‎In this paper‎, ‎we introduce the two-dimensional Legendre wavelets (2D-LWs)‎, ‎and develop them for solving a class of two-dimensional integro-differential equations (2D-IDEs) of fractional order‎. ‎We also investigate convergence of the method‎. ‎Finally‎, ‎we give some illustrative examples to demonstrate the validity and efficiency of the method.

Grid cells, defined by their striking periodic spatial responses in open 2D arenas, appear to respond differently on 1D tracks: the multiple response fields are not periodically arranged, peak amplitudes vary across fields, and the mean spacing between fields is larger than in 2D environments. We ask whether such 1D responses are consistent with the system's 2D dynamics. Combining analytical an...

We consider the feasibility problem OPP in higher-dimensional orthogonal packing: given a set of d-dimensional (d ≥ 2) rectangular items, decide whether all of them can be orthogonally packed in the given rectangular container without rotation. The 1D ‘bar’ LP relaxation of OPP reduces the latter to a 1D cutting-stock problem where the packing of each stock bar represents a possible 1D stitch t...

In some geophysical problems, it is sometimes possible to divide the subsurface resistivity distribution as a one dimensional (1D) contribution plus some two dimensional (2D) inhomogeneities. Assuming this scenario, we split the electromagnetic fields into their primary and secondary components, the former corresponding to the 1D contribution, and the latter to the 2D inhomogeneities. While the...

We introduce NIFTY, “Numerical Information Field Theory”, a software package for the development of Bayesian signal inference algorithms that operate independently from any underlying spatial grid and its resolution. A large number of Bayesian and Maximum Entropy methods for 1D signal reconstruction, 2D imaging, as well as 3D tomography, appear formally similar, but one often finds individualiz...

We evaluate the full current statistics (FCS) in the low dimensional ( 1D and 2D ) diffusive conductors in the incoherent regime, eV ≫ETh = D/L , ETh being the Thouless energy. It is shown that Coulomb interaction substantially enhances the probability of big current fluctuations for short conductors with ETh≫1/τE, τE being the energy relaxation time, leading to the exponential tails in the cur...

With the use of three-dimensional whole body scanning technology, this study compared the 'traditional' anthropometric model [one-dimensional (1D) measurements] to a 'new' model [1D, two-dimensional (2D), and three-dimensional (3D) measurements] to determine: (1) which model predicted more of the variance in self-reported best 2000-m ergometry rowing performance; and (2) what were the best anth...

An overview is presented of the various phases predicted to occur when gases are absorbed within a bundle of carbon nanotubes. The behavior may be characterized by an effective dimensionality, which depends on the species and the temperature. Small molecules are strongly attracted to the interstitial channels between tubes. There, they undergo transitions between ordered and disordered quasi-on...

In this paper, adaptive pilot-aided channel estimation for orthogonal frequency-division multiplexing (OFDM) transmission is addressed. For this purpose, instead of a theoretically optimum two-dimensional (2D) filter, two consecutive one-dimensional (2× 1D) filters are applied. In particular, three algorithms for the first 1D step are compared, namely normalized least-mean-squares (NLMS), norma...

Abstract Manipulating wave propagation and energy collection plays a core role in modern physics, for which topological insulators hosting robust boundary states offer an ideal platform. However, there exist challenges integrating multiple like two-dimensional (2D) surface state, one-dimensional (1D) hinge zero-dimensional (0D) corner state into single three-dimensional (3D) architecture. Here ...