, dispersity indices, and composition were determined through membrane/vapor pressure osmometry (MO/VPO), size exclusion chromatography (SEC), and proton nuclear magnetic resonance spectroscopy (1H NMR), respectively, while the thermal transitions were determined via differential scanning calorimetry (DSC). The morphological characterization results suggested that for common composition ratios, lamellar, cylindrical, and spherical phases with domain periodicities ranging from approximately 15 to 39 nm are formed. A post-polymerization chemical modification reaction to quaternize the nitrogen atom in some of the P2VP monomeric units in the copolymer with the highest P2VP content, and the additional characterizations through 1H NMR, infrared spectroscopy, DSC, and contact angle are reported. The synthesis, characterization, and quaternization of the copolymer structure are important findings toward the preparation of functional materials with enhanced properties suitable for various nanotechnology applications.

Effect of In‐Plane Electric Field on the Microphase Separation in Thin Films of a Symmetric ABA Triblock Copolymer

AbstractThe structure of a thin film of symmetric ABA triblock copolymer melts in an external in‐plane DC or AC electric field is studied theoretically. The situation is considered when the triblock copolymer forms a hexagonal morphology of standing cylinders in bulk in the absence of an external field. Self‐consistent field theory calculations are carried out to determine the most thermodynamically favorable thin film structure among the cylindrical phases perpendicular and parallel to the substrate and the lamellar phase perpendicular to the substrate. The results are presented as phase diagrams with the film thickness and electric field energy on the axes and as distributions of the local composition, which serve as an order parameter in the system. It is confirmed that electric fields only weakly affect the spinodal curves of block copolymers but they can reorient or markedly modify microphase‐separated morphologies in those systems. Such restructuring is consistent with a considerable modulation of the free surface of a copolymer film and it can lead to the coexistence of different phases that appear in the film areas with different local thicknesses.

Multi-objective optimization of fin shape in a cylindrical encapsulated phase change material for thermal energy storage applications

This study presents a novel fin design for a latent heat storage unit that improves its thermal performance through a methodology that integrates numerical simulation, the response surface method, and a multi-objective genetic optimization algorithm. The stored latent energy per mass (Em) and mean power (Pt) are chosen as the objectives for the optimization process. The fin parameters are optimized using the NSGA-II (non-dominated sorting genetic algorithm) to achieve the objectives of maximizing both the stored latent energy per mass (Em) and mean power (Pt). The proposed design is evaluated through simulations and the results are analyzed to determine the optimal fin configuration and the effect of the fin design parameters on the stored energy and power of the unit. The results show that the implementation of full-fin in the latent heat storage unit leads to a 7.2% reduction in total stored energy, but a 34% increase in power in comparison to the finless case. However, the use of an optimization approach results in a substantial increase in power output while maintaining minimal compromise to the stored latent energy. In particular, the optimal fin configuration, Design B, is recommended when power and stored energy are given equal importance, as it results in a 90.1% increase in power and a negligible 4.3% decrease in stored energy per mass.

Stereochemistry-dependent thermotropic liquid crystalline phases of monosaccharide-based amphiphiles.

Conformational rigidity controls the bulk self-assembly and liquid crystallinity from amphiphilic block molecules to copolymers. The effects of block stereochemistry on the self-assembly have, however, been less explored. Here, we have investigated amphiphilic block molecules involving eight open-chain monosaccharide-based polyol units possessing different stereochemistries, derived from D-glucose, D-galactose, L-arabinose, D-mannose and L-rhamnose (allylated monosaccharides t-Glc*, e-Glc*, t-Gal*, e-Gal*, t-Ara*, e-Ara*, t-Man*, and t-Rha*), end-functionalized with repulsive tetradecyl alkyl chain blocks to form well-defined amphiphiles with block molecule structures. All compounds studied showed low temperature crystalline phases due to polyol crystallization, and smectic (lamellar) and isotropic phases upon heating in bulk. Hexagonal cylindrical phase was additionally observed for the composition involving t-Man*. Cubic phases were observed for e-Glc*, e-Gal*, e-Ara*, and t-Rha* derived compounds. Therein, the rich array of WAXS-reflections suggested that the crystalline polyol domains are not ultra-confined in spheres as in classic cubic phases but instead show network-like phase continuity, which is rare in bulk liquid crystals. Importantly, the transition temperatures of the self-assemblies were observed to depend strongly on the polyol stereochemistry. The findings underpin that the stereochemistry in carbohydrate-based assemblies involves complexity, which is an important parameter to be considered in material design when developing self-assemblies for different functions.

Effects of heat transfer medium flow field changes on the heat storage and discharge performance of phase change heat accumulators

In this study, a numerical simulation was employed to assess the heat storage and exothermic behaviour of a phase change unit with different heat flow channel configurations, height-to-diameter ratios, inlet flow rates, and addition of different rib structural parameters. Thus, we aimed to explore the heat storage and exothermic behaviour of the phase change accumulator under changes to the heat transfer medium flow field. By analysing the variation in the velocity and temperature fields of the heat transfer medium and using the field synergy principle, the structure of the cylindrical phase change accumulator was optimised, and the liquid fraction, field synergy angle, and Nu number in different structures were compared. The results revealed that the H-type heat exchanger flow channel could effectively improve the heat exchanger field synergy and increase the heat storage rate by 6.3 %. Increasing the inlet flow velocity could accelerate the heat storage rate; however, the flow velocity caused the flow field synergy to fluctuate and the heat storage efficiency to increase gradually. On increasing the height-to-diameter ratio, the heat exchanger field synergy ‘increased first and then decreased’, reaching the optimal heat transfer effect when D = 1.932. Under the heat storage and release condition, the straight rib heat transfer was superior to that for the ring rib. The change in the built-in straight rib length played a dominant role in the heat storage rate. Accordingly, for optimal heat transfer, the rib length was set to >45 mm, rib thickness to 1.5–2 mm, and number of ribs to 10. Meanwhile, the heat release efficiency initially increased as the length of the external straight rib increased and subsequently decreased. For optimal heat transfer, the rib length was set between 15 and 25 mm, rib thickness to >1.5 mm, and the number of ribs to >10 ribs. Therefore, we determined the ranges of structural parameters that would provide appropriate references for this phase change accumulator in fields such as thermal energy storage and waste heat recovery.

Impact of process-induced ellipticity on the RESET process of cylindrical phase change memory devices

Phase change memory (PCM) is one of the promising candidates for the next-generation high-speed non-volatile memory which exhibits excellent scalability. The cylindrical-type PCM devices entering the nano-scale regime should show their tolerance to the variation in the manufacturing process. However, it is highly challenging to fabricate cylindrical-type nano-scale devices ideally with circular cross-sections. In general, the degree of variation in circular cross-section is dictated by a geometrical parameter called aspect ratio (AR). In this study, the impact of variation in AR of heater (ARheater) and active material, Ge2Sb2Te5 (ARGST) on the RESET programming of the mushroom-type cylindrical PCM device is systematically investigated by using 3D TCAD simulations. The simulation results reveal that the RESET current (IRESET) of the reference device (100 nm heater diameter) consisting of elliptical cross-sections increases significantly to ∼67% when ARheater = 2 and 1 ≤ ARGST ≤ 2, whereas for the scaled-down devices of 20 nm and 10 nm heater diameter with elliptical cross-sections, the IRESET increases to ∼35% and ∼38% when ARheater = 2 and ARGST = 1, and further IRESET increases to ∼54% and ∼63% when ARheater = 2 and ARGST = 2 leading to high-power RESET programming. In the case of the reference device, the ARGST did not play any significant role on IRESET. However, in the scaled-down devices, both ARheater and ARGST significantly affect the IRESET. Furthermore, the device employing a vertically-oriented elliptical heater and horizontally-oriented elliptical GST (where ARheater = 2 and ARGST = 0.5) shows the peculiar re-amorphization among all the cases considered in this study. Hence, the miniaturized cylindrical PCM devices comprising elliptical cross-sections due to process-induced variability require an accurate understanding of the programming characteristics for reliable modeling and simulations.