Studies in nuclear reactor dynamics : I. The accuracy of point kinetics. II. The effect of delayed neutrons on the spectrum of the group-diffusion operator

This thesis is a theoretical work on the space-time dynamic behavior of a nuclear reactor without feedback. Diffusion theory with G-energy groups is used.

In the first part the accuracy of the point kinetics (lumped-parameter description) model is examined. The fundamental approximation of this model is the splitting of the neutron density into a product of a known function of space and an unknown function of time; then the properties of the system can be averaged in space through the use of appropriate weighting functions; as a result a set of ordinary differential equations is obtained for the description of time behavior. It is clear that changes of the shape of the neutron-density distribution due to space-dependent perturbations are neglected. This results to an error in the eigenvalues and it is to this error that bounds are derived. This is done by using the method of weighted residuals to reduce the original eigenvalue problem to that of a real asymmetric matrix. Then Gershgorin-type theorems .are used to find discs in the complex plane in which the eigenvalues are contained. The radii of the discs depend on the perturbation in a simple manner.

In the second part the effect of delayed neutrons on the eigenvalues of the group-diffusion operator is examined. The delayed neutrons cause a shifting of the prompt-neutron eigenvalue s and the appearance of the delayed eigenvalues. Using a simple perturbation method this shifting is calculated and the delayed eigenvalues are predicted with good accuracy.

MODIFIED DIRECT TWOS-COMPLEMENT PARALLEL ARRAY MULTIPLICATION ALGORITHM FOR COMPLEX MATRIX OPERATION

A direct twos-complement parallel array multiplication algorithm is introduced and modified for digital optical numerical computation. The modified version overcomes the problems encountered in the conventional optical twos-complement algorithm. In the array, all the summands are generated in parallel, and the relevant summands having the same weights are added simultaneously without carries, resulting in the product expressed in a mixed twos-complement system. In a two-stage array, complex multiplication is possible with using four real subarrays. Furthermore, with a three-stage array architecture, complex matrix operation is straightforwardly accomplished. In the experiment, parallel two-stage array complex multiplication with liquid-crystal panels is demonstrated.

Paranormal operator on a Hilbert space

In this thesis an extensive study is made of the set P of all paranormal operators in B(H), the set of all bounded endomorphisms on the complex Hilbert space H. T ϵ B(H) is paranormal if for each z contained in the resolvent set of T, d(z, σ(T))//(T-zI)^-1 = 1 where d(z, σ(T)) is the distance from z to σ(T), the spectrum of T. P contains the set N of normal operators and P contains the set of hyponormal operators. However, P is contained in L, the set of all T ϵ B(H) such that the convex hull of the spectrum of T is equal to the closure of the numerical range of T. Thus, N≤P≤L.

If the uniform operator (norm) topology is placed on B(H), then the relative topological properties of N, P, L can be discussed. In Section IV, it is shown that: 1) N P and L are arc-wise connected and closed, 2) N, P, and L are nowhere dense subsets of B(H) when dim H ≥ 2, 3) N = P when dimH ˂ ∞ , 4) N is a nowhere dense subset of P when dimH ˂ ∞ , 5) P is not a nowhere dense subset of L when dimH ˂ ∞ , and 6) it is not known if P is a nowhere dense subset of L when dimH ˂ ∞.

The spectral properties of paranormal operators are of current interest in the literature. Putnam [22, 23] has shown that certain points on the boundary of the spectrum of a paranormal operator are either normal eigenvalues or normal approximate eigenvalues. Stampfli [26] has shown that a hyponormal operator with countable spectrum is normal. However, in Theorem 3.3, it is shown that a paranormal operator T with countable spectrum can be written as the direct sum, N ⊕ A, of a normal operator N with σ(N) = σ(T) and of an operator A with σ(A) a subset of the derived set of σ(T). It is then shown that A need not be normal. If we restrict the countable spectrum of T ϵ P to lie on a C²-smooth rectifiable Jordan curve G_o, then T must be normal [see Theorem 3.5 and its Corollary]. If T is a scalar paranormal operator with countable spectrum, then in order to conclude that T is normal the condition of σ(T) ≤ G_o can be relaxed [see Theorem 3.6]. In Theorem 3.7 it is then shown that the above result is not true when T is not assumed to be scalar. It was then conjectured that if T ϵ P with σ(T) ≤ G_o, then T is normal. The proof of Theorem 3.5 relies heavily on the assumption that T has countable spectrum and cannot be generalized. However, the corollary to Theorem 3.9 states that if T ϵ P with σ(T) ≤ G_o, then T has a non-trivial lattice of invariant subspaces. After the completion of most of the work on this thesis, Stampfli [30, 31] published a proof that a paranormal operator T with σ(T) ≤ G_o is normal. His proof uses some rather deep results concerning numerical ranges whereas the proof of Theorem 3.5 uses relatively elementary methods.

Multiplication in Riesz spaces

A.G. Vulih has shown how an essentially unique intrinsic multiplication can be defined in certain types of Riesz spaces (vector lattices) L. In general, the multiplication is not universally defined in L, but L can always be imbedded in a large space L^# in which multiplication is universally defined.

If ф is a normal integral in L, then ф can be extended to a normal integral on a large space L₁(ф) in L^#, and L₁(ф) may be regarded as an abstract integral space. A very general form of the Radon-Nikodym theorem can be proved in L₁(ф), and this can be used to give a relatively simple proof of a theorem of Segal giving a necessary and sufficient condition that the Radon-Nikodym theorem hold in a measure space.

In another application, the multiplication is used to give a representation of certain Riesz spaces as rings of operators on a Hilbert space.

Investment in fish seed multiplication farms in Bangladesh: Evidences of an attractive business

This study mainly evaluated the profitability of Fish Seed Multiplication Farms (FSMFs) having hatchery, nursery and hatchery-cum-nursery located in the districts of Jessore, Jhenidah and Narail in Bangladesh. The general findings of the study were that the investment in FSMFs with hatchery, nursery and hatchery-cum-nursery was highly profitable business. The results clearly indicated that the investment on hatchery was the most profitable than those of nursery and hatchery-cum-nursery operations from the viewpoints of individual investors. The results of sensitivity analysis suggested that the investment in nursery farm was a risky business with 20 per cent increase in operation and management as well was production costs or 20 per cent reduction in benefits if other things remaining the same. It was also evident from the study that the investors of FSMFs had currently been facing some crucial problems, which among others are: problems of inbreeding, shortage of brood fish, incidence of diseases, unavailability of certain inputs and lack of credit.

Examining the possibilty of multiplication and breeding of (Schizothorav [sic] zarudnyi) in order to restoration of regional aquatics reservations of Hamoon Lake and taking its advantag [sic] for aquaculture

Schizothorax zarudnvi, is an endemic fish of east country waters. (Triple lagoons of Hamoon and relevant water resources) that in the world it is reported in this resource specially. This fish named Hamoon mahi is one of the most economically valuable species in this region. Because of the recent years droughts, Hamoon logoon has been drive since 2000. Also, semi-wells (a semi natural resource) were affected drastically by recent drought years and their volume reduced to nearly one third of their real volume and resulted in changing at growth and reproduction physiology process in Schizothorax zanidnyi, brood stocks. Beginning of this project was done from October 2003. It's field studies begun (brood catching) since November 2001 by two methods including entangling gairs and at semi wells of Sistan that (Beach seine) had maximum rate of preparing qualified brood stocks. Broods transferred to Cyprinidea reproduction work shop of Zahak and after taking primary measures they stored in to the edaphic pools. Increasing the success safety factor (coefficient) for artificial reproduction of Sthizothorax zarudnyi , identifying the appropriate tune for Hormonal acceptance (physiological preparation of broods) is needed , so this important work was done regularly by histological studies and GSI measurements since November. Highest GSI rates of females (%80.51) and highest IV stage abundance of sexual maturity (%l 00) were observed an march. On the base of this date, Hormone therapy was done on broods on march. The used hormones are as follows Hypophysis. extraction, GnRHa and Anti Dopamin at the dozes of 3-6 ml, 20-30kg and 10-15 ml per kg body weight respectively and 2-3 times from 11-12-80 they were injected. Injected broods kept in to two circumstances, flow-through (rounded pool) and stagnant systems. In stagnant system 14 and 19 individuals of female and male (Schizothorax zauiulnri) broods, respectively injected in 11th, 15111, 19th, and 24th of march 1380. Non of the injected broods in 11 and 15 and 19th march (in stagnant Condition) answered to Hormone therapy. After final injection broods had general less activity and a few of them died. Mean temperature of brood pond waters (daily) which were injected. Fluctuated between 10-25-13. 63°c but injected broods on 24th march had different characteristics. They had pale color and had few fecundity. In this stage of injection they hadn't any successful vulation. After injection, Mean daily water temperature was 15, 88-17, 54°c. In Flowing system, 13-16 individual of males and females respectively were injected on 15th, 19th, 22th and 23th march. None of injected producers on 15th and 19th march with mean daily water temperature of 10, 25-12°c were prepared for spawning but injected producers on 22nd an 23th march with mean daily water temperature of 13.5-1 rc responded about 75-100 percent. (Schizothorax zarudnyi) brood stocks were prepared for spawning after 353-428 hours/day from final injection. Diameter of obtained eggs (before fertilization) was between 1.9-2.3 min and of fertilized eggs was 3.8mm. Fertilized eggs of (Schizothorax zarudnyi) were hatched after 6-7 days with mean water temperature of 17.08°c. Mean length of on one day larvae was 9.47 mm. Larvae was 9.47 mm. Larvae adsorbed the whole yolk sac after , 5-6 days at 17- 1°c and were prepared for releasing in to edaphic pools. Because of the lack of necessary and complementary facilities in the region , they had to release them in to veniros and growing them for 8 days. At the end of 18th day , 35000 larvae (at first) released into an edaphic pond with a volume of 150m2. After growing them for one moth , mean length and weight of new hatched larvae was 29.41 mm and 1.12►r , respectively. With respect to results of this investigation , artificial reproduction of (Schizothorax zarudnyi) Can be possible at 14-17°C and flowing water with Hormonal treatment. It -s breeding has increased development than other cultural specious in the region. Due to high economical value of this specious in Sistan and ti-s specialization east waters of Iran and having high resistance and proper growth There is a need of it's development and reproduction and culture in fish culture fanns (edaphic ponds• two-purpose pools) at the region and country.

A Stochastic Model for Electron Multiplication Charge-Coupled Devices - From Theory to Practice

Electron multiplication charge-coupled devices (EMCCD) are widely used for photon counting experiments and measurements of low intensity light sources, and are extensively employed in biological fluorescence imaging applications. These devices have a complex statistical behaviour that is often not fully considered in the analysis of EMCCD data. Robust and optimal analysis of EMCCD images requires an understanding of their noise properties, in particular to exploit fully the advantages of Bayesian and maximum-likelihood analysis techniques, whose value is increasingly recognised in biological imaging for obtaining robust quantitative measurements from challenging data. To improve our own EMCCD analysis and as an effort to aid that of the wider bioimaging community, we present, explain and discuss a detailed physical model for EMCCD noise properties, giving a likelihood function for image counts in each pixel for a given incident intensity, and we explain how to measure the parameters for this model from various calibration images. © 2013 Hirsch et al.

Ultrafast collinear scattering and carrier multiplication in graphene.

Graphene is emerging as a viable alternative to conventional optoelectronic, plasmonic and nanophotonic materials. The interaction of light with charge carriers creates an out-of-equilibrium distribution, which relaxes on an ultrafast timescale to a hot Fermi-Dirac distribution, that subsequently cools emitting phonons. Although the slower relaxation mechanisms have been extensively investigated, the initial stages still pose a challenge. Experimentally, they defy the resolution of most pump-probe setups, due to the extremely fast sub-100 fs carrier dynamics. Theoretically, massless Dirac fermions represent a novel many-body problem, fundamentally different from Schrödinger fermions. Here we combine pump-probe spectroscopy with a microscopic theory to investigate electron-electron interactions during the early stages of relaxation. We identify the mechanisms controlling the ultrafast dynamics, in particular the role of collinear scattering. This gives rise to Auger processes, including charge multiplication, which is key in photovoltage generation and photodetectors.

270GHz, 580fs Optical Pulse Generation from a single-section quantum-dash fabry-pérot laser using frequency multiplication

Pulse generation from a mode-locked single-section 1.55μm quantum-dash FP laser is demonstrated under continuous-wave operation. A 270GHz, 580fs pulse train is achieved by applying frequency multiplication using fiber dispersion. ©2009 Optical Society of America.