Incorporating Redox Conjugate Pair to Attain Electrical Bistability in Polymer Semiconductors

Owing to the advantages of 3-D printable stack, scalability and low cost solution state production, polymer-based resistive memory devices have been identified as the promising alternative for conventional oxide technology....

A Depth-First Iterative Algorithm for the Conjugate Pair Fast Fourier Transform

The Split-Radix Fast Fourier Transform has the same low arithmetic complexity as the related Conjugate Pair Fast Fourier Transform. Both transforms have an irregular datapath structure which is straightforwardly expressed only in recursive forms. Furthermore, the conjugate pair variant has a complicated input indexing pattern which requires existing iterative implementations to rely on precomputed tables. It however allows optimization of the memory bandwidth as it requires a single twiddle factor load per radix-4 butterfly. In existing algorithms, this comes at the cost of using additional precomputed tables or performing recursive function calls. In this paper we present two novel approaches that handle both the butterfly scheduling and the input index generation of the Conjugate Pair Fast Fourier Transform. The proposed algorithm is cache-friendly because it is depth-first, non-recursive and does not rely on precomputed index tables. In order to achieve this, we relate the butterfly execution pattern of the Split-Radix and Conjugate Pair FFTs to the binary carry sequence. Based on this finding, we describe how common integer arithmetic and bitwise operations can be used to perform input reordering and depth-first traversal of the transform datapath with O(1) space complexity.<br>

A Depth-First Iterative Algorithm for the Conjugate Pair Fast Fourier Transform

The Split-Radix Fast Fourier Transform has the same low arithmetic complexity as the related Conjugate Pair Fast Fourier Transform. Both transforms have an irregular datapath structure which is straightforwardly expressed only in recursive forms. Furthermore, the conjugate pair variant has a complicated input indexing pattern which requires existing iterative implementations to rely on precomputed tables. It however allows optimization of the memory bandwidth as it requires a single twiddle factor load per radix-4 butterfly. In existing algorithms, this comes at the cost of using additional precomputed tables or performing recursive function calls. In this paper we present two novel approaches that handle both the butterfly scheduling and the input index generation of the Conjugate Pair Fast Fourier Transform. The proposed algorithm is cache-friendly because it is depth-first, non-recursive and does not rely on precomputed index tables. In order to achieve this, we relate the butterfly execution pattern of the Split-Radix and Conjugate Pair FFTs to the binary carry sequence. Based on this finding, we describe how common integer arithmetic and bitwise operations can be used to perform input reordering and depth-first traversal of the transform datapath with O(1) space complexity.<br>

Differential migration of interstitial immiscible liquids in the Skaergaard Layered Series

&lt;p&gt;The liquid line of descent of the Skaergaard magma intersects a binodal creating an immiscible conjugate pair comprising a dense Fe-rich liquid and a buoyant Si-rich liquid. These two liquids have different wetting properties: the Si-rich liquid wets plagioclase, whereas the Fe-rich liquid wets oxides, pyroxene and olivine. The two liquids may therefore undergo differential migration within a gabbroic crystal mush: the Fe-rich liquid sinks and accumulates in mafic layers, while the Si-rich liquid rises and accumulates in plagioclase-rich regions.&lt;/p&gt;&lt;p&gt;Field-scale evidence of metre-scale differential migration of unmixed immiscible interstitial liquids is provided by paired felsic and mafic lenses spatially associated with gabbroic pegmatite bodies in the Skaergaard floor cumulates. These represent small batches of late-stage liquids rising from the pegmatite bodies into the overlying mush, and their subsequent separation into immiscible conjugates. The paired lenses form irregular, approximately layer-parallel clusters in thick mush, but thin concordant dendritic structures within strongly foliated thin mush. Invariably the melanocratic component lies stratigraphically below the felsic component.&lt;/p&gt;&lt;p&gt;Differential migration within the floor cumulates is also recorded by mm-scale mafic and felsic rims developed on the top and bottom margins of anorthositic blocks derived from the roof. Highly tabular blocks have an upper mafic rim and a lower leucocratic rim. As the block aspect ratio decreases, the rims disappear, with the mafic rim retained at lower aspect ratios than the leucocratic rim. We interpret rim formation as a consequence of trapping migrating unmixed interstitial liquid against the relatively impermeable blocks: tabular blocks are most effective at trapping these liquids.&lt;/p&gt;&lt;p&gt;On a smaller scale, the different wetting properties of the two immiscible conjugates result in post-accumulation pattern formation in rapidly deposited modally graded layers, imposing cm-scale internal layering on the overall modal grading. The tops of the modally-graded layers may also develop felsic flame-like structures interpreted as a consequence of upwards-migration of the immiscible Si-rich conjugate from high-porosity rapidly deposited layers into the overlying cumulates.&lt;/p&gt;&lt;p&gt;These observations demonstrate the complexity of behaviour in a crystal mush containing a two-phase interstitial liquid. Understanding cumulate evolution necessitates a consideration of the scale of migration of interstitial liquid and the possibility of the differential loss of one of the two conjugates.&lt;/p&gt;

Turbulence at the Lee bound: maximally non-normal vortex filaments and the decay of a local dissipation rate

This paper uses a tight mathematical bound on the degree of the non-normality of the turbulent velocity gradient tensor to classify flow behaviour within vortical regions (where the eigenvalues of the tensor contain a conjugate pair). Structures attaining this bound are preferentially generated where enstrophy exceeds total strain and there is a positive balance between strain production and enstrophy production. Lagrangian analysis of homogeneous, isotropic turbulence shows that attainment of this bound is associated with relatively short durations and an upper limit to the spatial extent of the flow structures that is similar to the Taylor scale. An analysis of the dynamically relevant terms using a recently developed formulation (Keylock, J. Fluid Mech., vol. 848, 2018, pp. 876–904), highlights the controls on this dynamics. In particular, in high enstrophy regions it is shown that the bound is attained when normal strain decreases rather than when non-normality increases. The near absence of normal total strain results in a source of intermittency in the dynamics of dissipation that is hidden in standard analyses. It is shown that of the two terms that contribute to the non-normal production dynamics, it is the one that is typically smallest in magnitude that is of greatest importance within these $\ell =1$ filaments. The typical distance between filament centroids is just less than a Taylor scale, implying a connection to the manner in which flow topology at the Taylor scale explains dissipation at smaller scales.