Entire Lattice Research Articles

Unconventional Flatband Line States in Photonic Lieb Lattices

Flatband systems typically host "compact localized states" (CLS) due to destructive interference and macroscopic degeneracy of Bloch wave functions associated with a dispersionless energy band. Using a photonic Lieb lattice (LL), such conventional localized flatband states are found to be inherently incomplete, with the missing modes manifested as extended line states that form noncontractible loops winding around the entire lattice. Experimentally, we develop a continuous-wave laser writing technique to establish a finite-sized photonic LL with specially tailored boundaries and, thereby, directly observe the unusually extended flatband line states. Such unconventional line states cannot be expressed as a linear combination of the previously observed boundary-independent bulk CLS but rather arise from the nontrivial real-space topology. The robustness of the line states to imperfect excitation conditions is discussed, and their potential applications are illustrated.

Behavior of eccentrically loaded welded hollow spherical joints after elevated-temperature exposure

Welded hollow spherical joint is an extremely widely used connection pattern in space lattice structures. Understanding the behavior of the welded hollow spherical joint after elevated-temperature exposure is critical for the fire damage assessment of the entire space lattice structures. In this study, both experimental and numerical studies were conducted to reveal the mechanical behavior of eccentrically loaded welded hollow spherical joints subjected to eccentric loads after cooling from three elevated temperatures up to 1000°C, wherein two different methods were considered, namely, air and water cooling. Associate mechanical performance, such as load versus longitudinal displacement and load versus steel tube rotation responses, initial stiffness, load-bearing capacities, and strain development, were obtained and further analyzed. The results showed that the behavior of welded hollow spherical joints began to change when the exposure temperatures exceeded 600°C, with obvious reductions in both stiffness and strength. In addition, the influences of different cooling methods were significant. The joints cooled by water generally presented higher load-bearing capacities than those cooled by air. Furthermore, three-dimensional finite element analysis was conducted via ABAQUS software. After validating the finite element model against experimental results, parametric studies were performed and a practical formula was proposed to calculate the load-bearing capacity of welded hollow spherical joints subjected to eccentric load after elevated-temperature exposure.

Acoustic nonreciprocity in a lattice incorporating nonlinearity, asymmetry, and internal scale hierarchy: Experimental study.

In linear time-invariant systems acoustic reciprocity holds by the Onsager-Casimir principle of microscopic reversibility, and it can be broken only by odd external biases, nonlinearities, or time-dependent properties. Recently it was shown that one-dimensional lattices composed of a finite number of identical nonlinear cells with internal scale hierarchy and asymmetry exhibit nonreciprocity both locally and globally. Considering a single cell composed of a large scale nonlinearly coupled to a small scale, local dynamic nonreciprocity corresponds to vibration energy transfer from the large to the small scale, but absence of energy transfer (and localization) from the small to the large scale. This has been recently proven both theoretically and experimentally. Then, considering the entire lattice, global acoustic nonreciprocity has been recently proven theoretically, corresponding to preferential energy transfer within the lattice under transient excitation applied at one of its boundaries, and absence of similar energy transfer (and localization) when the excitation is applied at its other boundary. This work provides experimental validation of the global acoustic nonreciprocity with a one-dimensional asymmetric lattice composed of three cells, with each cell incorporating nonlinearly coupled large and small scales. Due to the intentional asymmetry of the lattice, low impulsive excitations applied to one of its boundaries result in wave transmission through the lattice, whereas when the same excitations are applied to the other end, they lead in energy localization at the boundary and absence of wave transmission. This global nonreciprocity depends critically on energy (i.e., the intensity of the applied impulses), and reduced-order models recover the nonreciprocal acoustics and clarify the nonlinear mechanism generating nonreciprocity in this system.

Dynamics of structural and magnetic phase transitions in ferroborate YFe3(BO3)4

X-ray analysis of the YFe3(BO3)4 single crystal revealed different behavior of parameters of the crystal cell with an increase in temperature from 25 to 500 K. The parameters a and b initially increase monotonically and then rise sharply in the range between 360 and 380 K, which corresponds to the structural phase transition. The parameter c initially decreases linearly upon heating and then begins to increase, passing through a minimum at 90 K. In the interval of 200–500 K the parameter c grows linearly and does not undergo anomalies at the structural phase transition. The results of Mössbauer measurements at 57Fe nuclei in the paramagnetic phase of YFe3(BO3)4 correlate well with the XRD data, but they do not separate the two structural states of iron ions Fe1 and Fe2 arising in the P3121 phase during the structural phase transition. The temperature of the magnetic phase transition TN = 39.42(16) K is established, below which the iron ions form a 3D magnetic order of the Heisenberg type. The calculated “Mössbauer” Debye temperature ΘM = 340(2) K turned out to be three times lower than the Debye temperature of the entire crystal lattice TD = 1020 K. Mössbauer data indicate a weak bonding between the helicoidal chains of iron and the rest of the crystal lattice.

Principal component analysis for fermionic critical points

We use determinant Quantum Monte Carlo (DQMC), in combination with the principal component analysis (PCA) approach to unsupervised learning, to extract information about phase transitions in several of the most fundamental Hamiltonians describing strongly correlated materials. We first explore the zero temperature antiferromagnet to singlet transition in the Periodic Anderson Model, the Mott insulating transition in the Hubbard model on a honeycomb lattice, and the magnetic transition in the 1/6-filled Lieb lattice. We then discuss the prospects for learning finite temperature superconducting transitions in the attractive Hubbard model, for which there is no sign problem. Finally, we investigate finite temperature charge density wave (CDW) transitions in the Holstein model, where the electrons are coupled to phonon degrees of freedom, and carry out a finite size scaling analysis to determine $T_c$. We examine the different behaviors associated with Hubbard-Stratonovich auxiliary field configurations on both the entire space-time lattice and on a single imaginary time slice, or other quantities, such as equal-time Green's and pair-pair correlation functions.

Varieties of BL-Algebras II

In this paper we introduce a poset of subvarieties of BL-algebras, whose completion is the entire lattice of subvarietes; we exhibit also a description of this poset in terms of finite sequences of functions on the natural numbers.

Quasi-periodic solutions of the Belov–Chaltikian lattice hierarchy

Utilizing the characteristic polynomial of Lax matrix for the Belov–Chaltikian (BC) lattice hierarchy associated with a [Formula: see text] discrete matrix spectral problem, we introduce a trigonal curve with three infinite points, from which we establish the associated Dubrovin-type equations. The essential properties of the Baker–Akhiezer function and the meromorphic function are discussed, that include their asymptotic behavior near three infinite points on the trigonal curve and the divisor of the meromorphic function. The Abel map is introduced to straighten out the continuous flow and the discrete flow in the Jacobian variety, from which the quasi-periodic solutions of the entire BC lattice hierarchy are obtained in terms of the Riemann theta function.

Molecular interactions between tubulin tails and glutamylases reveal determinants of glutamylation patterns.

Posttranslational modifications of tubulin currently emerge as key regulators of microtubule functions. Polyglutamylation generates a variety of modification patterns that are essential for controlling microtubule functions in different cell types and organelles, and deregulation of these patterns has been linked to ciliopathies, cancer and neurodegeneration. How the different glutamylating enzymes determine precise modification patterns has so far remained elusive. Using computational modelling, molecular dynamics simulations and mutational analyses we now show how the carboxy-terminal tails of tubulin bind into the active sites of glutamylases. Our models suggest that the glutamylation sites on α- and β-tubulins are determined by the positioning of the tails within the catalytic pocket. Moreover, we found that the binding modes of α- and β-tubulin tails are highly similar, implying that most enzymes could potentially modify both, α- and β-tubulin. This supports a model in which the binding of the enzymes to the entire microtubule lattice, but not the specificity of the C-terminal tubulin tails to their active sites, determines the catalytic specificities of glutamylases.

Development of a vector algorithm of three-dimensional crystal lattice parametric identification based on estimation of the spacing between adjacent lattice planes

The analysis of a crystal nanostructure is provided by the information obtained from the electron microscopy. Mathematically, a crystal structure is described by unit cells – minimum building blocks, which form the entire crystal lattice by parallel transfer. Parametric identification is an important problem in the field of three-dimensional crystal lattice research. Application of the constant step size gradient descent method to solve this problem ensured sufficient increase of the identification accuracy. However, computational complexity of the applied algorithm significantly exceeds the computational complexity of the existing parametric identification algorithms, which has caused substantial increment of the execution time. In order to eliminate such disadvantage this work proposes vector algorithm of crystal lattice parametric identification implemented with CUDA technology.

Application of the trigonal curve to the Blaszak–Marciniak lattice hierarchy

We develop a method for constructing algebro-geometric solutions of the Blaszak–Marciniak (BM) lattice hierarchy based on the theory of trigonal curves. We first derive the BM lattice hierarchy associated with a discrete (3×3)-matrix spectral problem using Lenard recurrence relations. Using the characteristic polynomial of the Lax matrix for the BM lattice hierarchy, we introduce a trigonal curve with two infinite points, which we use to establish the associated Dubrovin-type equations. We then study the asymptotic properties of the algebraic function carrying the data of the divisor and the Baker–Akhiezer function near the two infinite points on the trigonal curve. We finally obtain algebro-geometric solutions of the entire BM lattice hierarchy in terms of the Riemann theta function.

Molecular mobility with respect to accessible volume in Monte Carlo lattice model for polymers

Abstract A three-dimensional cubic Monte Carlo lattice model is considered to test the impact of volume on the molecular mobility of amorphous polymers. Assuming classic polymer chain dynamics, the concept of locked volume limiting the accessible volume around the polymer chains is introduced. The polymer mobility is assessed by its ability to explore the entire lattice thanks to reptation motions. When recording the polymer mobility with respect to the lattice accessible volume, a sharp mobility transition is observed as witnessed during glass transition. The model ability to reproduce known actual trends in terms of glass transition with respect to material parameters, is also tested.

Modification of semiconductor or metal nanoparticle lattices in amorphous alumina by MeV heavy ions

In the present work we investigate effects of MeV heavy ions (from 0.4 MeV Xe to 15 MeV Si) on regularly ordered nanoparticle (NP) lattices embedded in amorphous alumina matrix. These nanostructures were produced by self-assembling growth using magnetron-sputtering deposition. From grazing incidence small-angle x-ray scattering measurements we have found that the used MeV heavy ions do not change the NP sizes, shapes or distances among them. However, ions cause a tilt of the entire NP lattice in the direction parallel to the surface. The tilt angle depends on the incident ion energy, type and the applied fluence and a nearly linear increase of the tilt angle with the ion fluence and irradiation angle was found. This way, MeV heavy ion irradiation can be used to design custom-made NP lattices. In addition, grazing incidence small-angle x-ray scattering can be effectively used as a method for the determination of material redistribution/shift caused by the ion hammering effect. For the first time, the deformation yield in amorphous alumina was determined for irradiation performed at the room temperature.

Thermalization after photoexcitation from the perspective of optical spectroscopy

We analyze the thermalization of a photoexcited charge carrier coupled to a single branch of quantum phonons within the Holstein model. To this end, we calculate the far-from-equilibrium time evolution of a pure many-body state and compare it with predictions of the thermal Gibbs ensemble. We show that at strong enough carrier excitation, the nonequilibrium system evolves towards a thermal steady state. Our analysis is based on two classes of observables. First, the occupations of fermionic momenta, which are the eigenvalues of the one-particle density matrix, match in the steady state the values in the corresponding Gibbs ensemble. This indicates thermalization of static fermionic correlations on the entire lattice. Second, the dynamic current-current correlations, including the time-resolved optical conductivity, also take the form of their thermal counterparts. Remarkably, both static and dynamic fermionic correlations thermalize with identical temperatures. Our results suggest that the subsequent relaxation processes, observed in time-resolved ultrafast spectroscopy, may be efficiently described by applying quasithermal approaches, e.g., multi-temperature models.

Doping Zn(2+) in CuS Nanoflowers into Chemically Homogeneous Zn0.49Cu0.50S1.01 Superlattice Crystal Structure as High-Efficiency n-Type Photoelectric Semiconductors.

Doping Zn(2+) in CuS nanoflower into chemically homogeneous superlattice crystal structure is proposed to convert p-type CuS semiconductor to an n-type CuS semiconductor for significantly enhanced photoelectric response performance. In this study, the chemically homogeneous Zn-doped CuS nanoflowers (Zn0.06Cu0.94S, Zn0.26Cu0.73S1.01, Zn0.36Cu0.62S1.02, Zn0.49Cu0.50S1.01, Zn0.58Cu0.40S1.02) are synthesized by reacting appropriate amounts of CuCl and Zn(Ac)2·2H2O with sulfur powders in ethanol solvothermal process. By tuning the Zn/Cu atomic ratios to ∼1:1, the chemically homogeneous Zn-doped CuS nanoflowers could be converted to the perfect Zn0.49Cu0.50S1.01 superlattice structure, corresponding to the periodic Cu-S-Zn atom arrangements in the entire crystal lattice, which can induce an effective built-in electric field with n-type semiconductor characteristics to significantly improve the photoelectric response performance, such as the lifetime of photogenerated charge carriers up to 6 × 10(-8)-6 × 10(-4) s with the transient photovoltage (TPV) response intensity to ∼44 mV. This study reveals that the Zn(2+) doping in CuS nanoflowers is a key factor in determining the superlattice structure, semiconductor type, and the dynamic behaviors of charge carriers.

Positive Discrete Spectrum of the Evolutionary Operator of Supercritical Branching Walks with Heavy Tails

We consider a continuous-time symmetric supercritical branching random walk on a multidimensional lattice with a finite set of the particle generation centres, i.e. branching sources. The main object of study is the evolutionary operator for the mean number of particles both at an arbitrary point and on the entire lattice. The existence of positive eigenvalues in the spectrum of an evolutionary operator results in an exponential growth of the number of particles in branching random walks, called supercritical in the such case. For supercritical branching random walks, it is shown that the amount of positive eigenvalues of the evolutionary operator, counting their multiplicity, does not exceed the amount of branching sources on the lattice, while the maximal of these eigenvalues is always simple. We demonstrate that the appearance of multiple lower eigenvalues in the spectrum of the evolutionary operator can be caused by a kind of ‘symmetry’ in the spatial configuration of branching sources. The presented results are based on Green’s function representation of transition probabilities of an underlying random walk and cover not only the case of the finite variance of jumps but also a less studied case of infinite variance of jumps.

Canonical transformations and loop formulation of SU(N) lattice gauge theories

We construct canonical transformations to reformulate SU(N) Kogut-Susskind lattice gauge theory in terms of a set of fundamental loop & string flux operators along with their canonically conjugate loop & string electric fields. We show that as a consequence of SU(N) Gauss laws all SU(N) string degrees of freedom become cyclic and decouple from the physical Hilbert space ${\cal H}^p$. The canonical relations between the initial SU(N) link operators and the final SU(N) loop & string operators over the entire lattice are worked out in a self consistent manner. The Kogut-Susskind Hamiltonian rewritten in terms of the fundamental physical loop operators has global SU(N) invariance. There are no gauge fields. We further show that the $(1/g^2)$ magnetic field terms on plaquettes create and annihilate the fundamental plaquette loop fluxes while the $(g^2)$ electric field terms describe all their interactions. In the weak coupling ($g^2 \rightarrow 0$) continuum limit the SU(N) loop dynamics is described by SU(N) spin Hamiltonian with nearest neighbour interactions. In the simplest SU(2) case, where the canonical transformations map the SU(2) loop Hilbert space into the Hilbert spaces of hydrogen atoms, we analyze the special role of the hydrogen atom dynamical symmetry group $SO(4,2)$ in the loop dynamics and the spectrum. A simple tensor network ansatz in the SU(2) gauge invariant hydrogen atom loop basis is discussed.

Singular optical lattice generation using light beams with orbital angular momentum.

In this Letter we numerically and experimentally demonstrated that a lattice with an optical vortex distributed over the entire lattice can be generated in the Fourier space using three higher-order Laguerre-Gauss beams placed at the vertices of an equilateral triangle in real space. In this scheme the optical vortice's lattice presents a topological defect in its central region. Probing the net topological charge of the whole lattice, we found that it corresponds to the topological charge associated with the orbital angular momentum of each beam in real space.

Mapping the interactions of the single-stranded DNA binding protein of bacteriophage T4 (gp32) with DNA lattices at single nucleotide resolution: gp32 monomer binding.

Combining biophysical measurements on T4 bacteriophage replication complexes with detailed structural information can illuminate the molecular mechanisms of these ‘macromolecular machines’. Here we use the low energy circular dichroism (CD) and fluorescent properties of site-specifically introduced base analogues to map and quantify the equilibrium binding interactions of short (8 nts) ssDNA oligomers with gp32 monomers at single nucleotide resolution. We show that single gp32 molecules interact most directly and specifically near the 3′-end of these ssDNA oligomers, thus defining the polarity of gp32 binding with respect to the ssDNA lattice, and that only 2–3 nts are directly involved in this tight binding interaction. The loss of exciton coupling in the CD spectra of dimer 2-AP (2-aminopurine) probes at various positions in the ssDNA constructs, together with increases in fluorescence intensity, suggest that gp32 binding directly extends the sugar-phosphate backbone of this ssDNA oligomer, particularly at the 3′-end and facilitates base unstacking along the entire 8-mer lattice. These results provide a model (and ‘DNA map’) for the isolated gp32 binding to ssDNA targets, which serves as the nucleation step for the cooperative binding that occurs at transiently exposed ssDNA sequences within the functioning T4 DNA replication complex.

Wave propagation in two-dimensional anisotropic acoustic metamaterials of K4 topology

An acoustic metamaterial is envisaged as a synthesised phononic material the mechanical behaviour of which is determined by its unit cell. The present study investigates one aspect of mechanical behaviour, namely the band structure, in two-dimensional (2D) anisotropic acoustic metamaterials encompassing locally resonant mass-in-mass units connected by massless springs in a K4 topology. The 2D lattice problem is formulated in the direct space (r-space) and the equations of motion are derived using the principle of least action (Hamilton’s principle). Only proportional anisotropy and attenuation-free shock wave propagation have been considered. Floquet–Bloch’s principle is applied, therefore a generic unit cell is studied. The unit cell can represent the entire lattice regardless of its position. It is transformed from the direct lattice in r-space onto its reciprocal lattice conjugate in Fourier space (k-space) and point symmetry operations are applied to Wigner–Seitz primitive cell to derive the first irreducible Brillouin Zone (BZ). The edges of the first irreducible Brillouin Zone in the k-space have then been traversed to generate the full band structure. It was found that the phenomenon of frequency filtering exists and the pass and stop bands are extracted. A follow-up parametric study appreciated the degree and direction of influence of each parameter on the band structure.

Are the amide bonds inN-acyl imidazoles twisted? A combined solid-state17O NMR, crystallographic, and computational study

We report synthesis of17O-labeling and solid-state17O NMR measurements of three N-acyl imidazoles of the type R-C(17O)-Im: R = p-methoxycinnamoyl (MCA-Im), R = 4-(dimethylamino)benzoyl (DAB-Im), and R = 2,4,6-trimethylbenzoyl (TMB-Im). Solid-state17O NMR experiments allowed us to determine for the first time the17O quadrupole coupling and chemical shift tensors in this class of organic compounds. We also determined the crystal structures of these compounds using single-crystal X-ray diffraction. The crystal structures show that, while the C(O)–N amide bond in DAB-Im exhibits a small twist, those in MCA-Im and TMB-Im are essentially planar. We found that, in these N-acyl imidazoles, the17O quadrupole coupling and chemical shift tensors depend critically on the torsion angle between the conjugated acyl group and the C(O)–N amide plane. The computational results from a plane-wave DFT approach, which takes into consideration the entire crystal lattice, are in excellent agreement with the experimental solid-state17O NMR results. Quantum chemical computations also show that the dependence of17O NMR parameters on the Ar–C(O) bond rotation is very similar to that previously observed for the C(O)–N bond rotation in twisted amides. We conclude that one should be cautious in linking the observed NMR chemical shifts only to the twist of the C(O)–N amide bond.