Double Lattice Research Articles

Double Grothendieck Polynomials and Colored Lattice Models

Abstract We construct an integrable colored six-vertex model whose partition function is a double Grothendieck polynomial. This gives an integrable systems interpretation of bumpless pipe dreams and recent results of Weigandt relating double Grothendieck polynomias with bumpless pipe dreams. For vexillary permutations, we then construct a new model that we call the semidual version model. We use our semidual model and the five-vertex model of Motegi and Sakai to give a new proof that double Grothendieck polynomials for vexillary permutations are equal to flagged factorial Grothendieck polynomials. Taking the stable limit of double Grothendieck polynomials, we obtain a new proof that the stable limit is a factorial Grothendieck polynomial as defined by McNamara. The states of our semidual model naturally correspond to families of nonintersecting lattice paths, where we can then use the Lindström–Gessel–Viennot lemma to give a determinant formula for double Schubert polynomials corresponding to vexillary permutations.

Homogeneous Incorporation of Gallium into Layered Double Hydroxide Lattice for Potential Radiodiagnostics: Proof-of-Concept.

Trivalent gallium ion was successfully incorporated into chemically well-defined MgAl-layered double hydroxide (LDH) frameworks through postsynthetic hydrothermal treatment. Quantitative analysis with inductively coupled plasma-mass spectroscopy exhibited that Ga3+ was first incorporated into LDH through partial dissolution-precipitation at the edge of LDH particle and homogeneously distributed throughout the particle by substitution of Ga3+ for Al3+ in LDH frame works. The powder X-ray diffraction patterns showed that the Ga3+ incorporation did not affect the crystal structure without evolution of unexpected impurities. The morphology and surface property of LDH evaluated by scanning electron microscopy and light scattering showed the preservation of physicochemical properties throughout 24 h of hydrothermal reaction. The distribution of incorporated Ga3+ was visualized with energy dispersive spectroscopy-assisted transmission electron microscopy, suggesting the homogeneous location of Ga3+ in an LDH particle. The X-ray absorption near-edge structure and extended X-ray absorption fine structure suggested that the Ga moiety was immobilized in LDH from 0.5 h and readily crystallized upon reaction time.

Phase equilibria and surface tension in castor oil‐based polyols‐water–methanol mixture: Thermodynamic basis

AbstractConsidering the current environmental issues with petro‐polymers, castor oil is a promising green alternative to the polyols to be used as the main raw material for polyurethane. However, the basic information regarding the processability of castor oil‐based polyol (CP) such as its miscibility in different solvents is still elusive. Herein we have investigated the phase equilibria and surface tension of various CP solutions using thermo‐optical analysis and pendent drop method, respectively. The modified double lattice (MDL) model was employed to theoretically describe those phase equilibria and surface behaviors. The phase diagrams of CPs/methanol binary systems represent upper critical solution temperature (UCST) behaviors, and CPs/methanol/water ternary systems show Treybal Type 2 behaviors. The surface tension results exhibit preferential solvent adsorption, which means affinity of the solvent to be present in surface is higher than that of the polymer. The calculated results showed good agreement with the experimental observations.

Modulation Effect Generated by A Cations in Hybrid A2BB’X6 Double Halogen Perovskite Materials

The double perovskite A2BB'X6, including all-inorganic and hybrid organic inorganic composition, show great potential applica-tions. The role of A cations (organic molecules or inorganic ions) in double perovskite is distinct from that in standard perovskite. Therefore, we carried out systematic analyses on the geometric and electronic structures of Cs2AgBiBr6 and (MA)2AgBiBr6 (MA=CH3NH3) double perovskite. Cs2AgBiBr6 maintains the standard cubic double perovskite lattice. While MA molecules pre-fer to align with [110] direction in (MA)2AgBiBr6 and give birth to the obvious lattice distortion. The band gap of (MA)2AgBiBr6 is slightly less than that of Cs2AgBiBr6. Because of the spherical or quasi-spherical wave functions of the s/d orbitals, the lattice distortion and the transverse shift between Ag/Bi and Br induced by MA molecules don't change the composition of the band edges. But the complex bonding interactions between MA and the inorganic frameworks make the Ag-Br or Bi-Br bond lengths no longer one identical value, so the bond strength and the energy level of each bonding states are dispersed and the band is ex-panded, which reduces the band gap of the hybrid organic inorganic double perovskite (MA)2AgBiBr6. Making the role of A cati-ons in A2BB'X6 double perovskite clear, we could find excellent double perovskite to put forward their applications.

Linearized lattice Boltzmann Method for time periodic electro-osmotic flows in micro- and nanochannels

Time periodic electro-osmosis (TPEO) is a popular means to pump liquids or manipulate species of interest in today’s micro- and nanofluidic devices. In this article, we propose a double distribution-function lattice Boltzmann (LB) model to describe its oscillatory flows coupled with electrokinetics in micro- and nanochannels. To remove advective effects, we derive the LB model from a linearized Boltzmann Bhatnagar–Gross–Krook-like equation and formulate its equations depending on the alternating current (AC) frequency, instead of time. This treatment facilitates a direct comparison of the LB results to experimental measurements in practical applications. We assessed accuracy of the proposed frequency-based Linearized LB model by simulating time periodic electro-osmotic flows (TPEOFs) with a thin and a thick electric double layer (EDL) at different Stokes parameters. The results are in excellent agreement with analytical solutions. The model was used to simulate TPEOFs with various EDL thicknesses and those driven by an AC electric field combined with an oscillatory pressure gradient. The simulations show distinct distributions of the electric potential and solution velocity subject to different length ratios and frequency ratios in the flows and interesting flow responses to compounding influences of the applied electric and mechanical driving fields. Importantly, diverse vortex patterns and vorticity variations were also revealed for TPEOFs in heterogeneously charged channels. These results demonstrate that the LB model developed in this article can well capture rich TPEO flow characteristics in micro- and nanochannels. It is effective for design and optimization of TPEO-based micro- and nanofluidic devices.

Thermodynamic framework for switching the lower critical solution temperature of thermo-sensitive particle gels in aqueous solvent

Switching the lower critical solution temperatures (LCSTs) of thermo-sensitive particle gels including poly(N-isopropylacrylamide) (PNIPAM), poly(N-diethylacrylamide) (PNDEAM), and poly(N-vinylcaprolactam) (PNVCL) was investigated in various aqueous solvents. Three prepared particle gels represented a single LCST in a pure water solution near human body temperature. By adding a chaotropic co-solvent, such as dimethylformamide (DMF) or dimethyl sulfoxide (DMSO), to given gels in aqueous solution, the degree of influence on change of LCST was significantly different due to the difference in chemical structures. LCSTs of polymer solutions were affected by changing solvent conditions from pure water to mixed solvents. The LCST behaviors of linear PNIPAM, PNDEAM, and PNVCL in water/DMF or DMSO were determined by thermo-optical analysis (TOA), which supported the switchability of LCSTs in hydrogel systems. We used the photon correlation spectroscopy (PCS) technique to measure the switched LCSTs of hydrogel particles in mixed solvent systems. The switched LCSTs of the investigated systems exhibited a non-linear trend by varying co-solvent contents. A molecular thermodynamic framework, a combination of the modified double lattice with chain length dependence (MDL-CL) model and the Flory-Rehner (F-R) model, was utilized to describe and correlate the liquid-liquid equilibrium (LLE) and thermosensitive swelling behaviors between linear and cross-linked polymer solutions. With the addition of chaotropic co-solvents, a non-linear trend for phase behaviors of the three polymers was described after taking into account temperature and composition dependence on the association fraction (ηij) between the species. We assumed the donor-acceptor concept and competitive hydrogen bonding between polymer/water and water/co-solvent. The association fraction for the secondary lattice model was modified from an arbitrarily determined value to a physically meaningful value. Accordingly, the phase equilibrium of the amphiphilic polymers influenced by the structure-breaker characteristics of the co-solute was properly implemented in both experimental and modeling aspects.

Compressive behavior and failure modes of the wood-based double X-type lattice sandwich structure

In this paper, a wood-based double X-type lattice sandwich structure was manufactured where wood-plastic composites (WPC) and Oriented Strand Boards (OSB) were used as panels, birch and glass fiber reinforced plastic (GFRP) were used as cores via a type of insertion-glue method. The compressive behavior and failure modes of the wood-based double X-type lattice sandwich structure were investigated by a flatwise compressive test and an analytical model. Results from the flatwise compressive test and the analytical model showed that the failure modes of the combination of WPC + GFRP and OSB + GFRP were primarily panel failure, while the failure modes of the combination of WPC + birch and OSB + birch were primarily core shear failure. The diameter of the core influenced the compressive performance of the double X-type lattice sandwich structure. The combination of OSB + birch with both core and panel damaged had better compression performance. The theoretical model was better suited for the combination of OSB + birch. The combination of OSB + GFRP and OSB + birch had larger specific strength and modulus, which was lighter in weight and higher in strength.

Crystal structure and cation ordering in novel perovskite type oxides PrBaCoTa(Nb)O6–δ

Novel complex oxides PrBaCoNbO6–δ (PBCN) and PrBaCoTaO6–δ (PBCT) are obtained via solid state reactions. X-ray and electron diffraction data for PBCN and PBCT demonstrate cubic space symmetry (S.G. Fm–3m) of the double perovskite crystalline lattice characterized by the rock salt type ordered arrangement of Co/Nb and Co/Ta and random distribution of Pr/Ba atoms. The ab initio electronic structure calculations reveal that the disordered elementary cell is distinguished with the minimum energy. The optical measurements show that PBCN and PBCT compounds are semiconducting materials having maximum light absorption in ultraviolet (UV) region which is consistent with the computer simulations of electronic structure. The thermodynamic modeling results suggest that the structural robustness of PBCN and PBCT phases at heating may be related with large absolute values of oxygen partial enthalpies.

MRT-LBM simulation of mixed convection in a horizontal channel heated from below by sinusoidal temperature profile

In this work, a numerical study is carried out to investigate the effect of Rayleigh number on mixed convection in a horizontal channel heated from below by sinusoidal temperature profile and cooled from above. The multiple relaxation time double population thermal lattice Boltzmann method (MRT-TLBM) is used. A validation of our code is done by comparing our results with those found in the literature. Particle oscillation amplitude and temperature profile are plotted for Ra = 5 103, while the Reynolds number, the aspect ratio and Prandtl number are fixed at Re = 10, B=10, Pr = 0.667 respectively. The effect of Rayleigh number on the heat transfer is also discussed.

Exchange bias and spin glass states driven by antisite disorder in the double perovskite compound LaSrCoFeO6

Antisite (B-site) disorder in double perovskite lattice is responsible for various magnetic phenomena such as exchange bias, spin glass, memory effect, colossal magnetoresistance, etc. By controlling the antisite disorder in the antiferromagnetic double perovskite ${\mathrm{LaSrCoFeO}}_{6}$, we achieve intrinsic exchange bias effect with a large exchange bias field ($\ensuremath{\sim}1.2$ kOe) and giant coercive field ($\ensuremath{\sim}12.8$ kOe). Further, we find that the effect of such antisite disorder induces a spin-glass state in ${\mathrm{LaSrCoFeO}}_{6}$. Multiple signatures of slow dynamics were confirmed by frequency-dependent peak shift, slow spin relaxation, and memory effect over a wide temperature regime ($5\ensuremath{-}80$ K). The AC susceptibility data near the spin-glass temperature ($\ensuremath{\sim}72.1\ifmmode\pm\else\textpm\fi{}0.6$ K) are best fit by a critical slowing down model described by a dynamical exponent $\mathrm{z}\ensuremath{\nu}=7.5\ifmmode\pm\else\textpm\fi{}0.5$ and ${\ensuremath{\tau}}_{0}=1.05\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ s. The origin of exchange bias and spin glass are briefly discussed.

Optimization and Measurements on the Double Mini-Betay Lattice in the TPS Storage Ring

The Taiwan Photon Source (TPS) is capable of operating in multi-bunch and single-bunch mode. To operate in a hybrid mode as requested by users, we developed a lattice with chromaticities of 0.8/2 (ξx/ξy) to provide higher single bunch currents. Beam dynamics simulations and lattice characterizations including dynamic aperture, frequency map analysis, tune shift with energy, tune shift with amplitude, and betatron coupling will be discussed in this report.

Optimization and Measurements on the Double Mini-Betay Lattice in the TPS Storage Ring

The Taiwan Photon Source (TPS) is capable of operat-ing in multi-bunch and single-bunch mode. To operate in a hybrid mode as requested by users, we developed a lattice with chromaticities of 0.8/2 (x/y) to provide higher single bunch currents. Beam dynamics simulations and lattice characterizations including dynamic aperture, frequency map analysis, tune shift with energy, tune shift with amplitude, and betatron coupling will be discussed in this report.

Effect of modelling complexities on extreme wind hazard performance of steel lattice transmission towers

Reliable computational models of transmission towers are key to improved hurricane risk management of transmission systems. However, a comprehensive understanding of involved complexities and their effects on the extreme wind performance of towers is not available. Particularly, buckling effects have not been captured properly and the failure of joints and the post-buckling behaviour of towers have not been investigated. Moreover, contributions of these and other complexities to key tower responses in the presence of uncertainties are not known. This paper presents an approach to modelling lattice towers that captures buckling and post-buckling, and joint slippage and failure and analyses their effects, while considering uncertainties, through a set of probabilistic, nonlinear pushover analyses in OpenSEES. Results for a double circuit vertical lattice tower indicate that buckling can lead to 30% reduction in the load-bearing capacity of towers. Joint slippage reduces the load-bearing capacity of the tower by 6%. It also considerably increases tower displacement. Connection failure can also occur in rare cases and it subsequently, changes tower’s failure mode. The proposed modelling approach can be used in risk analysis of transmission systems to investigate various performance levels and improve the design of towers.

Embedded solitons in the double sine-Gordon lattice with next-neighbor interactions.

Topological solitons can propagate without radiation in discrete media. These solutions are known as embedded solitons (ES). They come as isolated solutions and exist despite their resonance with the linear spectrum of the respective lattices. In this paper the properties of embedded solitons in the discrete double sine-Gordon equation with next-neighbor and second-neighbor interactions are investigated. Depending on the sign of these interactions they can be either destructive or favorable for the ES creation. The ES existence area depends on the width of the linear spectrum: narrowing of the spectrum widens the ES existence range and vice versa. The application to the Josephson junction arrays is discussed.

Landing-limited aggregation and prime number detection

An aggregation model is introduced based on the principles that N freely diffusing monomers stick together to form a cluster when they touch, the motion of clusters is directed, and limited by the requirement that a cluster be displaced over its entire size in one go if space permits. A successful displacement thus implies that the cluster lands on an unoccupied space adjacent to, and of the same size and shape as, the space which it occupied before the move. This “landing-limited aggregation” (LLA) can be motivated, for example, in the context of statistical mechanical modelling of the migration of animals herds, either self-organized in the wild or under human surveillance. This LLA is studied at fixed monomer density 1/2 on a periodic 1d lattice, or variations of it (staircase or double chain lattice), and on the 2d square lattice. In general the dynamics leads to three possible final states for the aggregate: a single cluster or “N-mer” containing the entire population, an arrested state in which multiple clusters are stuck in place, or multiple clusters that continue to move on the lattice without ever aggregating. On the 1d and the staircase lattices prime numbers play an interesting role in excluding certain final states. For example, for an initial condition on the periodic 1d lattice consisting of N monomers mutually separated by a vacant site, the final state never consists of just two clusters if and only if N is prime.

Three-body constrained bosons in a double-well optical lattice

We analyse the ground-state properties of three-body constrained bosons in a one dimensional optical lattice with staggered hoppings analogous to the double well optical lattice. By considering attractive and repulsive on-site interactions between the bosons, we obtain the phase diagram which exhibits various quantum phases. Due to the double-well geometry and three-body constraint several gapped phases such as the Mott insulators and dimer/bond-order phases emerge at commensurate densities in the repulsive interaction regime. Attractive interaction leads to the pair formation which leads to the pair bond order phase at unit filling which resembles the valence-bond solid phase of composite bosonic pairs. At incommensurate densities we see the signatures of the gapless pair superfluid phase.

Lithium Ion Conductivity in Double Antiperovskite Li6.5OS1.5I1.5: Alloying and Boundary Effects

Solid electrolytes based on theoretically identified double antiperovskite phases Li6OSI2 were successfully synthesized. Experimental characterization supported the theoretical prediction that S substitution of O leads to stabilization of the double antiperovskite structure and lattice softening to significantly enhance ionic conductivity, so that the total Li+ conductivity in Li6.5OS1.5I1.5 was two to three orders better than that of the best stoichiometric antiperovskite phase Li3OCl. However, both antiperovskite and double antiperovskite materials are fundamentally susceptible to surface reconstruction, which is behind significant boundary resistances typically known for materials based on antiperovskite hali-chalcogenides. Such a surface related problem was then effectively reduced through amorphous phase formation, thus offering a feasible route to exploit the full potential of this class of new materials as competitive candidates for solid Li-ion batteries.

Lower estimate of the fundamental frequency of natural oscillations of a truss with an arbitrary number of panels

Introduction: the paper deals with oscillations of a statically definable plane, truss with a double lattice of racks and descending braces with massive loads in the nodes of the lower chord. The weight of the truss rods is not taken into account. It is assumed that the freights are moved only vertically. The fundamental frequency of natural oscillations is estimated from the Dunkerley formula by the values of partial frequencies. Materials and methods: an analytical estimate is obtained by generalizing formulas obtained from a series of estimates for trusses with a consistently increasing number of panels. The stiffness of the truss was determined using the Mohr’s integral. The double lattice of the truss does not allow using the cross-section method; therefore, the forces in the rods were calculated (or estimated) in an analytical form using the method of cutting nodes with the compilation of a system of equilibrium equations simultaneously for all rods and three support reactions. The matrix of equilibrium equations was compiled in a software program written in the language of the Maple computer mathematics system based on the coordinates of the nodes and the values of the direction cosines of the forces. For a sequence of coefficients of the desired formula, linear homogeneous recurrent equations were found and solved by means of special operators of the Maple system. Results: the resulting formula estimating the relationship between the fundamental frequency and the panels number has the form of a sixth degree polynomial with coefficients depending on the parity of the number of panels. The analytical result is compared with the smallest frequency obtained numerically from the solution of the problem of oscillation of the cargo system. It is shown that the main frequency, depending on the truss height, has an extremum. Conclusions: the method of generalizing particular solutions using the Maple system operators allowed authors to obtain and analyze a formula for a lower estimate of the fundamental frequency of oscillation of a truss model with an arbitrary number of panels. The resulting estimate can be used as a test for numerically obtained solutions. The formula is especially efficient for systems with a large number of panels; as numerical methods for their calculation are time-consuming require considerable time and have a tendency for accumulating rounding errors.

Site occupancy and spectroscopic properties of Mn4+ in double perovskites, La2MgGeO6

The spectroscopic properties of Mn4+ (3 d3) in the La2MgGeO6 double perovskite is the subject of this investigation. The optical data have been used to perform detailed crystal field calculation of the Mn4+ energy level scheme. In La2GeMgO6, the Mn4+ can occupy either the octahedral Mg2+ or the Ge4+ sites. To address the question of site occupation, the Mn4+ energy levels were calculated when the ion substitutes for the Mg2+ and Ge4+ sites of the double perovskite lattice. An unambiguous decision on the site occupation cannot be reached based on our calculations. A comparative study of the variations in the energy of the 2Eg→4A2g emission transition in a series of materials with the double perovskite structure is presented. The energy of the 2Eg→4A2g emission transition tends to increase with increasing distortion of the octahedral O–Mn–O bond angle from the ideal 90°.

Droplet condensation and jumping on structured superhydrophobic surfaces

A complete cycle of droplet nucleation, growth, coalescence and jumping on different textured hydrophobic and superhydrophobic surfaces is studied for the first time, using a 2-D double distribution function thermal lattice Boltzmann method. First, droplet nucleation mechanism on smooth and rough surfaces is studied in detail. The results reveal the presence of cooled vapor layer instability in the condensation on completely smooth surfaces. However, on the rough surfaces and near the roughness a completely different mechanism is observed and the nucleation occurs on the roughness wedges. Also, the condensation on different textured surfaces with nominal contact angles θa=90°,120°,155° is studied. On all these surfaces it is observed that for small textures the nucleation occurs normally near the structure wedges. However, increasing the height of the textures displaces the nucleation sites to the top of the structure, near the structure edge. After growing the droplets different behaviors are observed for different contact angles, i.e., the Wenzel or suspended droplets are formed and the droplets even jump out. Moreover, based on the non-dimensional numbers a complete study of droplet jumping is carried out and a method for proper designing the textured surfaces is presented. Finally, the benefits of using hybrid textured surfaces and the mechanism of droplet jumping on these surfaces are explained.