Preliminary engineering report for design of a subscale ejector/diffuser system for high expansion ratio space engine testing

The design of a subscale jet engine driven ejector/diffuser system is examined. Analytical results and preliminary design drawings and plans are included. Previously developed performance prediction techniques are verified. A safety analysis is performed to determine the mechanism for detonation suppression

Study of high altitude plume impingement

Computer program has been developed as analytical tool to predict severity of effects of exhaust of rocket engines on adjacent spacecraft surfaces. Program computes forces, moments, pressures, and heating rates on surfaces immersed in or subjected to exhaust plume environments. Predictions will be useful in design of systems where such problems are anticipated

Additional Constants of Motion for a Discretization of the Calogero--Moser Model

The maximal super-integrability of a discretization of the Calogero--Moser model introduced by Nijhoff and Pang is presented. An explicit formula for the additional constants of motion is given.Comment: 7 pages, no figure

Quasi-point separation of variables for the Henon-Heiles system and a system with quartic potential

We examine the problem of integrability of two-dimensional Hamiltonian systems by means of separation of variables. The systematic approach to construction of the special non-pure coordinate separation of variables for certain natural two-dimensional Hamiltonians is presented. The relations with SUSY quantum mechanics are discussed.Comment: 11 pages, Late

Spectral asymmetry for bag boundary conditions

We give an expression, in terms of boundary spectral functions, for the spectral asymmetry of the Euclidean Dirac operator in two dimensions, when its domain is determined by local boundary conditions, and the manifold is of product type. As an application, we explicitly evaluate the asymmetry in the case of a finite-length cylinder, and check that the outcome is consistent with our general result. Finally, we study the asymmetry in a disk, which is a non-product case, and propose an interpretation.Comment: Some minor changes. To appear in Journal of Physics A: Mathematical and Genera

Novel Features Arising in the Maximally Random Jammed Packings of Superballs

Dense random packings of hard particles are useful models of granular media and are closely related to the structure of nonequilibrium low-temperature amorphous phases of matter. Most work has been done for random jammed packings of spheres, and it is only recently that corresponding packings of nonspherical particles (e.g., ellipsoids) have received attention. Here we report a study of the maximally random jammed (MRJ) packings of binary superdisks and monodispersed superballs whose shapes are defined by |x_1|^2p+...+|x_2|^2p<=1 with d = 2 and 3, respectively, where p is the deformation parameter with values in the interval (0, infinity). We find that the MRJ densities of such packings increase dramatically and nonanalytically as one moves away from the circular-disk and sphere point. Moreover, the disordered packings are hypostatic and the local arrangements of particles are necessarily nontrivially correlated to achieve jamming. We term such correlated structures "nongeneric". The degree of "nongenericity" of the packings is quantitatively characterized by determining the fraction of local coordination structures in which the central particles have fewer contacting neighbors than average. We also show that such seemingly special packing configurations are counterintuitively not rare. As the anisotropy of the particles increases, the fraction of rattlers decreases while the minimal orientational order increases. These novel characteristics result from the unique rotational symmetry breaking manner of the particles.Comment: 20 pages, 8 figure

Elliptic operators in even subspaces

In the paper we consider the theory of elliptic operators acting in subspaces defined by pseudodifferential projections. This theory on closed manifolds is connected with the theory of boundary value problems for operators violating Atiyah-Bott condition. We prove an index formula for elliptic operators in subspaces defined by even projections on odd-dimensional manifolds and for boundary value problems, generalizing the classical result of Atiyah-Bott. Besides a topological contribution of Atiyah-Singer type, the index formulas contain an invariant of subspaces defined by even projections. This homotopy invariant can be expressed in terms of the eta-invariant. The results also shed new light on P.Gilkey's work on eta-invariants of even-order operators.Comment: 39 pages, 2 figure

Nonlinear optical materials formed by push-pull (bi)thiophene derivatives functionalized with di(tri)cyanovinyl acceptor groups

Studies of the second-order nonlinear optical susceptibilities of six NLOphores bearing di(tri)cyanovinyl acceptor groups linked to (bi)thiophene heterocyclic donor systems were performed for the first time in polymethyl methacrylate (PMMA) matrices with a 1064 nm laser working in the 20 ns time pulse regime. Absorption spectra and DFT calculations were also performed. This multidisciplinary study showed that modulation of the optical (linear and nonlinear) properties can be achieved by increasing the length of the -conjugated heterocyclic system (thiophene vs. bithiophene), the strength of the electron donor groups (HMeO/EtOEt2N) as well as the strength of the electron acceptor moieties (DCV vs. TCV, two vs. three electron withdrawing cyano groups). Due to the relatively high second-order susceptibilities (0.08 to 6.45 pm/V), the studied push-pull chromophores can be denote as very potent NLOphores.Fundação para a Ciência e a Tecnologia (FCT

Quantized W-algebra of sl(2,1) and quantum parafermions of U_q(sl(2))

In this paper, we establish the connection between the quantized W-algebra of ${\frak sl}(2,1)$ and quantum parafermions of $U_q(\hat {\frak sl}(2))$ that a shifted product of the two quantum parafermions of $U_q(\hat {\frak sl}(2))$ generates the quantized W-algebra of ${\frak sl}(2,1)$

Design and clinical application of injectable hydrogels for musculoskeletal therapy

Musculoskeletal defects are an enormous healthcare burden and source of pain and disability for individuals. With an ageing population, the proportion living with these medical indications will increase. Simultaneously, there is pressure on healthcare providers to source efficient solutions, which are cheaper and less invasive than conventional technology. This has led to an increased research focus on hydrogels as highly biocompatible biomaterials that can be delivered through minimally invasive procedures. This review will discuss how hydrogels can be designed for clinical translation, particularly in the context of the new European Medical Device Regulation (MDR). We will then do a deep dive into the clinically used hydrogel solutions that have been commercially approved or have undergone clinical trials in Europe or the US. We will discuss the therapeutic mechanism and limitations of these products. Due to the vast application areas of hydrogels, this work focuses only on treatments of cartilage, bone, and the nucleus pulposus. Lastly, the main steps towards clinical translation of hydrogels as medical devices are outlined. We suggest a framework for how academics can assist small and medium MedTech enterprises conducting the initial clinical investigation and Post-Market Clinical Follow-up (PMCF) required in the MDR. It is evident that the successful translation of hydrogels is governed by acquiring high-quality pre-clinical and clinical data confirming the device mechanism of action and safety