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[en] Nanomagnets are a promising low-power alternative to traditional computing. However, the successful implementation of nanomagnets in logic gates has been hindered so far by a lack of reliability. Here, we present a novel design with dipolar-coupled nanomagnets arranged on a square lattice to (i) support transfer of information and (ii) perform logic operations. We introduce a thermal protocol, using thermally active nanomagnets as a means to perform computation. Within this scheme, the nanomagnets are initialized by a global magnetic field and thermally relax on raising the temperature with a resistive heater. We demonstrate error-free transfer of information in chains of up to 19 square rings and we show a high level of reliability with successful gate operations of ∼94% across more than 2000 logic gates. Finally, we present a functionally complete prototype NAND/NOR logic gate that could be implemented for advanced logic operations. Here we support our experiments with simulations of the thermally averaged output and determine the optimal gate parameters. Our approach provides a new pathway to a long standing problem concerning reliability in the use of nanomagnets for computation. (paper)
[en] We consider closed 2-manifolds (2-manifolds without boundary) embedded in tubes in the hypercubic lattice, Z d, . For orientable 2-manifolds with fixed genus, , we prove that the exponential growth rate is independent of the genus and we use this to prove a pattern theorem for manifolds with fixed genus. We prove a similar theorem for the non-orientable case for . If the genus is not fixed then we prove a pattern theorem and use this to show that 2-manifolds with genus less than any fixed number are exponentially rare so the typical genus increases with the size of the manifold. In four and higher dimensions we prove that orientable manifolds are exponentially rare and are dominated by non-orientable manifolds. In four dimensions, all except exponentially few 2-manifolds, both orientable and non-orientable, contain a local knotted -ball pair. (paper)
[en] In this paper we investigate the integrability properties of a two-state vertex model on the square lattice whose microstates at a vertex always have an odd number of incoming or outcoming arrows. This model was named the odd eight-vertex model by Wu and Kunz (2004 J. Stat. Phys. 116 67) to distinguish it from the well-known eight-vertex model possessing an even number of arrow orientations at each vertex. When the energy weights are invariant under arrow inversion we show that the integrable manifold of the odd eight-vertex model coincides with that of the even eight-vertex model. The form of the -matrix for the odd eight-vertex model is however not the same as that of the respective Lax operator. Altogether we find that these eight-vertex models give rise to a generic sheaf of -matrices satisfying the Yang–Baxter equations resembling intertwiner relations associated to equidimensional representations. (paper)
[en] Highlights: •Cooperation macrocosmically refers to the overall cooperation rate, while reputation microcosmically records individual choices. •Therefore, reputation should be preferred in order to investigate how individual choices evolve. •Both the mean and standard deviation of reputation follow clear patterns, and some factors have quadratic effects on them. -- Abstract: Cooperation is vital for our society, but the temptation of cheating on cooperative partners undermines cooperation. The mechanism of reputation is raised to countervail this temptation and therefore promote cooperation. Reputation microcosmically records individual choices, while cooperation macrocosmically refers to the group or averaged cooperation level. Reputation should be preferred in order to investigate how individual choices evolve. In this work, we study the distribution of reputation to figure out how individuals make choices within cooperation and defection. We decompose reputation into its mean and standard deviation and inspect effects of their factors respectively. To achieve this goal, we construct a model where agents of three groups or classes play the prisoners’ dilemma game with neighbors on a square lattice. It indicates in outcomes that the distribution of reputation is distinct from that of cooperation and both the mean and standard deviation of reputation follow clear patterns. Some factors have negative quadratic effects on reputation's mean or standard deviation, and some have merely linear effects
[en] In a recent work Povolotsky (2013 J. Phys. A: Math. Theor. 46 465205) provided a three-parameter family of stochastic particle systems with zero-range interactions in one-dimension which are integrable by coordinate Bethe ansatz. Using these results we obtain the corresponding condition for integrability of a class of directed polymer models with random weights on the square lattice. Analyzing the solutions we find, besides known cases, a new two-parameter family of integrable DP model, which we call the Inverse-Beta polymer, and provide its Bethe ansatz solution. (paper)
[en] A one-dimensional crystal growth model along the preferential growth direction is established. The simulation model is performed on a square lattice substrate. First, particles are deposited homogeneously and, as a result, each of the lattice sites is occupied by one particle. In the subsequent stage, N nuclei are selected randomly on the substrate, then the growth process starts by adsorbing the surrounding particles along the preferential growth directions of the crystals. Finally, various one-dimensional crystals with different length and width form. The simulation results are in good agreement with the experimental findings. - Highlights: • A one-dimensional crystal growth model along the preferential growth direction is established successfully. • A new growth mechanism of one-dimensional crystals on isotropic substrates is shown. • All the simulation results are in good agreement with the experimental findings.
[en] Knots are ubiquitous in nature and their analysis has important implications in a wide variety of fields including fluid dynamics, material science and molecular and structural biology. In many systems particles are found in crowded environments hence it is natural to rigorously characterize the properties of knots in confined volumes. In this work we combine analytical and numerical work on the simple cubic lattice to determine the minimal number of lattice steps, minimum step number, needed to make a knot inside a tubular region. Our complementary approaches help us establish a detailed enumeration of minimal knot lengths and/or conformations of knots in tubular regions. Analytical results characterize the types of knots and links that can be embedded in a tubular regions and determines the minimum number of steps required to construct all 2-bridge knots and links up to ten crossings in the -tube. Simulation results, on the other hand, estimate the minimum step number and provide exact trajectories of all knot types up to eight crossings for wider tubular regions. These findings not only determine what knots and links can be built in a highly confined volume but also provide further evidence that the minimum step number required to realize a knot type increases with confining volume. (paper)
[en] Application of multivariate creative telescoping to a finite triple sum representation of the discrete space-time Green’s function for an arbitrary numeric (non-symbolic) lattice point on a 3D simple cubic lattice produces a fast, no-neighbours, seventh-order, eighteenth-degree, discrete-time recurrence scheme. For arbitrary numeric lattice points outside the diagonal symmetry planes, the seven numeric eighteenth-degree polynomial coefficients of the recurrence scheme are products of polynomials with integer coefficients that are linear in the recurrence index n, and two polynomials of degree four, and five polynomials of degree twelve that are irreducible over the field of integers. Owing to the symmetry of the scalar Green’s function upon interchanging any of the lattice point coordinates, the twelfth degree polynomials with integer coefficients may each be expanded in terms of 102 elementary symmetric polynomials in symbolic lattice point coordinates. The recurrence schemes determined by the telescoper for 102 distinct numeric lattice points can be used to form linear systems of equations. These are solved for the coefficients of the elementary symmetric polynomials required to construct the symbolic polynomial coefficients of the generic 3D recurrence scheme. Given its compact and straightforward 2D counterpart, this 3D recurrence scheme is far more intricate than expected, and is most efficiently presented through tables of coefficients. However, the scheme and the resulting lattice Green’s function sequences also exhibit more features. The complexity reduces for lattice points on diagonal symmetry planes, yielding a fast no-neighbours, fifth-order, twelfth-degree, discrete-time recurrence scheme. An illustrative example reveals unexpected phenomena, e.g. a late-time, high-frequency interplay of resonances that appears anomalous but can be fully explained, and the possible occurrence of removable recurrence scheme singularities. These effects are studied in detail in separate papers. (paper)
[en] An explicit expression for the energy of interaction between two spherically symmetric particles via the strain field in cubic crystals is obtained with an accuracy up to quadratic terms with respect to the anisotropy parameter d = c11 – c12 – 2c44. The diagrams depicting the regions of attraction and repulsion between particles projected onto the xy plane are drawn. It is found that at d < 0, the attraction regions are formed mostly along the x and y axes. At d > 0, the directions preferable for the attraction in the linear approximation with respect to the anisotropy parameter d are diagonals. However, each such direction becomes “split” into two directions if the nonlinear corrections are taken into account. In passing, we reveal the errors and misprints in the earlier papers based on the isotropic medium approximation (d = 0) and on the linear approximation with respect of parameter d.
[en] We investigated the susceptible-infected-susceptible model on a square lattice in the presence of a conjugated field based on recently proposed reactivating dynamics. Reactivating dynamics consists of reactivating the infection by adding one infected site, chosen randomly when the infection dies out, avoiding the dynamics being trapped in the absorbing state. We show that the reactivating dynamics can be interpreted as the usual dynamics performed in the presence of an effective conjugated field, named the reactivating field. The reactivating field scales as the inverse of the lattice number of vertices n, which vanishes at the thermodynamic limit and does not affect any scaling properties including ones related to the conjugated field. (paper: classical statistical mechanics, equilibrium and non-equilibrium)