Planar Phase Research Articles

Design and demonstration of DEA-based tunable planar liquid crystal Alvarez lenses

Traditional liquid crystal lenses realize the tunability of focal length by controlling the rotation angle of the liquid crystal molecule. In this paper, a tunable planar liquid crystal Alvarez lenses, which can tune the focal length via the lateral displacement of two planar liquid crystal phase plates actuated by dielectric elastomer actuators (DEA), was designed and fabricated. The maskless laser direct writing technology is employed to fabricate the tunable planar liquid crystal Alvarez lenses. The experiments show that liquid crystal Alvarez lenses achieved a wide varifocal range of 1476 mm ∼ 118 mm with lateral displacement of the two planar liquid crystal phase plates varying from 0.2 mm ∼ 2.5 mm. The proposed varifocal lens has a dynamic response with a rise time of 185 ms and a fall time of 296 ms. Experiments are designed to verify the varifocal capability of the proposed Alvarez lenses, and the experimental results show that it can focus virtual images of an object at different depths in the real environment. The proposed liquid crystal Alvarez lenses have potential applications in compact and miniaturized imaging systems such as camera modules, medical imaging, enhanced displays, etc.

Bifurcation, chaotic behaviors and solitary wave solutions for the fractional Twin-Core couplers with Kerr law non-linearity

The main purpose of this article is to analyze the bifurcation, chaotic behaviors, and solitary wave solutions of the fractional Twin-Core couplers with Kerr law non-linearity by using the planar dynamical system method. This equation has profound physical significance and application value in the areas of optics and optical communication. Firstly, the traveling wave transformation is applied to convert the beta-derivative Twin-Core couplers with Kerr law non-linearity into the ordinary differential equations. Secondly, phase portraits and Poincaré sections of two-dimensional dynamical system and its perturbation system are plotted by using mathematical software. For different initial values, the planar phase diagram and three-dimensional phase diagram in red and blue are plotted, respectively. Finally, the solitary wave solutions of the fractional Twin-Core couplers with Kerr law non-linearity are obtained by using theory of planar dynamical system. In addition, three-dimensional graphs, two-dimensional graphs, and the contour graphs of the solitary wave solutions are drawn.

Three-dimensional vortex and multipole quantum droplets in a toroidal potential

We investigate the existence, stability, and evolution dynamics of three-dimensional quantum droplets (QDs) in binary Bose–Einstein condensates trapped in a toroidal potential. The interplay of competing mean-field (MF) and beyond-MF nonlinear terms (attractive and repulsive ones) with the potential enables the formation of a variety of stable QDs with complex structures, from higher-order vortices and multipoles to necklace complexes. There are two branches of the vortex and multipole QDs with opposite slopes of the norm-vs.-chemical-potential curves. The upper-branch vortex QDs are completely stable, regardless of the value of their topological charge (winding number), m. On the other hand, multipole QDs are stable only near the turning point of the curves. Although the stability region shrinks with the growth of the number of poles, necklace-shaped QDs remain stable for the number up to 16. Applying a torque perpendicular to the original QD’s angular momentum, we observe stable precession of vortex QDs. Periodic rotation is also observed when multipole QDs are set in motion by a planar phase torque.

Counterion Release from Macroion Assemblies of Planar Geometry.

Macroions such as nanoparticles, polyelectrolytes, ionic gels, and amphiphiles can form condensed, often self-assembled, phases that are embedded in a solvent region. The condensed phase contains not only the partially or fully immobile charges of their macroions but also corresponding counterions that are mobile and thus free to migrate out of their confinement into the solvent region where they benefit from high translational entropy. Based on the nonlinear Poisson-Boltzmann model for monovalent ions, we quantify the corresponding fraction of released counterions for a planar slab geometry of the macroion phase. Slab thickness, extension of the solvent phase, fixed background charge density provided by the macroions, and dielectric constants inside slab and solvent combine into three dimensionless parameters that the fraction of released counterions depends on. We calculate that fraction and analyze the limits of a thin macroion phase, a large solvent phase, and linearized theory, where simple analytic results become available. Of particular interest is the presence of a single-planar interface that separates a bulk macroion phase from an extended solvent region. We calculate the apparent surface charge density that emerges due to the released counterions. Our model yields a comprehensive description of counterion partitioning between a planar macroion phase and a solvent region on the level of mean-field electrostatics in the absence of added salt ions.

Development of a five-axis printer for the fabrication of hybrid 3D scaffolds: From soft to hard phases and planar to curved surfaces

Three-dimensional (3D) printing of hybrid scaffolds with material gradients, combining soft and hard phases, is an appealing frontier in additive manufacturing. However, most 3D printers are limited to either three-axis or mono-material capabilities, rendering them unsuitable for fabricating hybrid scaffolds. Additionally, printing on curved surfaces requires advanced printing capabilities. Our work aims to advance additive manufacturing by developing a hybrid piezoelectric inkjet-extrusion printer equipped with five-axis functionalities. The printer could be used to fabricate customized hybrid scaffolds, surpassing conventional mono-material or linear three-axis printing strategies. The soft phase comprises a low-viscosity photocurable resin and a high-viscosity peptide hydrogel, while the hard phase comprises 3D-printed polylactic acid and hydroxyapatite parts. To validate the system, we fabricated three hybrid scaffolding use cases, characterized by multi-material porous structures fabricated on planar, single-curved, and free-form surfaces. The scaffolds were subsequently analyzed using digital microscopy to assess their accuracy, particularly the feature sizes of pores and struts (i.e., 0.8–3.6 mm). In the first part of the study, we demonstrated the versatility of inkjet and extrusion printing by hybrid printing an interconnected network in the soft phase on top of a planar ceramic hard phase. A pore width and height deviation of 6% was achieved compared to the intended design. In the second part of the study, we evaluated the 3D inkjet printing of a multi-material porous scaffold on a single-curved surface for osteochondral defects. The circumferential pore width and radial pore height deviated by 0.8% and 2%, respectively. Finally, we inkjet-printed a mesh structure on a free-form surface, which acted as a membrane for palatal implants. In this case, the pore width deviations were -16% in the printing direction and 2% perpendicular to the printing direction.

Nonlinear dynamics of cantilevered hyperelastic pipes conveying fluid: Comparative study of linearelasticity and hyperelasticity

In light of the softness and lightweight characteristics, hyperelastic pipes are prone to large deformation. Intending to provide accurate predictions of their large deformation vibrations, the present study aims to establish a rotation-angle-based geometrically exact model for cantilevered pipes conveying fluid composed of hyperelastic materials. Additionally, given the presence of nonlinear geometric relations, it is imperative to assess the role of hyperelasticity in the nonlinear dynamics of fluid-conveying pipes in comparison to linearelastic pipes. The modeling process integrates the Mooney-Rivlin hyperelastic model with a geometrically exact description of the pipe. And the final governing equation is developed through energy analysis and the extended Hamilton's principle. Subsequently, Galerkin's method and the finite difference method are employed to address the governing equation. Following the verification of the proposed model, parametric studies are conducted in the form of planar oscillation diagrams, time histories, phase trajectories, and bifurcation diagrams. The findings of the present study highlight three critical insights. Firstly, the hyperelastic model introduces numerous complicated nonlinear terms as function of the rotation angle with high-order nonlinearity. In the present study, at least fifth-order nonlinear terms should be preserved to adequately predict large deformation vibrations. Secondly, the Mooney-Rivlin hyperelastic model imparts a hardening effect in comparison to the linearelastic model, significantly reducing vibration amplitudes. Lastly, the third-order approximate model is demonstrated to be inadequate in predicting large deformation vibrations at high flow velocity, as it contains the approximation on not only the geometric description but the hyperelasticity-related terms.

Formation of self-assembled nanodomain structure as a result of motion of oriented planar phase boundary in single crystals of tetragonal PMN-PT

We studied the formation of the domain structure as a result of the motion of a planar interphase boundary in the {001}-cut tetragonal PMN-PT crystals during cooling with oriented temperature gradient. The specialized heating/cooling stage was assembled for this purpose. Piezoresponse force microscopy was used to image the domain structure at the (001) and (010) surfaces of the samples with high spatial resolution, revealing a complex quasi-periodic domain pattern with a periodicity from 300 to 400 nm.

Qualitative analysis and explicit solutions of perturbed Chen–Lee–Liu equation with refractive index

The main purpose of this article is to study the qualitative analysis and explicit solutions of perturbed Chen–Lee–Liu equation with refractive index. By utilizing wave transformation, two-dimensional dynamics in a plane are obtained. Using the qualitative theory of planar dynamical systems, a series of planar phase portraits are presented. By analyzing the bifurcations of these phase portraits and the characteristics of equilibrium points, some explicit solutions such as Jacobian function solutions and hyperbolic function solutions are constructed. These can further understand the dynamic behavior of perturbed Chen–Lee–Liu equation and their wave propagation.

Bifurcation, chaotic behavior and solitary wave solutions for the Akbota equation

<p>In this article, the dynamic behavior and solitary wave solutions of the Akbota equation were studied based on the analysis method of planar dynamic system. This method can not only analyze the dynamic behavior of a given equation, but also construct its solitary wave solution. Through traveling wave transformation, the Akbota equation can easily be transformed into an ordinary differential equation, and then into a two-dimensional dynamical system. By analyzing the two-dimensional dynamic system and its periodic disturbance system, planar phase portraits, three-dimensional phase portraits, Poincaré sections, and sensitivity analysis diagrams were drawn. Additionally, Lyapunov exponent portrait of a dynamical system with periodic disturbances was drawn using mathematical software. According to the maximum Lyapunov exponent portrait, it can be deduced whether the system is chaotic or stable. Solitary wave solutions of the Akbota equation are presented. Moreover, a visualization diagram and contour graphs of the solitary wave solutions are presented.</p>

Optimizing the grain boundary structure of sintered Nd-Dy-Fe-Co-B magnets by low-melting-point alloys grain boundary addition

To respond to the gradually increasing demand for thermal stability of sintered NdFeB magnets and grasp the evolution rules of their phase structure, research on sintered Nd-Dy-Fe-Co-B magnets was conducted. The magnets used in this study were prepared by the powder metallurgy method (Strip Casting + Hydrogen Decrepitation + Jet Milling). The room temperature magnetic properties of the magnet sample were Br = 11.45 kGs and Hcj = 22.42 kOe, with a low-temperature coefficient of Br (αBr(20 °C∼100 °C) = −0.059 %/°C) and a high Curie temperature (Tc = 460 °C). Based on the microstructure observation, there were planar anisotropic soft magnetic phase Nd2Co17 within grain boundaries and the "Cu-Co Opposite Distribution". Low-melting-point binary alloy Pr80Cu20 was introduced into the magnet by grain boundary addition to eliminate Nd2Co17 phases and improve the coercivity. After the grain boundary addition, the "Cu-Co Opposite Distribution" was used to eliminate the Nd2Co17 phase, the grain boundary structure was optimized, and the coercivity was increased by approximately 2.6 kOe, which was approximately 10 % of the total coercivity. Therefore, Cu-containing low-melting-point binary alloy grain boundary addition is an effective method for optimizing the grain boundary structure of Nd-Dy-Fe-Co-B magnets, thereby improving the high-temperature stability and coercivity.

An augmented QCD phase portrait: Mapping quark-hadron deconfinement for hot, dense, rotating matter under magnetic field

The quark-hadron transition that happens in ultra-relativistic heavy-ion collisions is expected to be influenced by the effects of rotation and magnetic field, both present due to the geometry of a generic non-head-on impact. We augment the conventional T–μB planar phase diagram for QCD matter by extending it to a multi-dimensional domain spanned by temperature T, baryon chemical potential μB, external magnetic field B and angular velocity ω. Using two independent approaches, one from a rapid rise in entropy density and another dealing with a dip in the squared speed of sound, we identify deconfinement in the framework of a modified statistical hadronization model. We find that the deconfinement temperature TC(μB,ω,eB) decreases nearly monotonically with increasing μB,ω and eB with the most prominent drop (by nearly 40 to 50 MeV) in TC occurring when all the three quasi-control (via collision energy and centrality) parameters are simultaneously tuned to finite values that are typically achievable in present and upcoming heavy-ion colliders.

Observations of the occurrence and disappearance of peritectic couple growth performed under microgravity conditions

Peritectic couple growth (PCG) is an unusual growth form at which the peritectic and pro-peritectic solid phases solidify like a regular eutectic. To investigate the dynamics of PCG formation and growth, experiments with the transparent, organic peritectic alloy Tris(hydroxymethyl)aminomethane–Neopentylglycol are performed at the International Space Station. Fully planar and partly planar/cellular PCGs are found and analyzed. In any case, PCG starts with the formation of lateral bands from the peritectic phase that overgrow most of the pro-peritectic phase but not completely. During coupled growth, the remaining patches transform into rods and/or lamellae. Depending on the conditions, PCG either terminates by the disappearance of pro-peritectic rods or by transforming the rods into cells. The second mechanism goes hand in hand with the formation of a single-phase 2D layer at the top of a tilted interface. At low pulling velocities, planar pro-peritectic phase growth transforms into planar peritectic phase growth via PCG.

Traveling spiral wave chimeras in coupled oscillator systems: emergence, dynamics, and transitions

Systems of coupled nonlinear oscillators often exhibit states of partial synchrony in which some of the oscillators oscillate coherently while the rest remain incoherent. If such a state emerges spontaneously, in other words, if it cannot be associated with any heterogeneity in the system, it is generally referred to as a chimera state. In planar oscillator arrays, these chimera states can take the form of rotating spiral waves surrounding an incoherent core, resembling those observed in oscillatory or excitable media, and may display complex dynamical behavior. To understand this behavior we study stationary and moving chimera states in planar phase oscillator arrays using a combination of direct numerical simulations and numerical continuation of solutions of the corresponding continuum limit, focusing on the existence and properties of traveling spiral wave chimeras as a function of the system parameters. The oscillators are coupled nonlocally and their frequencies are drawn from a Lorentzian distribution. Two cases are discussed in detail, that of a top-hat coupling function and a two-parameter truncated Fourier approximation to this function in Cartesian coordinates. The latter allows semi-analytical progress, including determination of stability properties, leading to a classification of possible behaviors of both static and moving chimera states. The transition from stationary to moving chimeras is shown to be accompanied by the appearance of complex filamentary structures within the incoherent spiral wave core representing secondary coherence regions associated with temporal resonances. As the parameters are varied the number of such filaments may grow, a process reflected in a series of folds in the corresponding bifurcation diagram showing the drift speed s as a function of the phase-lag parameter α.

Orientational Transitions in Magnetically Compensated Liquid-Crystal Suspensions of Ferromagnetic Carbon Nanotubes

Purpose of research is to study the influence of ferromagnetic carbon nanotubes on orientational transitions in magnetically compensated liquid-crystal suspensions.Methods. The problem was solved in the framework of the continuum theory. By minimizing the Helmholtz free energy functional, a system of Lagrange-Euler equations is obtained that determines the equilibrium dependences of the orientation angles of liquid crystal and impurity ferromagnetic carbon nanotubes directors, as well as the concentration distributions of the dispersed phase of the suspension as a function of the transverse coordinate, material parameters, and magnetic field strength.Results. It is shown that in the presence of an external magnetic field, a liquid-crystal suspension of ferromagnetic carbon nanotubes can be in a non-uniform phase (angular phase) and two uniform phases (planar and homeotropic phases). Expressions for the threshold fields of transitions between coexisting orientational phases are obtained analytically as functions of the material parameters of the composite. Diagrams of the orientational phases of the suspension are plotted.Conclusion. As a result of the research, it was shown that the addition of low concentrations of ferromagnetic carbon nanotubes can significantly reduce the threshold of the magnetic Fréedericksz transition compared to a pure liquid crystal, which is important for various technical applications. The obtained analytical formulas for the threshold fields of transitions between different orientational phases can be used to determine the anchoring energy and material parameters of suspensions of ferromagnetic carbon nanotubes in a liquid crystal.

Interfacial reactions in the Sn-9.0 wt.% Zn/Cu-Ti alloy (C1990 HP) couple

PurposeThe purpose of this study was to examine the influence of adding a small amount of Ti to a Cu-based alloy, specifically the commercial Hyper Titanium Copper alloy (C1990 HP), which contains Cu-3.28 wt.% Ti, on its interfacial reaction with Sn-9.0 wt.% Zn (SnZn) solder, using the liquid/solid reaction couple technique.Design/methodology/approachThe SnZn/C1990 HP couples were subjected to a reaction temperature of 240–270°C for a duration of 0.5–5 h. The resulting reaction couple was characterized using a scanning electron microscope, energy dispersive spectrometer, electron probe microanalyzer and X-ray diffractometer.FindingsIt was observed that the scallop-shaped CuZn5 and planar Cu5Zn8 phases were formed in almost all SnZn/C1990 HP couples. With increased reaction duration and temperature, the Cu-rich intermetallic compound (IMC)-Cu5Zn8 phase became a dominant IMC formed at the interface. The total thickness of the IMCs was increased with the increase in the reaction duration and temperature. The IMC growth obeyed the parabolic law, and the IMC growth mechanism was diffusion controlled. The activation energy of the SnZn/C1990 HP couple was 64.71 kJ/mol.Originality/valueThis article presents an analysis of the IMC thickness in each sample using ImageJ software, followed by kinetic analysis using Origin software at various reaction temperatures of SnZn/C1990 HP in liquid/solid couples. The study also includes detailed reports on the morphology, interface composition and X-ray diffraction analysis, as well as the activation energy. The findings can serve as a valuable reference for electronic packaging companies that utilize C1990 HP substrates.

The impact of convection on morphological instability of a planar crystallization front

A linear morphological stability analysis of a planar solid-liquid phase interface describing the solidification processes of a binary melt with convection is carried out. The developed theory includes conductive and convective heat and mass transfer mechanisms near the phase interface and generalizes previously known theories of morphological stability. The amplification rate as a function of wavenumber of perturbations and neutral stability curve that divides the stability/instability parametric domains are obtained. It is shown that these domains are highly dependent of convection intensity, which represents a stabilizing factor for solidification processes. A criterion of concentration supercooling in the steady-state solidification conditions with convection is found. The obtained dispersion relation and neutral stability curve define various crystallization scenarios such as (i) morphological instability and concentration supercooling appearing to the formation of a two-phase mushy layer, (ii) morphological stability and concentration supercooling leading to the existence of a slurry layer, (iii) morphological stability without concentration supercooling when the planar solidification front is stable, and (iv) morphological instability without concentration supercooling forming the mesoscopically rough phase interface.

Thermochromic Behavior of Polydiacetylene Nanomaterials Driven by Charged Peptide Amphiphiles.

The tunability of chromatic phases adapted by chromogenic polymers such as polydiacetylene (PDA) is key to their utility for robust sensing applications. Here, we investigated the influence of charged peptide interactions on the structure-dependent thermochromicity of amphiphilic PDAs. Solid-state NMR and circular dichroism analyses show that our oppositely charged peptide-PDA samples have distinct degrees of structural order, with the coassembled sample being in between the β-sheet-like positive peptide-PDA and the relatively disordered negative peptide-PDA. All solutions exhibit thermochromicity between 20 and 80 °C, whereby the hysteresis of the blue, planar phase is much larger than that of the red, twisted phase. Resonance Raman spectroscopy of films demonstrates that only coassemblies with electrostatic complementarity stabilize coexisting blue and red PDA phases. This work reveals the nature of the structural changes responsible for the thermally responsive chromatic transitions of biomolecule-functionalized polymeric materials and how this process can be directed by sequence-dictated electrostatic interactions.

Quantification of porosity in composite plates using planar X-ray phase contrast imaging

The application of planar Edge-Illumination X-ray Phase-Contrast imaging (EI-XPCi) for the non-destructive quantification of porosity in carbon fiber reinforced polymer (CFRP) specimens, a significant concern in aerospace applications, was investigated. The method enables fast, planar (2D) scans providing access to large samples. A set of woven CFRP plates with porosity content ranging from 0.7% to 10.7% was examined. In addition to standard X-ray attenuation, EI-XPCi provides differential phase and dark-field signals, sensitive to inhomogeneities and interfaces at scales above and below the system spatial resolution, respectively. The correlation with the porosity content from matrix digestion obtained from the dark-field signal was comparable to that from ultrasonic attenuation. The novel analysis of the standard deviation of differential phase (STDP), sensitive to inhomogeneities above the system resolution (approximately 12 μm), resulted in a very high correlation (R2 = 0.995) with the matrix digestion porosity content, outperforming ultrasonic attenuation measurements.

Technical concepts on blood pool phase SPECT (acquisition, reconstruction).

Guidelines for bone scintigraphy are well established and recommend the use of planar early phase images to investigate a number of clinical indications. With recent advances in gamma camera technology the use of SPECT/CT imaging in the early phases is now possible, offering the potential of improved diagnostic confidence and prognostic value. To date little work has been carried out to optimize the acquisition of early phase bone images using SPECT/CT with most of the available studies acquiring SPECT images after the traditional planar images to allow comparison of the two techniques. Imaging durations of 7 to 10 minutes have been commonly used. However, the use of iterative reconstruction algorithms has been investigated with rapid SPECT imaging to allow imaging durations as low as 4 minutes. The use of CZT based systems with increased sensitivity and improved energy and spatial resolution also offers the potential to reduce imaging times. The optimization of projection measurement order has been investigated as a method of reducing image artefacts as a result of changing tracer distribution during the SPECT acquisition. In this article we consider the current state of early phase SPECT imaging and possible areas for future investigation as well as recommendations for departments looking to adopt blood pool SPECT imaging as part of their routine clinical practice.

Achieving exceptional ultrahigh-strength in low-alloy Mg-1Al-1Ca-0.4Mn (wt%) alloy by regulating bimodal microstructure

A Mg-1Al-1Ca-0.4Mn (AXM1104, wt%) alloy extruded at 250 ℃ with a ram speed of 0.1 mm/s obtains a unique bimodal microstructure. As-extruded alloy exhibits a high tensile yield strength (YS) of 474 MPa but a low ductility of 2.1%, in which the YS exceeds conventionally extruded rare-earth-free Mg alloys reported so far. After annealing at 300 ℃ for 10 min, the annealed alloy achieves a good strength-ductility balance, with a YS of 426 MPa and an elongation of 5.4%. The ultrahigh YS of the as-extruded alloy is attributed to the combined strengthening efect of grain boundary, dislocation and texture, while the as-annealed alloy is mainly strengthened by both grain boundary strengthening and precipitation strengthening from planar Al2Ca nano phase.