The differential spectrum of a ternary power mapping

Postponed access: the file will be available after 2022-03-06A function f(x)from the finite field GF(pn)to itself is said to be differentially δ-uniform when the maximum number of solutions x ∈GF(pn)of f(x +a) −f(x) =bfor any a ∈GF(pn)∗and b ∈GF(pn)is equal to δ. Let p =3and d =3n−3. When n >1is odd, the power mapping f(x) =xdover GF(3n)was proved to be differentially 2-uniform by Helleseth, Rong and Sandberg in 1999. Fo r even n, they showed that the differential uniformity Δfof f(x)satisfies 1 ≤Δf≤5. In this paper, we present more precise results on the differential property of this power mapping. Fo r d =3n−3with even n >2, we show that the power mapping xdover GF(3n)is differentially 4-uniform when n ≡2 (mod 4) and is differentially 5-uniform when n ≡0 (mod 4). Furthermore, we determine the differential spectrum of xdfor any integer n >1.acceptedVersio

Exact resolution method for general 1D polynomial Schr\"odinger equation

The stationary 1D Schr\"odinger equation with a polynomial potential $V(q)$ of degree N is reduced to a system of exact quantization conditions of Bohr-Sommerfeld form. They arise from bilinear (Wronskian) functional relations pairing spectral determinants of (N+2) generically distinct operators, all the transforms of one quantum Hamiltonian under a cyclic group of complex scalings. The determinants' zeros define (N+2) semi-infinite chains of points in the complex spectral plane, and they encode the original quantum problem. Each chain can now be described by an exact quantization condition which constrains it in terms of its neighbors, resulting in closed equilibrium conditions for the global chain system; these are supplemented by the standard (Bohr-Sommerfeld) quantization conditions, which bind the infinite tail of each chain asymptotically. This reduced problem is then probed numerically for effective solvability upon test cases (mostly, symmetric quartic oscillators): we find that the iterative enforcement of all the quantization conditions generates discrete chain dynamics which appear to converge geometrically towards the correct eigenvalues/eigenfunctions. We conjecture that the exact quantization then acts by specifying reduced chain dynamics which can be stable (contractive) and thus determine the exact quantum data as their fixed point. (To date, this statement is verified only empirically and in a vicinity of purely quartic or sextic potentials $V(q)$.)Comment: flatex text.tex, 4 files Submitted to: J. Phys. A: Math. Ge

Characterisation of High Current Density Resonant Tunneling Diodes for THz Emission Using Photoluminescence Spectroscopy

We discuss the numerical simulation of high current density InGaAs/AlAs/InP resonant tunneling diodes with a view to their optimization for application as THz emitters. We introduce a figure of merit based upon the ratio of maximum extractable THz power and the electrical power developed in the chip. The aim being to develop high efficiency emitters as output power is presently limited by catastrophic failure. A description of the interplay of key parameters follows, with constraints on strained layer epitaxy introduced. We propose an optimized structure utilizing thin barriers paired with a comparatively wide quantum well that satisfies strained layer epitaxy constraints

Epitaxial designs for maximizing efficiency in resonant tunnelling diode based terahertz emitters

We discuss the modelling of high current density InGaAs/AlAs/InP resonant tunneling diodes to maximize their efficiency as THz emitters. A figure of merit which contributes to the wall plug efficiency, the intrinsic resonator efficiency, is used for the development of epitaxial designs. With the contribution of key parameters identified, we analyze the limitations of accumulated stress to assess the manufacturability of such designs. Optimal epitaxial designs are revealed, utilizing thin barriers, with a wide and shallow quantum well that satisfies the strained layer epitaxy constraint. We then assess the advantages to epitaxial perfection and electrical characteristics provided by devices with a narrow InAs sub-well inside a lattice-matched InGaAs alloy. These new structures will assist in the realization of the next-generation submillimeter emitters

Synthesis and thermoelectric properties of noble metal ternary chalcogenide systems of Ag-Au-Se in the forms of alloyed nanoparticles and colloidal nanoheterostructures

The optimization of a material functionality requires both the rational design and precise engineering of its structural and chemical parameters. In this work, we show how colloidal chemistry is an excellent synthetic choice for the synthesis of novel ternary nanostructured chalcogenides, containing exclusively noble metals, with tailored morphology and composition and with potential application in the energy conversion field. Specifically, the Ag–Au–Se system has been explored from a synthetic point of view, which leads to a set of Ag2Se-based hybrid and ternary nanoparticles including the room temperature synthesis of the rare ternary Ag3AuSe2 fischesserite phase. An in-depth structural and chemical characterization of all nanomaterials has been performed, which proofed especially useful for unravelling the reaction mechanism behind the formation of the ternary phase in solution. The work is complemented with the thermal and electric characterization of a ternary Ag–Au–Se nanocomposite with promising results: we found that the use of the ternary nanocomposite represents a clear improvement in terms of thermoelectric energy conversion as compared to a binary Ag–Se nanocomposite analogue.Peer ReviewedPostprint (author's final draft

The Differential Spectrum of the Power Mapping xpn−3

Let n be a positive integer and p a prime. The power mapping xpn−3 over Fpn has desirable differential properties, and its differential spectra for p=2,3 have been determined. In this paper, for any odd prime p , by investigating certain quadratic character sums and some equations over Fpn , we determine the differential spectrum of xpn−3 with a unified approach. The obtained result shows that for any given odd prime p , the differential spectrum can be expressed explicitly in terms of n . Compared with previous results, a special elliptic curve over Fp plays an important role in our computation for the general case p≥5.acceptedVersio

Mechanisms of High Temperature Degradation of Thermal Barrier Coatings.

Thermal barrier coatings (TBCs) are crucial for increasing the turbine inlet temperature (and hence efficiency) of gas turbine engines. The thesis describes PhD research aimed at improving understanding of the thermal cycling failure mechanisms of electron beam physical vapour deposited (EB-PVD) yttria stabilised zirconia (YSZ) TBCs on single crystal superalloys. The research consisted of three different stages. The first stage involved designing a coupled one-dimensional thermodynamic-kinetic oxidation and diffusion model capable of predicting the concentration profiles of alloying elements in a single-phase γ nickel-rich Ni-Al-Cr ternary alloy by the finite difference method. The aim of this investigation was to improve the understanding of interactions between alloying species and developing oxide. The model demonstrated that in the early stages of oxidation, Al consumption by oxide scale growth is faster than Al replenishment by diffusion towards the scale, resulting in an initial Al depletion in the alloy near the scale. The second stage involved a systematic study of the life-time of TBC systems on different single crystal superalloys. The study aimed at demonstrating that the compatibility of modern nickel-based single crystal superalloys with TBC systems is influenced strongly by the content of alloying element additions in the superalloy substrate. The results can be explained by postulating that the fracture toughness parameters controlling decohesion are influenced strongly by small changes in composition arising from interdiffusion with the bond coat, which itself inherits elemental changes from the substrate. The final stage of study involved a detailed study of different bond coats (two β-structured Pt-Al types and a γ/γ’ Pt-diffusion type) in TBC systems based on an EB-PVD YSZ top coat and a substrate material of CMSX-4 superalloy. Generation of stress in the thermally grown oxide (TGO) on thermal cycling, and its relief by plastic deformation and fracture, were investigated experimentally in detail