Semi-implicit two-level predictor–corrector methods for non-linearly coupled,hydrostatic, barotropic/baroclinic flows

The unsteady shallow-water equations for barotropic/baroclinic (free-surface/density-stratified) flows with non-linear coupling of density transport and momentum are solved using a family of two-time-level, semi-implicit predictor–corrector methods (PC2). The PC2 methods are a general family that includes the popular TRIM method for hydrostatic flows. PC2 is characterised by four ‘θ’ parameters controlling the time ‘n’ and ‘n + 1’ weighting of (1) free surface gradient, (2) predictor step, (3) baroclinic gradient and (4) density temporal interpolation. Stability of the non-linear coupling between momentum and density transport for PC2 is examined in the inviscid limit. Central difference and quadratic (QUICK) spatial interpolation for density are compared. Second-order temporal accuracy for both barotropic and baroclinic flows is simultaneously obtained with appropriate θ parameters, which has previously been shown to be impractical for TRIM. The 2nd-order PC2 method has near-neutral non-linear stability (slightly positive amplification factor) where linear theory predicts exactly neutral stability. QUICK is shown to be preferable to central difference spatial discretisation to reduce the amplification factor. Adjusting the baroclinic weighting or adding small artificial viscosities can stabilise the model for non-linear internal wave simulations.     

Optical encryption with a reference wave in a joint transform correlator architecture

In this work we introduce a digital holographic configuration in a Joint Transform Correlator (JTC) architecture for encryption purposes. Conceptually, it is a Mach-Zender interferometer, with a JTC in one arm and a reference wave in the other. We describe the practical implementation of this architecture, along with experimental results that support the proposal. We analyze the noise influence caused by intensity saturation during image capture, and this information allows us a filtering process to reduce the information to be handled, with a consequent increase in the speed of the total procedure.     

Synthesis of Amphiphilic Graft Copolymers with Poly(2‐methyl‐2‐oxazoline) Side Chains and a Backbone Containing Chloromethylstyrene and Methyl Methacrylate

New amphiphilic graft copolymers were synthesized by means of a cationic ring‐opening polymerization of 2‐methyl‐2‐oxazoline initiated with a statistical copolymer of methyl methacrylate and chloromethylstyrene. The synthesis was carried out in benzonitrile at 110°C. The grafting reaction was quantitative and the yield of grafting was more than 90%percent;. The graft copolymers were characterized by means of NMR, FT‐IR, and UV‐VIS spectroscopy, as well as elemental analysis and viscosity measurements of their aqueous solutions. The graft copolymers revealed amphiphilic properties and evidence for the formation of micelles and molecular aggregates in aqueous solution. Graft copolymers with relatively short lateral chains are soluble in methanol but insoluble in water, while the copolymers with longer lateral chains are soluble in both methanol and water.     

Pietsch's factorization theorem for dominated polynomials

We prove that, like in the linear case, there is a canonical prototype of a p-dominated homogeneous polynomial through which every p-dominated polynomial between Banach spaces factors.     

Duality in nonlinear multiobjective programming using augmented Lagrangian functions

A vector-valued generalized Lagrangian is constructed for a nonlinear multiobjective programming problem. Using the Lagrangian, a multiobjective dual is considered. Without assuming differentiability, weak and strong duality theorems are established using Pareto efficiency.The research of the second author was partially supported a GTE/SLU grant while visiting St. Lawrence University in the summer of 1991.     

Finite dimensional representations of invariant differential operators

Let be an algebraically closed field of characteristic , , and let be an algebraic torus acting diagonally on the ring of algebraic differential operators . We give necessary and sufficient conditions for to have enough simple finite dimensional representations, in the sense that the intersection of the kernels of all the simple finite dimensional representations is zero. As an application we show that if is a representation of a reductive group and if zero is not a weight of a maximal torus of on , then has enough finite dimensional representations. We also construct examples of FCR-algebras with any integer GK dimension .

     

Summability of multilinear mappings: Littlewood, Orlicz and beyond

In this paper we prove new results concerning summability properties of multilinear mappings between Banach spaces, such as an extension of Littlewood’s 4/3 Theorem. The role of the Littlewood–Orlicz property in the theory is established, especially in the question of determining when multilinear mappings are (1; 2, . . . , 2)-summing.     

Generalized fractional programming: Optimality and duality theory

The generalized fractional programming problem with a finite number of ratios in the objective is studied. Optimality and duality results are established, some with the help of an auxiliary problem and some directly. Convexity and stability of the auxiliary problem play a key role in the latter part of the paper.The authors are grateful to an unknown referee for suggesting the statement of Theorem 3.3.     

Exploration of a possible cumulative action of the zero-point field on intergalactic particles and implications for cosmic rays and a X-ray background from the intergalactic medium

Summary The intergalactic space (IGS) has ideal conditions to test the weak but cumulative action that the electromagnetic (EM) zero-point field (ZPF) of ordinary quantum theory (QT), if conceived as a real field, may have on EM interacting particles. Recent results (classical stochastic and quantum) indicate that if the EM ZPF of ordinary QT is conceptually assimilated to a real random field, electrically polarizable particles perform a random walk in velocity space to ever-increasing translational kinetic energies. As the ZPF has a Lorentz-invariant energy density spectrum, statistically it keeps the same form and is homogeneous and isotropic in all inertial frames of reference. No velocity-dependent forces can hence appear on particles moving through the ZPF. Acceleration is thus possible in a high vacuum. The hierarchy of dissipation mechanisms for the accelerated ultrarelativistic protons in the IGS is established in detail. In the IGS outside superclusters cosmic expansion is the most significant dissipation mechanism. The previously derivedE ^−η particle energy spectrum is obtained except for a cut-off: cosmic expansion puts a drastic cut-off to the energy spectrum of ZPF accelerated particles in the IGS out-side clusters or superclusters. This cut-off does not appear for CR primaries confined to the magnetic cavities of clusters or superclusters. When this confinement is effective, the ZPF acceleration may still be as relevant a CR acceleration mechanism as previously contended. The possible relevance of the ZPF in energizing the intergalactic medium (IGM) is briefly discussed. As it has recently been shown that electrons are not accelerated by the ZPF, electrons can only receive energy from the proton component of the IGM plasma and should display an approximately Maxwellian distribution. This could not occur, would electrons absorb energy directly from the ZPF. In that case they would display the Lorentz-invariant distribution. The electron component loses energy mainly by thermal bremsstrahlung or by inverse Compton collisions with the 2.7 K photons depending on the assumed number density of IGS electrons. The X-ray emission of the proton component can be dismissed in comparison with that of the electrons, despite the usual higher energies of protons in their distribution which is not Maxwellian. The relevance of the ZPF acceleration model for explaining the observed X-ray background is preliminarily discussed. The inherent thermodynamic limitations of the model are also briefly outlined.

---

Riassunto Lo spazio intergalattico (IGS) ha condizioni ideali per provare l'azione debole ma cumulativa che il campo elettromagnetico (EM) del punto zero (ZPF) della normale teoria quantica (QT), se considerato come campo reale, può avere su particelle interagenti EM. Risultati recenti (classci stocastici e quantici) indicano che se lo ZPF EM della normale QT è assimilato concettualmente a un campo reale causuale, particelle elettricamente polarizzabili effettuano un percorso casuale nello spazio delle velocità a energie cinetiche traslazionali in continuo aumento. Poiché lo ZPF ha uno spettro di densità dell'energia invariante secondo Lorentz, statisticamente mantiene la stessa forma ed è omogeneo e isotropo in tutti i sistemi di riferimento inerziali. Nessuna forza dipendente dalla velocità può quindi apparire su particelle che si muovono nel ZPF. L'accelerazione è quindi possibile in un alto vuoto. La gerarchia dei meccanismi di dissipazione per i protoni ultrarelativistici accertati nell'IGS è stabilita dettagliatamente. Nell'IGS al di fuori dei superammassi l'espansione cosmica è il piú significativo meccanismo di dissipazione. Si ottiene lo spettro di energia delle particelleE ^η) precedentemente derivato tranne che per un taglio: l'espansione cosmica mette un taglio drastico nello spettro di energia delle particelle accelerate dallo ZPF nell'IGS all'esterno agli ammassi e ai superammassi. Questo taglio non compare per primari di CR confinati in cavità magnetiche di ammassi e superammassi. Quando questo confinamento è efficace, l'accelerazione del ZPF può ancora essere un meccanismo di accelerazione dei raggi cosmici cosí rilevante come precedentemente arguito. Si discute brevemente la possibile importanza dello ZPF nell'energizzare il mezzo intergalattico (IGM). Poiché è stato mostrato recentemente che gli elettroni non sono accelerati dallo ZPF, gli elettroni possono solo ricevere energia dalla componente protonica del plasma dell'IGM e dovrebbero mostrare una distribuzione approssimativamente maxwelliana. Questo non accadrebbe se gli elettroni assorbissero energia direttamente dallo ZPF. In quel caso mostrerebbero una distribuzione invariante secondo Lorentz. La componente elettronica perde energia principalmente attraverso bremsstrahlung termico, o attraverso collisioni di Compton inverse con i fotoni a 2.7 K a seconda della densità numerica degli elettroni IGS considerata. L'emissione di raggi X della componente protonica può essere trascurata in confronto con quella degli elettroni malgrado le usuali energie maggiori degli elettroni nella loro distribuzione che non è maxwelliana. Si discute preliminarmente l'importanza del modello di accelerazione dello ZPF per spiegare il sottofondo di raggi X osservato. Si delineano anche brevemente gl'inerenti limiti termodinamici del modello.

---

Резюме Межгалактическое пространство обладает идеальными условиями для проверки слабого, но кумулятивного действия, которое может оказывать электромагнитное поле с нулевой точкой в обычной квантовой теории, если оно рассматривается как реальное поле, на частицы, взаимодействующие электромагнитным образом. Недавние результаты (классические стохастические и квантовые) показывают, что если злектромагнитное поле с нулевой точкой в обычной квантовой теории концептуально приравнивается реальному случайному полю, то электрически поляризуемые частицы соверщают случайные блуждания в скоростном пространстве, увеличивая трансляционную кинетическую знергию. Когда поле с нулевой точкой имеет Лоренц-инвариантный спектр плотности знергии, то статистически он сохраняет форму и является однородным и изотронным во всех инерциальных системах отсчета. Следовательно, на частицы, движущиеся через поле с нулевой точкой, не могут действовать силы, зависяшие от скорости. Поэтому оказывается возможным ускорение в глубоком вакууме. Подробно описывается иерархия механизмов диссипации для ускоренных ультрарелятивистских протонов в межгалактическом пространстве. В межгалактическом пространстве, вне суперкластеров, космическое расщирение представляет наиболее существенный механизм диссипации. Получается ранее выведенный энердетический спектр частиц, за исключением обрезания. Космическое расщирение накладывает сушественное обрезание на энергетический спектр частиц, ускоренных в поле с нулевой точкой, в междалактическом пространстве, вне кластеров или суперкластеров. Указанное обрезание не возникает для первичных космических лучей, удерживаемых в магнитных полостях кластеров или суперкластеров. Когда это удержание является эффективным, то ускорение полем с нулевой точкой может представлять возможный механизм ускорения космич=yeских лучей, как утверждалось ранее. Вкратце овсуждается роль поля с нулевой точкой в энергетике межгалактической среды. Как было недавно показано, что электроны не ускоряются полем с нулевой точкой, электроны могут только получать энергию от протонной компоненты плазмы межгалактической среды и должны обладать приблизительно максвелловским распределением. Это может не иметь место, тогда электроны могут поглощать энергию прямо из поля с нулевой точкой. В этом случае они обладают Лоренц-инвариантным распределением. Электронная компонента теряет энергию, в основном, за счет теплового тормозного излучения или обратного комптоновского соударения с протонами, имеющими температуру 2.7 К, в зависимости от предлагаемого числа электронов межгалактической среды. Рентгеновским излучением для протонной компоненты можно пренебречь по сравнению с излучением для электронов, несмотря на обычные высокие энергии протонов в распределении, которое не является максвелловским. Предварительно обсуждается уместность модели ускорения полем с нулевой точкой для обьяснения наблюденного фона рентгеновских лучей. Вкратце отмечаются специфические термодинамические ограничения предложенной модели.