One-dimensional Ca Research Articles

A faster algorithm for the Birthday Song Singers Synchronization Problem (FSSP) in one-dimensional CA with multiple speeds

In cellular automata with multiple speeds for each cell i there is a positive integer p_i such that this cell updates its state still periodically but only at times which are a multiple of p_i. Additionally there is a finite upper bound on all p_i. Manzoni and Umeo have described an algorithm for these (one-dimensional) cellular automata which solves the Firing Squad Synchronization Problem. This algorithm needs linear time (in the number of cells to be synchronized) but for many problem instances it is slower than the optimum time by some positive constant factor. In the present paper we derive lower bounds on possible synchronization times and describe an algorithm which is never slower and in some cases faster than the one by Manzoni and Umeo and which is close to a lower bound (up to a constant summand) in more cases.

Origin of Ising magnetism in Ca3Co2O6 unveiled by orbital imaging

The one-dimensional cobaltate Ca{}_{3}Co{}_{2}O{}_{6} is an intriguing material having an unconventional magnetic structure, displaying quantum tunneling phenomena in its magnetization. Using a newly developed experimental method, s-core-level non-resonant inelastic x-ray scattering (s-NIXS), we were able to image the atomic Co 3d orbital that is responsible for the Ising magnetism in this system. We can directly observe that corrections to the commonly accepted ideal prismatic trigonal crystal field scheme occur in Ca{}_{3}Co{}_{2}O{}_{6}, and it is the complex {d}_{2} orbital occupied by the sixth electron at the high-spin Co{}_{,text{trig},}^{3+} ({d}^{6}) sites that generates the Ising-like behavior. The ability to directly relate the orbital occupation with the local crystal structure is essential to model the magnetic properties of this system.

Crashworthiness optimization of VRB thin-walled structures under manufacturing constraints by the eHCA-VRB algorithm

Variable-thickness rolled blanks (VRBs) represent an important approach for constructing lightweight structures. However, the optimization of the crashworthiness and thickness distribution of VRB thin-walled structures under manufacturing constraints is a nonlinear dynamic-response structural-optimization problem that has a large number of design variables. To tackle this problem, this paper has extended and improved the hybrid cellular automaton for thin-walled structures (HCATWS) algorithm, and has proposed an extended hybrid cellular automaton for VRB thin-walled structures (eHCA-VRB) algorithm. This algorithm consists of an outer loop and an inner loop. The outer loop performs crash simulation analysis to define an appropriate target mass for the inner loop, whereas the inner loop adjusts cell thicknesses according to the internal energy density (IED) of the current cell and its neighboring cells so that the IED in the design domain becomes evenly distributed. A one-dimensional CA model is defined along with the rolling direction based on the thickness distribution of VRB thin-walled structures. Furthermore, the eHCA-VRB algorithm also generates a mapping relationship between the one-dimensional CA model and the FE model. To optimize the thickness distribution of VRB thin-walled structures under manufacturing constraints, our method uses cell thickness as a design variable and incorporates the constraints of the VRB rolling process in the cell thickness update rules. To verify the convergence and efficiency of the eHCA-VRB algorithm, VRB top-hat thin-walled structures are optimized for crashworthiness with/or without manufacturing constraints (M.C.), respectively. The results show that the eHCA-VRB algorithm can be used to efficiently solve the optimization problems of crashworthiness and the thickness distribution of VRB thin-walled structures under manufacturing constraints.

An Equivalent of XOR Operator and Its Application in One-Dimensional CA Model

An Equivalent of XOR Operator and Its Application in One-Dimensional CA Model

Calcium Coordination Solids for pH-Triggered Release of Olsalazine.

Calcium coordination solids were synthesized and evaluated for delivery of olsalazine (H4 olz), an anti-inflammatory compound used for treatment of ulcerative colitis. The materials include one-dimensional Ca(H2 olz)⋅4 H2 O chains, two-dimensional Ca(H2 olz)⋅2 H2 O sheets, and a three-dimensional metal-organic framework Ca(H2 olz)⋅2DMF (DMF=N,N-dimethylformamide). The framework undergoes structural changes in response to solvent, forming a dense Ca(H2 olz) phase when exposed to aqueous HCl. The compounds Ca(H2 olz)⋅x H2 O (x=0, 2, 4) were each pressed into pellets and exposed to simulated gastrointestinal fluids to mimic the passage of a pill from the acidic stomach to the pH-neutral intestines. All three calcium materials exhibited a delayed release of olsalazine relative to Na2 (H2 olz), the commercial formulation, illustrating how formulation of a drug within an extended coordination solid can serve to tune its solubility and performance.

A series of s-block (Ca, Sr and Ba) metal–organic frameworks: synthesis and structure–property correlation

A series of metal–organic frameworks based on alkaline earth metal ions (Ca, Sr and Ba) and 1,3,5-benzenetribenzoic acid (BTB) have been synthesized and characterized. These are [H2N(CH3)2][Ca7(BTB)5(H2O)8(DMF)4]·4H2O (1), [H2N(CH3)2]2[Sr5(H2O)6(BTB)4] (2) and [H2N(CH3)2][Ba(H2O)(BTB)] (3). All the structures are three-dimensional in nature with different secondary building units. Compound 1 contains one-dimensional Ca–O–Ca zigzag chains while compound 2 contains Sr5O28 pentameric clusters and compound 3 contains one-dimensional Ba–O–Ba chains. Both compounds 1 and 3 form (3,6)-net connectivity while compound 2 forms (3,12)-net connectivity. Optical band gap energy measurements show that compound 1 (2.65 eV) has low band gap energy compared to 2 (3.22 eV) and 3 (3.32 eV). This variation in band gap energy may be due to the difference in structural arrangement. Compound 3 crystallizes in a non-centrosymmetric space group (Pna21), which belongs to the polar point group C2v. This compound displays a strong SHG response and good ferroelectric and piezoelectric properties.

Stochastic Cellular Automata Solutions to the Density Classification Problem

In the density classification problem, a binary cellular automaton should decide whether an initial configuration contains more 0s or 1s. The answer is given when all cells of the CA agree on a given state (0 or 1). This problem is known for having no exact solution in the case of binary deterministic one-dimensional CA. We investigate how randomness in CA may help us solve the problem. We analyse the behaviour of stochastic CA rules that perform the density classification task. We show that describing stochastic rules as a ''blend'' of deterministic rules allows us to derive quantitative results on the classification time and the classification time of previously studied rules. We introduce a new rule whose effect is to spread defects and to wash them out. This stochastic rule solves the problem with an arbitrary precision, that is, its quality of classification can be made arbitrarily high, though at the price of a longer time to converge. We experimentally demonstrate that this rule exhibits good scaling properties and that it attains qualities of classification never reached so far.

Thickness-dependent optical band gap in one-dimensional Ca 3Co 2O 6 nanometric films

Recent studies on the physical properties of Ca 3Co 2O 6 nanometric samples have shown that their properties are significantly different from those of the bulk samples. The origin of this change is not trivial. We have carried out optical measurements on Ca 3Co 2O 6 thin films with different thicknesses in order to characterize their electronic structure using optical spectroscopy measurements. The absorption spectra show a dependence on the film thickness that is correlated to the grain size in the polycrystalline layers. We found that the optical band gap increases from 1.3 to 1.55 eV when the thickness changes from 35 to 100 nm. The change in the band gap evolution with the film thickness is discussed in terms of both the amorphous effect and the grain size in the Ca 3Co 2O 6 thin films. Finally, we show that these results are consistent with recent measurements concerning magnetic and electrical properties of Ca 3Co 2O 6 nanometric samples.

The fabrication of one-dimensional Ca 4Y 6(SiO 4) 6O: Ln 3+ (Ln = Eu, Tb) phosphors by electrospinning method and their luminescence properties

One-dimensional Ca 4Y 6(SiO 4) 6O: Ln 3+ (Ln = Eu, Tb) microfibers were fabricated by a simple and cost-effective electrospinning method. X-ray diffraction (XRD) pattern and high-resolution transmission electron microscopy (HRTEM) confirmed that the fibers were composed of hexagonal Ca 4Y 6(SiO4) 6O phase. Thermogravimetric and differential scanning calorimetry (TG–DSC) results showed that the Ca 4Y 6(SiO4) 6O phase began to crystallize at 740 °C. Scanning electron microscopy (SEM) and transmission electron microscopy (TEM) results indicated that the diameter of as-prepared microfibers ranged from 390 to 900 nm and the diameter of the microfibers annealed at 1000 °C ranged from to 120 to 260 nm. Under ultraviolet and low-voltage electron beams (3–5 kV) excitation, the Ca 4Y 6(SiO 4) 6O: Ln 3+ (Ln = Eu, Tb) samples showed the red and green emission, corresponding to 5D 0 → 7F 2 transition of Eu 3+ and 5D 4 → 7F 5 transition of Tb 3+, respectively.

ChemInform Abstract: Crystal Structure and Magnetic Properties of a One Dimensional Complex Oxide Ca3NiMnO6.

Abstract The results of structural refinements and magnetic properties of one-dimensional oxide Ca 3 NiMnO 6 are presented. The structure of Ca 3 NiMnO 6 was solved by Rietveld analysis of powder neutron date in space group R -3 c with a =9.1227(9) A, c =10.5811(17) A, z=6 (type of K 4 CdCl 6 ). Infinite chains of MnO 6 octahedra and (Ni,Mn)O 6 trigonal prisms sharing faces run parallel to the c axis. The chains are separated by Ca 2+ cations, which are located in a distorted square antiprismatic environment. Magnetic susceptibility obeys the Curie-Weiss law at 300–600 K with μ eff value 5.00 μ B consistent with the valence cationic combination Ni 2+ -Mn 4+ . Magnetic measurements display the antiferromagnetic ordering in Ca 3 NiMnO 6 at 16 K.

On the effect of memory in one-dimensional [formula omitted] automata on networks

The effect of implementing memory in cells of one-dimensional CA, and on nodes of various types of automata on networks with increasing degrees of random rewiring is studied in this article, paying particular attention to the case of four inputs. As a rule, memory induces a moderation in the rate of changing nodes and in the damage spreading, albeit in the latter case memory turns out to be ineffective in the control of the damage as the wiring network moves away from the ordered structure that features proper one-dimensional CA. This article complements the previous work done in the two-dimensional context.

On cellular automata over Galois rings

In this paper we study the invertibility of one-dimensional cellular automata, determined by a local rule, acting on the space of all doubly-infinite sequences taking values in a finite Galois ring. We also compute the topological entropy of one-dimensional CA generated by additive local rule over a finite Galois ring. We conclude by showing that the topological entropy of an additive invertible CA over a finite Galois ring is equal to its inverse.

Crystal structure analysis of [Ca(O3SC18H37)2(DMSO)2], a lamellar coordination polymer and its relevance for model studies in biomineralization

Single crystals of a one-dimensional Ca coordination polymer of the surfactant octadecyl sulfonate (C(18)H(37)SO(3)(-)) have been grown from hot DMSO solution. The X-ray structure analysis of the compound [Ca(O(3)SC(18)H(37))(2)(DMSO)(2)] (1) shows a lamellar interdigitated arrangement of hydrophobic tails of the amphiphilic ligands. Each Ca ion is coordinated by four different sulfonate groups, and its nearly octahedral coordination environment is completed by two dimethyl sulfoxide (DMSO) ligands. The octadecyl sulfonate ligand coordinates to Ca ions in a micro(2)-bridging mode, which contrasts to information from literature suggesting a micro(3)-bridging coordination mode. Since the growth of highly oriented calcite single crystals underneath Langmuir monolayers of this particular surfactant is often regarded as textbook example of a heteroepitaxy ("template") mechanism in biomineralization, we present a critical discussion of the crystal structure of the title compound in this context.

The topological entropy of nth iteration of an additive cellular automata

In this paper, our aim is to investigate the topological entropy of nth iteration of an one-dimensional additive cellular automata (CA hereafter), i.e. the maps T : Z m Z → Z m Z which are given by Tx = ( y n ) n = - ∞ ∞ , y n = F ( x n - r , … , x n + r ) = ∑ i = - r r λ i x n + i ( mod m ) , x = ( x n ) n = - ∞ ∞ ∈ Z m Z and F : Z m 2 r + 1 → Z m , over Z m ( m ⩾ 2 ) by means of both the algorithm and Lyapunov exponents of the CA T that is given by D’amico et al. [Theor. Comput. Sci. 290 (2003) 1629–1646]. We show that if the local rule F is bipermutative (in Hedlund’s terminology), then the topological entropy of nth iteration of one-dimensional additive CA is 2 nr log m. We obtain necessary and sufficient conditions for the topological entropy of nth iteration of CA to be 2 nr log m. We show that the uniform Bernoulli measure is a measure of maximal entropy for the nth iteration of the CA generated by bipermutative local rule F.

A new fast cellular automata orthogonal least-squares identification method

A novel fast cellular automata orthogonal least squares (FCA-OLS) identification method is introduced by extending and developing the CA-OLS identification method presented in a previous study by Billings and Yang. Both one-dimensional CA and two-dimensional CA were identified with FCA-OLS as the simulation examples. The simulation results show that the new method significantly reduces the computational time compared with existing methods.

A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART IV: FROM BERNOULLI SHIFT TO 1/f SPECTRUM

By exploiting the new concepts of CA characteristic functions and their associated attractor time-τ maps, a complete characterization of the long-term time-asymptotic behaviors of all 256 one-dimensional CA rules are achieved via a single "probing" random input signal. In particular, the graphs of the time-1 maps of the 256 CA rules represent, in some sense, the generalized Green's functions for Cellular Automata. The asymptotic dynamical evolution on any CA attractor, or invariant orbit, of 206 (out of 256) CA rules can be predicted precisely, by inspection. In particular, a total of 112 CA rules are shown to obey a generalized Bernoulli στ-shift rule, which involves the shifting of any binary string on an attractor, or invariant orbit, either to the left, or to the right, by up to 3 pixels, and followed possibly by a complementation of the resulting bit string. The most intriguing result reported in this paper is the discovery that the four Turing-universal rules [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], and only these rules, exhibit a 1/f power spectrum.

The Pascal matroid as a home for generating sets of cellular automata configurations defined by quasigroups

Consider a one-dimensional CA whose local evolution rule is defined by a quasigroup ( G,★). When the initial state is only known over a finite string of adjacent cells, the CA's orbit (state-time diagram) is only defined on a triangular array of cells. This well-defined triangular part of the orbit, in which each cell has a value in G, is called a ( G,★)-configuration. A generating set is a subset of the triangular array such that any attribution of G-values to the cells of this subset determines a unique ( G,★)-configuration. It turns out that the collection of all potential generating sets form a particular matroid, which we have called the Pascal matroid. The main subject of this work is related to the question whether every base of this matroid actually occurs as a generating set for a ( G,★)-configuration.

Extended moment formation and magnetic ordering in the trigonal chain compound Ca 3Co 2O 6

The results of electronic structure calculations for the one-dimensional magnetic chain compound Ca 3Co 2O 6 are presented. The calculations are based on density functional theory and the local density approximation and used the augmented spherical wave (ASW) method. Our results allow for deeper understanding of recent experimental findings. In particular, alternation of Co 3d low- and high-spin states along the characteristic chains is related to differences in the oxygen coordination at the inequivalent cobalt sites. Strong hybridization of the d states with the O 2p states lays ground for polarization of the latter and the formation of extended localized magnetic moments centered at the high-spin sites. In contrast, strong metal–metal overlap along the chains gives rise to intrachain ferromagnetic exchange coupling of the extended moments via the d 3z 2–r 2 orbitals of the low-spin cobalt atoms.

Magnon thermal conductivity in the spin-gap state and the antiferromagnetically ordered state of low-dimensional copper oxides

We have looked for large thermal-conductivity due to magnons, κ magnon, in various kinds of low-dimensional quantum spin systems, such as the two-leg spin-ladder system Sr 14Cu 24O 41, the two-dimensional spin-dimer system SrCu 2(BO 3) 2, the four-leg spin-ladder system La 2Cu 2O 5, the two-dimensional spin system Cu 3B 2O 6 and the one-dimensional spin system Ca 2Y 2Cu 5O 10, using large-sized single-crystals grown by the TSFZ method. Large κ magnon has been found in the spin-gap state of Sr 14Cu 24O 41 whose bandwidth of the triplet excitation is large, owing to the enhancement of the mean free path of magnons. In gapless systems, it has been found that κ magnon increases with increasing magnon-velocity, which increases with increasing exchange-interaction between Cu 2+ spins and is larger in antiferromagnetic spin-correlation systems than in ferromagnetic spin-correlation systems. Therefore, it is concluded that essential factors of large κ magnon are a large bandwidth of the triplet excitation in a spin-gap system, a large exchange-interaction and antiferromagnetic spin-correlation rather than ferromagnetic spin-correlation.

Surface electronic structures of Ca-induced reconstructions on Si(111)

Angle-resolved photoemission experiment was performed on the single-domain 3 X 2 and 2 X I surfaces induced by Ca adsorption on a Si(111) surface. For the 3 X 2 surface, we identify three fully occupied surface states within the Si bulk-band gap with clear dispersions of 0.3-0.6 eV. These surface-state bands resemble those observed for the similar 3×2 phase induced by Ba and are roughly consistent with the theoretical calculation for the 3 X I phase of Li on the same substrate. This result generally favors the honeycomb-chained channel model for the 3×2 surface induced by alkali-earth adsorbates with a common Si topmost layer (host) reconstruction to the 3×1 surface by alkali metals. In addition, we observe a rather obvious ×2 symmetry in the surface-state dispersions, which differentiates the surface band structure of the 3×2 phase from that of the host 3×I reconstruction. The apparent ×2 periodicity, which is also clear in electron diffraction, is attributed to the alternating occupation of the T4 sites along the Si channels by Ca adatoms with a coverage of l/6 ML. In case of the 2×I reconstruction formed at a higher coverage, we observe only one surface state within the bulk-band-gap region at a binding energy of 1.1-1.5 eV. This state exhibits a larger dispersion along the chain (×1) direction, which agrees reasonably with the theoretical prediction for the π-bonded Seiwatz chain structure of the bare Si(111)2 X I surface. This result supports the recent structure model of the 2×1 surface with one-dimensional Ca chains in between π-honded Si chains. It is deduced from the present observations that the surface electronic band structures of the Si surface phases with alkali-earth adsorbates are largely and rigidly determined by the reconstruction of the Si topmost layer itself.