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Zigzag strip bundles are combinatorial models realizing the crystals B (∞) and the highest weight crystals B (λ) over quantum affine algebras U q (g) , and they are closely related with Nakajima monomials and Kashiwara embeddings of specific type. In this paper, we introduce new zigzag strip bundles for U q (g) , which we call reverse zigzag strip bundles in order to distinguish from the previous ones, and we give explicit 1-1 correspondences with the set of Nakajima monomials and the image of Kashiwara embedding which are different from those appeared in the study of the zigzag strip bundles. Another main result is to give different points of view about zigzag strip bundles and reverse zigzag strip bundles. Indeed, the previous 1-1 correspondences between the sets of zigzag strip bundles or reverse zigzag strip bundles, and the sets of Nakajima monomials or images of Kashiwara embeddings were determined based on the number of blocks in the columns of these strip bundles. In our work, we use the number of blocks in the rows of zigzag strip bundles and reverse zigzag strip bundles to provide characterizations of Nakajima monomials and images of Kashiwara embeddings that differ from the previous ones. That is, we give characterizations of Nakajima monomials and Kashiwara embeddings of 4 types. Further, we discuss the connection between zigzag strip bundles and reverse zigzag strip bundles. [ABSTRACT FROM AUTHOR]

[Display omitted] The nanoporous polydimethylsiloxane (PDMS) surfaces of a rectangular microfluidic channel, selectively uptakes water molecules, concentrating the solute molecules in an aqueous phase, that could drive phase transitions. Factors such as surface wettability, channel geometry, the surface-to-volume ratio, and surface topography of the confinements could play a key role in tuning the phase transitions spatio-temporally. Using a lyotropic chromonic liquid crystal as model biological material, confined within nanoporous microfluidic environments, we study molecular assembly driven by nanoporous substrates. By combining timelapse polarized imaging, quantitative image processing, and a simple mathematical model, we analyze the phase transitions and construct a master diagram capturing the role of surface wettability, channel geometry and embedded topography on programmable lyotropic phase transitions. Intrinsic PDMS nanoporosity and confinement cross-section, together with the imposed wettability regulate the rate of the N -M phase transition; whereas the microfluidic geometry and embedded topography enable phase transition at targeted locations. We harness the emergent long-range order during N -M transition to actuate elasto-advective transport of embedded micro-cargo, demonstrating particle manipulation concepts governed by tunable phase transitions. Our results present a programmable physical route to material assembly in microfluidic environment, and offer a new paradigm for assembling genetic components, biological cargo, and minimal synthetic cells. [ABSTRACT FROM AUTHOR]

Bacterial chemoreceptors sense the extracellular signals and regulate bacterial motilities, biofilm formation, etc. The periplasmic ligand binding domains of chemoreceptors occur as different structural folds and recognize a diversity of chemical molecules. In Pseudomonas aeruginosa (PAO1), two bacterial chemoreceptors, McpN (PA2788) and PilJ (PA0411), are proposed to both contain a PilJ-like ligand-binding domain (LBD) (Pfam motif PF13675) and involved in nitrate chemotaxis and type IV pilus-mediated motility, respectively. The LBDs of McpN and PilJ consist of 135 and 263 residues, respectively, and share very low sequence identity, suggesting they might occur as different structures. Here, we found that PilJ-LBD folded into an HBM module, the same as the sensor domains of McpS-LBD and TorS-LBD, but it differed from that of McpN-LBD. We also observed a trimer in SEC and AUC and proposed a trimeric model based on the crystal structure. Based on the sequence, we classified the Pfam containing McpN-LBD and PilJ-LBD into three classes: sPilJ (single PilJ) represented by McpN-LBD with only one PilJ domain, dPilJ (dual PilJ) that contained dual PilJ domains, and hPilJ (hybrid PilJ) that comprises of a PilJ domain and another non-PilJ domain. Our work indicates a significant structural difference between the ligand binding domains of PilJ and McpN and will help our further study on both kinds of chemoreceptors. • The ligand binding domain of PilJ has an HBM fold. • A trimer of PilJ-LBD were observed. • The PilJ-type LBDs in PilJ and McpN fold as HBM and 4HB, respectively. • Pfam domain PF13675 are classified into three branches, sPilJ, dPilJ and hPilJ. [ABSTRACT FROM AUTHOR]

This paper continues to study linear and unconditionally modified-energy stable (abbreviated as SAV-GL) schemes for the gradient flows. The schemes are built on the SAV technique and the general linear time discretizations (GLTD) as well as the extrapolation for the nonlinear term. Different from [44] , the GLTDs with three parameters discussed here are not necessarily algebraically stable. Some algebraic identities are derived by using the method of undetermined coefficients and further used to establish the modified-energy inequalities for the unconditional modified-energy stability of the semi-discrete-in-time SAV-GL schemes. It is worth emphasizing that those algebraic identities or energy inequalities are not necessarily unique for some choices of three parameters in the GLTDs. Numerical experiments on the Allen-Cahn, the Cahn-Hilliard and the phase field crystal models with the periodic boundary conditions are conducted to validate the unconditional modified-energy stability of the SAV-GL schemes, where the Fourier pseudo-spectral method is employed in space with the zero-padding to eliminate the aliasing error and the time stepsizes for ensuring the original-energy monotonous decay are estimated by using the stability regions of our SAV-GL schemes for the test equation. The resulting time stepsize constraints for the SAV-GL schemes are almost consistent with the numerical results on the above gradient flow models. [ABSTRACT FROM AUTHOR]

Dynamic protein-protein interactions (PPIs) are fundamental to spatiotemporal control of protein functions in biological systems. Dissecting binding interfaces in aqueous solution (i.e., biological interfaces) is of great importance for identifying molecular determinants that contribute to the affinity and specificity of PPIs. Herein, we describe a biochemical method, termed site-specific proximity ligation (SPL), that enables the identification and reconstruction of native binding interfaces distinct from those present in crystal structures and models from computational prediction. SPL involves the strategic incorporation of an aryl azide-containing unnatural amino acid (AZF) into residues of interest in a particular protein that forms a multiprotein complex. Depending on the interfacial role of a targeted residue, a photo-inducible highly reactive incorporated AZF moiety may react with neighboring functional groups to covalently capture an otherwise non-covalent or weak interaction with a specific partner protein, thereby revealing the landscape of biological interfaces. Using a heterotrimeric nuclear pore protein as a model, we show that the biological interfaces of the complex mapped by SPL provide new insight into dynamic molecular recognition that is missed by, or even in conflict with, static models. Image 1 • Exploring binding interfaces of a multiprotein complex is of great importance. • Site-specific proximity ligation (SPL) allows crosslinks between interacting residues. • SPL revealed new binding interfaces of the nuclear pore complex in solution. • SPL compensates for the limitations of X-ray crystallography and in silico prediction. [ABSTRACT FROM AUTHOR]

We combine the total variation flow suitable for crystal modeling and image analysis with the dynamic boundary conditions. We analyze the behavior of facets at the parts of the boundary where these conditions are imposed. We devote particular attention to the radially symmetric data. We observe that the boundary layer detachment actually can happen at concave parts of the boundary. [ABSTRACT FROM AUTHOR]

The Landau–Brazovskii model is a well-known Landau model for finding the complex phase structures in microphase-separating systems ranging from block copolymers to liquid crystals. It is critical to design efficient numerical schemes for the Landau–Brazovskii model with energy dissipation and mass conservation properties. Here, we propose a mass conservative and energy stable scheme by combining the spectral deferred correction (SDC) method with the convex splitting technique to solve the Landau–Brazovskii model efficiently. An adaptive correction strategy for the SDC method is implemented to reduce the cost time and preserve energy stability. Numerical experiments, including two- and three-dimensional periodic crystals in Landau–Brazovskii model, are presented to show the efficiency of the proposed numerical method. • We proposed a spectral deferred correction method combined with convex splitting. • We proved the mass conservative and energy stable properties. • The spectral deferred correction method can achieve arbitrary order accuracy. • An adaptive correction strategy can reduce time cost and preserve energy stability. [ABSTRACT FROM AUTHOR]

Abstract Following outbreaks of feed and food adulterations with a melamine and cyanuric acid mixture in 2007 and melamine in 2008 respectively, the kinetics and toxicodynamics of the mixture have been investigated particularly in sensitive species such as the rainbow trout. Tissue concentrations and intensity of the adverse effect, melamine-cyanurate crystal formation in kidney, were reported in similar experimental conditions. Here, a recent PBTK model for rainbow trout has been applied to model the kinetics of both single compounds based on residue levels in tissues. Both PBTK models for the single compounds were combined and a model of crystal formation for the mixture melamine-cyanuric acid was also added to predict the intensity of crystal formation under the assumptions that crystals formed either in urine or in kidney tissue. Modelling the kinetics of melamine and cyanuric acid provided a better understanding and prediction of intensity of crystal formation in case of sequential exposures with varying intensity or co-exposure. This study demonstrates, for the first time, how fish PBTK models can play a key role in the understanding and prediction of toxicokinetics and toxicodynamics of mixtures. This study also illustrates how adverse effects may potentially occur even when the compounds are not administered together as a mixture. Highlights • Formation of melamine cyanurate crystals was modelled as a first order process. • A toxicodynamic component was added to a toxicokinetic model in fish. • Intensity in case of sequential exposure depends on single compound toxicokinetics. • Lack of data on chemical-specific excretion in fish hinders model development. [ABSTRACT FROM AUTHOR]

Abstract Using the advantage of phase field crystal model in microstructure evolution, we simulated the details of two-dimensional triangular phase on atomic scale and diffusion time scale. The results show that the annihilation process of grain boundaries can be divided into three stages. The energy changes of the system at different stages are accurately calculated and the process is quantitatively analyzed. By comparing the atomic density distributions at different temperatures and orientation angles, it is shown that the grain boundary is sensitive to temperature. Within the range of low-angle, the increase of orientation angle inhibits the occurrence of annihilation and decreases the grain boundary migration rate. Under the applied stress, the orientation angle has a certain response relationship with the yield strength of the material. This work has some practical significance in the influence of microstructure on the mechanical properties of materials. Graphical abstract Image 107272 Highlights • Analyzing the grain boundary structure of a pure material at low-angle symmetrical tilt grain boundaries. • The annihilation process of the grain boundary during the isovolumic assumption deformation of the crystal was revealed. • Combined with the change of system energy, the influence of parameters on grain boundary annihilation was analyzed. [ABSTRACT FROM AUTHOR]

Negative thermal expansion (NTE) in trifluorides of rare earth elements (REEs – R ) is considered. The electronic structure of R divides R F 3 into two homological series : 1) short ScF 3 , YF 3 , LaF 3 of d- elements and 2) long LaF 3 and 14 fluorides of 4f -elements (lanthanides - Ln ) from CeF 3 to LuF 3. The type of NTE is different for different series. The Periodic Table of R F 3 (R F 3 are in the locations of elements R in the Periodic Table of Elements) sets the periodicity of NTE types for the first time. In the short series only ScF 3 (ReO 3 type) has NTE-I in a wide temperature range. Eight Ln F 3 (out of 15 R F 3) have polymorphic transition (PolTr). The only PolTr β- (β-YF 3 type) → t- (LaF 3 type) of three possible ( β- → t-; β- →α- YF 3 ; t- → α- YF 3) gives denser high-temperature t- modification. It is evidence of a giant NTE-II. The unit cell parameters of the model crystal 61(58Ce 0.5 64Gd 0.5)F 3 (« pseudo 61PmF 3 ») were measured in situ by X-ray diffraction to calculate V form of PmF 3. The unit cell parameters of β- ​« pseudo PmF 3 » were obtained. PmF 3 belongs to the structural subgroup (SSG) B of Ln F 3. PolTrs in these four Ln F 3 are accompanied by a giant NTE-II up to ∼4.7 %. These Ln F 3 form a new group of single component materials with non-adjustable NTE-II parameters. Multicomponent materials with adjustable NTE-II parameters arise in Ln F 3 - Ln' F 3 systems. [Display omitted] • The periodicity of NTE in R F 3 (R = Sc, Y, La-Lu) has been established, correlating with the position of R elements in the Periodic Table of Elements. [ABSTRACT FROM AUTHOR]

In this article, we first establish a new flow-coupled binary phase-field crystal model and prove its energy law. Then by using some newly introduced variables, we reformulate this three-phase model into an equivalent form, which makes it possible to construct a fully discrete linearized decoupling scheme with unconditional energy stability and second-order time accuracy to solve this model for the first time. The energy law of the reformulated model is also proved. Then we incorporate the explicit-IEQ (invariant energy quadratization) method for the nonlinear potentials, the projection method for the Navier-Stokes equations, the Crank-Nicolson method for time marching, and the finite element method for spatial discretization together to develop the fully discrete scheme for the reformulated and equivalent system. By using the nonlocal splitting technique, at each time step, only a few decoupled constant-coefficient elliptic equations are required to be solved, even though the original and reformulated models are much more complicated in the form. The developed algorithm is further proved to be unconditionally energy stable, and a detailed implementation process is also provided. Various numerical experiments in 2D and 3D are carried out to verify the effectiveness of the developed scheme, including the binary crystal growth under the action of shear flow and the sedimentation process of many binary particles. • The first phase field model for the flow-coupled binary crystal problem. • Energy stability of the proposed model. • The first decoupled, linear, second order, unconditionally stable finite element method for the proposed model. [ABSTRACT FROM AUTHOR]

Many solids crystallize as microcrystalline powders, thus precluding the application of single crystal X-Ray diffraction in structural elucidation. In such cases, a joint use of high-resolution solid-state NMR and crystal structure prediction (CSP) calculations can be successful. However, for molecules showing significant conformational freedom, the CSP-NMR protocol can meet serious obstacles, including ambiguities in NMR signal assignment and too wide conformational search space to be covered by computational methods in reasonable time. Here, we demonstrate a possible way of avoiding these obstacles and making as much use of the two methods as possible in difficult circumstances. In a simple case, our experiments led to crystal structure elucidation of a cocrystal of linezolid (LIN), a wide-range antibiotic, with 2,3-dihydroxybenzoic acid, while a significantly more challenging case of a cocrystal of LIN with 2,4-dihydroxybenzoic acid led to the identification of the most probable conformations of LIN inside the crystal. Having four rotatable bonds, some of which can assume many discreet values, LIN molecule poses a challenge in establishing its conformation in a solid phase. In our work, a set of 27 conformations were used in CSP calculations to yield model crystal structures to be examined against experimental solid-state NMR data, leading to a reliable identification of the most probable molecular arrangements. [Display omitted] • SsNMR and CSP were used to determine crystal structure of LIN:2,3-DHBA cocrystal. • SsNMR data indicated the most probable conformation of LIN in LIN:2,4-DHBA cocrystal. • Optimization of only atomic positions is not enough to yield reliable NMR data. [ABSTRACT FROM AUTHOR]

This paper studies a class of linear unconditionally energy stable schemes for the gradient flows. Such schemes are built on the SAV technique and the general linear time discretization (GLTD) as well as the linearization based on the extrapolation for the nonlinear term, and may be arbitrarily high-order accurate and very general, containing many existing SAV schemes and new SAV schemes. It is shown that the semi-discrete-in-time schemes are unconditionally energy stable when the GLTD is algebraically stable, and are convergent with the order of min ⁡ { q ˆ , ν } under the diagonal stability and some suitable regularity and accurate starting values, where q ˆ is the generalized stage order of the GLTD and ν denotes the number of the extrapolation points in time. The energy stability results can be easily extended to the fully discrete schemes, for example, if the Fourier spectral method is employed in space when the periodic boundary conditions are specified. Some numerical experiments on the Allen-Cahn, Cahn-Hilliard, and phase field crystal models are conducted to validate those theories as well as the effectiveness, the energy stability and the accuracy of our schemes. [ABSTRACT FROM AUTHOR]

Abstract: Atomistic computer simulation techniques have been used, for the first time, to reproduce the crystal structure of MgTa2O6 and to investigate the defect chemistry and dopant properties of this material. The calculated defect energetics suggest that the concentration of intrinsic atomic defects in this phase is insignificant and that the system is probably stable to both oxidation and reduction. Dopant solution energy versus ion size trends are found for both isovalent and aliovalent dopant incorporation at Mg and Ta sites. Divalent dopants (e.g. Ca, Cu) preferentially occupy the Mg site whereas dopants with higher charge (e.g. Sc, Zr, Nb) are more favorable on the Ta site. High migration activation energies (>2eV) predict limited ionic conductivity in this material. [Copyright &y& Elsevier]

• A new fluid-structure circular cylindrical shell spectral element is proposed. • Periodic structures and phononic crystals (PCs) are modeled by spectral element. • Simulated examples with in vacuo and fluid-filled cylindrical shell are evaluated. • Dispersion diagrams and force responses are obtained for the PCs. Cylindrical shells are frequently applied as structural elements in engineering, and have been used for many applications due to their favorable stiffness to weight ratio. More recently they have been used as new periodic composite materials known as phononic crystals, which are a periodic arrangement of unit cells built as a combination of layers with high impedance variation. Periodicity generates Bragg wave scattering that produces stop bands or band gaps where waves do not propagate. This attribute allows us to search by new and efficient solutions to control noise and vibration in structures. The aim of this paper is to propose a spectral element based on the analytical model of a closed circular cylindrical shell with internal fluid. The formulation is verified and its performance and efficiency in calculating periodic structures and elastic phononic crystals are evaluated. In this sense, the band gaps generated by the Bragg scattering effect and the attenuation bands of forced responses are calculated for phononic crystals modeled with the proposed cylindrical shell spectral element. The Spectral Element model involves exactly (or approximately) solving the governing equations of motion in the frequency domain and uses the solutions to derive the dynamic stiffness matrix formulated in a way analogous to the conventional Finite Element method. Free and forced responses for homogeneous cylindrical shells are investigated and the results are verified. Simulated examples using conventional structures and phononic crystals modeled with the proposed cylindrical shell spectral element (with and without internal fluid) are presented and the results are shown as dispersion diagrams and displacement responses. [ABSTRACT FROM AUTHOR]

We consider a family of evolution equations that generalize the Peierls-Nabarro model for crystal dislocations. They can be seen as semilinear parabolic reaction-diffusion equations in which the diffusion is regulated by a fractional Laplace operator of order 2 s ∈ (0 , 2) acting in one space dimension and the reaction is determined by a 1-periodic multi-well potential. We construct solutions of these equations that represent the typical propagation of N ⩾ 2 equally oriented dislocations of size 1. For large times, the dislocations occur around points that evolve according to a repulsive dynamical system. When s ∈ (1 / 2 , 1) , these solutions are shown to be asymptotically stable with respect to odd perturbations. [ABSTRACT FROM AUTHOR]

• Detailed description of photonic crystal fiber modeling technique. • Model outputs provide accurate properties of the studied photonic crystal fiber. • Possible imprecisions due to model simplification are presented. • Model accuracy is proven by measurements. We present a simple but highly accurate modeling technique for real photonic crystal fibers (PCFs) characterization. We determine the influence caused by idealized model parameters. Our technique can be applied to arbitrary PCF air-hole structures, as it takes into account all structural distortions. It requires only an image of the PCF cross-section to create an accurate PCF model. Model outputs are presented in comparison with the measurement of chromatic dispersion curve and the effective mode area. We provide a study on the impact of imprecise determination of glass refractive index on the PCF model accuracy. We demonstrate how the simplification of the air-hole deformations can influence the chromatic dispersion curve. Finally, we show the effect of precise PCF modeling on example of supercontinuum generation. [ABSTRACT FROM AUTHOR]

Sodium cobalt di(phosphate/arsenate) Na 2 CoP 1.5 As 0.5 O 7 has been synthesized as polycrystalline powder and single crystals by solid state reaction. The structure has been determined by X-ray diffraction at room temperature. The title material crystallizes in the tetragonal system, space group P 4 2 / mnm with the unit cell parameters: a = 7.764(3) Å, c = 10.385(3) Å, V = 626.0(4) Å3 and Z = 4. The two tools of crystal structure validation, Bond Valence Sum (BVS) and Charge distribution (CHARDI) methods, have confirmed the crystal structure model. The anionic framework is built of layers of corner sharing (P/As)O 4 and CoO 6 polyhedra. The sodium atoms are located in the interlayer space. Quantitative analysis using ICP-MS is used to confirm the elemental composition of the polycrystalline powder. Thermal analyzes show a phase transition at 675 °C before the melting point of 700 °C. The electrical properties of the title compound have been characterized by impedance spectroscopy in the 240°C–360 °C temperature range. At 240 °C, the conductivity value of the sample with relative density of 85% is 4 10−6 Scm−1 and the activation energy was Ea = 0.56 eV. The calculated conductivity corrected for porosity is σ d (240°C) = 1.88 10−5 Scm−1. The Na+ transport pathways in the interlayer space was simulated using the Band Valence Site Energy (BVSE) model. The BVSE model was also used to explain the effect of the P/As substitution on the electrical properties of the title compound. Correlation between structure and ionic conductivity using BVSE model simulation. Image 1 • Na 2 CoP 1.5 As 0.5 O 7 was synthesized by solid state reaction and its structure determined by XRD. • DTA-TG analysis were used to determine the thermal stability of Na 2 CoP 1.5 As 0.5 O 7 of the tetragonal form. • Electrical properties of Na 2 CoP 1.5 As 0.5 O 7 was characterized by impedance spectroscopy in the 240°C–360 °C temperature range. • Na+ migration pathways are simulated by means of the bond valence site energy (BVSE) model. [ABSTRACT FROM AUTHOR]

• Reduced models and numerical methods for electroconvection in thin liquid crystals. • Comparison between infinite and slim electrodes configurations. • Extensive numerical parameter study. We propose a finite element method for the numerical simulation of electroconvection of thin liquid crystals. The liquid is located in between two concentric circular electrodes which are either assumed to be of infinite height or slim. Each configuration results in a different nonlocal electro-magnetic model defined on a two dimensional bounded domain. The numerical method consists in approximating the surface charge density, the liquid velocity and pressure, and the electric potential in the two dimensional liquid region. Finite elements for the space discretization coupled with standard time stepping methods are put forward. Unlike for the infinite electrodes configuration, our numerical simulations indicate that slim electrodes are favorable for electroconvection to occur and are able to sustain the phenomena over long period of time. Furthermore, we provide a numerical study on the influence of the three main parameters of the system: the Rayleigh number, the Prandtl number and the electrodes aspect ratio. [ABSTRACT FROM AUTHOR]

A rotor is a core component of rotating machinery, but a cracked rotor should seriously threat its safe operation. In order to describe cracks in the rotor conveniently and improve the accuracy of the cracked position comparing with the lumped mass model, a novel crystal format model (CFM) of a rotor system is proposed in the paper. The CFM is made up of crystal grains which are arranged according to the certain rule, and the grain mass and the rotational inertia are considered. Specially, adjoined two crystal grains in the axial direction are connected by a massless elastic rod with a certain bending rigidity, and neighbor two crystal grains in y direction are connected by a massless spring and a torsion spring. The dynamic equations of the CFM are obtained by the bidirectional matrix derivation. The numerical simulations with using the CFM are studied systematically. In addition, the position and depth of a crack can be accurately expressed by the CFM of the rotor system with a breathing crack model and the vibration characteristics are also analyzed. The experimental results fully verify the correctness of the proposed CFM. [ABSTRACT FROM AUTHOR]