BET surface area of carbonaceous adsorbents: verification using geometric considerations and GCMC simulations on virtual porous carbon models

The applicability of BET model for calculation of surface area of activated carbons is checked by using molecular simulations. By calculation of geometric surface areas for the simple model carbon slit-like pore with the increasing width, and by comparison of the obtained values with those for the same systems from the VEGA ZZ package (adsorbate-accessible molecular surface), it is shown that the latter methods provide correct values. For the system where a monolayer inside a pore is created the ASA approach (GCMC, Ar, T = 87 K) underestimates the value of surface area for micropores (especially, where only one layer is observed and/or two layers of adsorbed Ar are formed). Therefore, we propose the modification of this method based on searching the relationship between the pore diameter and the number of layers in a pore. Finally BET; original andmodified ASA; and A, B and C-point surface areas are calculated for a series of virtual porous carbons using simulated Ar adsorption isotherms (GCMC and T = 87 K). The comparison of results shows that the BET method underestimates and not, as it was usually postulated, overestimates the surface areas of microporous carbons.

Composite control of non-linear singularly perturbed systems: a geometric approach

Using a geometric approach, a composite control—the sum of a slow control and a fast control—is derived for a general class of non-linear singularly perturbed systems. A new and simpler method of composite control design is proposed whereby the fast control is completely designed at the outset. The slow control is then free to be chosen such that the slow integral manifold of the original system approximates a desired design manifold to within any specified order of ε accuracy.

Composite control of non-linear singularly perturbed systems: a geometric approach

Using a geometric approach, a composite control—the sum of a slow control and a fast control—is derived for a general class of non-linear singularly perturbed systems. A new and simpler method of composite control design is proposed whereby the fast control is completely designed at the outset. The slow control is then free to be chosen such that the slow integral manifold of the original system approximates a desired design manifold to within any specified order of ε accuracy.

Alternating sums of binomial coefficients with unit fraction arithmetic sequence coefficients

Expressions for finite sums involving the binomial coefficients with unit fraction coefficients whose denominators form an arithmetic sequence are determined.

A closer look at chaotic advection in the stratosphere: part I: geometric structure

The relevance of chaotic advection to stratospheric mixing and transport is addressed in the context of (i) a numerical model of forced shallow-water flow on the sphere, and (ii) a middle-atmosphere general circulation model. It is argued that chaotic advection applies to both these models if there is suitable large-scale spatial structure in the velocity field and if the velocity field is temporally quasi-regular. This spatial structure is manifested in the form of “cat’s eyes” in the surf zone, such as are commonly seen in numerical simulations of Rossby wave critical layers; by analogy with the heteroclinic structure of a temporally aperiodic chaotic system the cat’s eyes may be thought of as an “organizing structure” for mixing and transport in the surf zone. When this organizing structure exists, Eulerian and Lagrangian autocorrelations of the velocity derivatives indicate that velocity derivatives decorrelate more rapidly along particle trajectories than at fixed spatial locations (i.e., the velocity field is temporally quasi-regular). This phenomenon is referred to as Lagrangian random strain.

Solution-free sets for sums of binary forms

In this paper, we obtain quantitative estimates for the asymptotic density of subsets of the integer lattice Z2 that contain only trivial solutions to an additive equation involving binary forms. In the process we develop an analogue of Vinogradov’s mean value theorem applicable to binary forms.

Towards the computer-aided diagnosis of dementia based on the geometric and network connectivity of structural MRI data

We present an intuitive geometric approach for analysing the structure and fragility of T1-weighted structural MRI scans of human brains. Apart from computing characteristics like the surface area and volume of regions of the brain that consist of highly active voxels, we also employ Network Theory in order to test how close these regions are to breaking apart. This analysis is used in an attempt to automatically classify subjects into three categories: Alzheimer’s disease, mild cognitive impairment and healthy controls, for the CADDementia Challenge.

Environmental impact of geometric earthwork construction in pre-Columbian Amazonia

There is considerable controversy over whether pre-Columbian (pre-A.D. 1492) Amazonia was largely “pristine” and sparsely populated by slash-and-burn agriculturists, or instead a densely populated, domesticated landscape, heavily altered by extensive deforestation and anthropogenic burning. The discovery of hundreds of large geometric earthworks beneath intact rainforest across southern Amazonia challenges its status as a pristine landscape, and has been assumed to indicate extensive pre-Columbian deforestation by large populations. We tested these assumptions using coupled local- and regional-scale paleoecological records to reconstruct land use on an earthwork site in northeast Bolivia within the context of regional, climate-driven biome changes. This approach revealed evidence for an alternative scenario of Amazonian land use, which did not necessitate labor-intensive rainforest clearance for earthwork construction. Instead, we show that the inhabitants exploited a naturally open savanna landscape that they maintained around their settlement despite the climatically driven rainforest expansion that began ∼2,000 y ago across the region. Earthwork construction and agriculture on terra firme landscapes currently occupied by the seasonal rainforests of southern Amazonia may therefore not have necessitated large-scale deforestation using stone tools. This finding implies far less labor—and potentially lower population density—than previously supposed. Our findings demonstrate that current debates over the magnitude and nature of pre-Columbian Amazonian land use, and its impact on global biogeochemical cycling, are potentially flawed because they do not consider this land use in the context of climate-driven forest–savanna biome shifts through the mid-to-late Holocene.

Geometric polarimetry − part I: spinors and wave states

A new formal approach for representation of polarization states of coherent and partially coherent electromagnetic plane waves is presented. Its basis is a purely geometric construction for the normalised complex-analytic coherent wave as a generating line in the sphere of wave directions, and whose Stokes vector is determined by the intersection with the conjugate generating line. The Poincare sphere is now located in physical space, simply a coordination of the wave sphere, its axis aligned with the wave vector. Algebraically, the generators representing coherent states are represented by spinors, and this is made consistent with the spinor-tensor representation of electromagnetic theory by means of an explicit reference spinor we call the phase flag. As a faithful unified geometric representation, the new model provides improved formal tools for resolving many of the geometric difficulties and ambiguities that arise in the traditional formalism.

Gál-type GCD sums beyond the critical line

We prove that ∑k,ℓ=1N(nk,nℓ)2α(nknℓ)α≪N2−2α(logN)b(α) holds for arbitrary integers 1≤n1<⋯sums when 0<α<1/20<α<1/2.