Dissertations / Theses on the topic 'Cubic'

Let Nm(f(x)) denote the number of solutions of the congruence equation f(x)≡0 (modm), where m≥2 is any composite integer and f(x) is a cubic polynomial. In this thesis, we use different theorems and corollaries to find a number of solutions of the congruence equations without solving then we also construct the general expression of corresponding congruence equations to demonstrate the solutions of the equations. In this thesis, we use Mathematica software as a tool.

It is well-known that the set of rational points on an elliptic curve forms an abelian group. When the curve is given as a plane cubic in Weierstrass form the group operation is defined via tangent and secant operations. Let S be a smooth cubic surface over a field K. Again one can define tangent and secant operations on S. These do not give S(K) a group structure, but one can still ask for the size of a minimal generating set. In Chapter 2 of the thesis I show that if S is a smooth cubic surface over a field K with at least 4 elements, and if S contains a skew pair of lines defined over K, then any non-Eckardt K-point on either line generates S(K). This strengthens a result of Siksek [20]. In Chapter 3, I show that if S is a smooth cubic surface over a finite field K = Fq with at least 8 elements, and if S contains at least one K-line, then there is some point P > S(K) that generates S(K). In Chapter 4, I consider cubic surfaces S over finite fields K = Fq that contain no K-lines. I find a lower bound for the proportion of points generated when starting with a non-Eckardt point P > S(K) and show that this lower bound tends to 1/6 as q tends to infinity. In Chapter 5, I define c-invariants of cubic surfaces over a finite field K = Fq with respect to a given K-line contained in S, give several results regarding these c-invariants and relate them to the number of points SS(K)S. In Chapter 6, I consider the problem of enumerating cubic surfaces over a finite field, K = Fq, with a given point, P > S(K), up to an explicit equivalence relation.

Thermodynamic properties are essential for the design of chemical processes, and they are most useful in the form of an equation of state (EOS). The motivating force of this work is the need for accurate prediction of the phase behavior and thermophysical properties of natural gas for practical engineering applications. This thesis presents a new cubic EOS for pure argon. In this work, a theoretically based EOS represents the PVT behavior of pure fluids. The new equation has its basis in the improved Most General Cubic Equation of State theory and forecasts the behavior of pure molecules over a broad range of fluid densities at both high and low pressures in both single and multiphase regions. With the new EOS, it is possible to make accurate estimations for saturated densities and vapor pressures. The density dependence of the equation results from fitting isotherms of test substances while reproducing the critical point, and enforcing the critical point criteria. The EOS includes analytical functions to fit the calculated temperature dependence of the new EOS parameters.

Determining whether a number field admits a power integral basis is a classical problem in algebraic number theory. It is well known that every quadratic number field is monogenic, that is they admit power bases. However, when we talk about cubic or higher degree number fields we may discover fields without power integral bases. In 1878, Dedekind gave the first example of a cubic field without a power integral basis. It is known that a number field is monogenic if and only if the minimal index is one. In 1937, Hall proved that the minimal index of pure cubic fields can be arbitrarily large. We extend this result by showing that the minimal index of a family of infinitely many pure cubic fields have an element of index n but no element of index less than n for a positive integer n.
Irving K. Barber School of Arts and Sciences (Okanagan)
Mathematics, Department of (Okanagan)
Graduate

The varied properties of Silicon Carbide (SiC) are helping to launch the material into many new applications, particularly in the field of novel semiconductor devices. In this work, the cubic form of SiC is of interest as a basis for developing integrated optical components. Here, the formation of a suitable SiO2 buried cladding layer has been achieved by high dose oxygen ion implantation. This layer is necessary for the optical confinement of propagating light, and hence optical waveguide fabrication. Results have shown that optical propagation losses of the order of 20 dB/cm are obtainable. Much of this loss can be attributed to mode leakage and volume scattering. Mode leakage is a function of the effective oxide thickness, and volume scattering related to the surface layer damage. These parameters have been shown to be controllable and so suggests that further reduction in the waveguide loss is feasible. Analysis of the layer growth mechanism by RBS, XTEM and XPS proves that SiO2 is formed, and that the extent of formation depends on implant dose and temperature. The excess carbon generated is believed to exit the oxide layer by a number of varying mechanisms. The result of this appears to be a number of stable Si-C-O intermediaries that form regions to either depth extreme of the SiO2 layer. Early furnace tests suggest a need to anneal at temperatures approaching the melting point of the silicon substrate, and that the quality of the virgin material is crutial in controlling the resulting oxide growth.

The main subject of this thesis is solitons due to degenerate parametric four-wave mixing. Derivation of the governing equations is carried out for both spatial solitons (slab waveguide) and temporal solitons (optical fibre). Higher-order effects that are ignored in the standard paraxial approximation are discussed and estimated. Detailed analysis of conventional solitons is carried out. This includes discovery of various solitons families, linear stability analysis of fundamental and higher-order solitons, development of theory describing nonlinear dynamics of higher-order solitons. The major findings related to the stationary problem are bifurcation of a two-frequency soliton family from an asymptotic family of infinitely separated one-frequency solitons, jump bifurcation and violation of the bound state principle. Linear stability analysis shows a rich variety of internal modes of the fundamental solitons and existence of a stability window for higher-order solitons. Theory for nonlinear dynamics of higher-order solitons successfully predicts the position and size of the stability window, and various instability scenarios. Equivalence between direct asymptotic approach and invariant based approach is demonstrated. A general analytic approach for description of localised solutions that are in resonance with linear waves (quasi-solitons and embedded solitons) is given. This includes normal form theory and approximation of interacting particles. The main results are an expression for the amplitude of the radiating tail of a quasi-soliton, and a two-fold criterion for existence of embedded solitons. Influence of nonparaxiality on soliton stability is investigated. Stationary instability threshold is derived. The major results are shift and decreasing of the size of the stability window for higher-order solitons. The latter is the first demonstration of the destabilizing influence of nonparaxiality on higher-order solitons. Analysis of different aspects of solitons is based on universal approaches and methods. This includes Hamiltonian formalism, consideration of symmetry properties of the model, development of asymptotic models, construction of perturbation theory, application of general theorems etc. Thus, the results obtained can be extended beyond the particular model of degenerate four-wave mixing. All theoretical predictions are in good agreement with the results of direct numerical modeling.

This dissertation addresses optimization of cubic polynomial problems. Heuristics for finding good quality feasible solutions and for improving on existing feasible solutions for a complex industrial problem, involving cubic and pooling constraints among other complicating constraints, have been developed. The heuristics for finding feasible solutions are developed based on linear approximations to the original problem that enforce a subset of the original problem constraints while it tries to provide good approximations for the remaining constraints, obtaining in this way nearly feasible solutions. The performance of these heuristics has been tested by using industrial case studies that are of appropriate size, scale and structure. Furthermore, the quality of the solutions can be quantified by comparing the obtained feasible solutions against upper bounds on the value of the problem. In order to obtain these upper bounds we have extended efficient existing techniques for bilinear problems for this class of cubic polynomial problems. Despite the efficiency of the upper bound techniques good upper bounds for the industrial case problem could not be computed efficiently within a reasonable time limit (one hour). We have applied the same techniques to subproblems with the same structure but about one fifth of the size and in this case, on average, the gap between the obtained solutions and the computed upper bounds is about 3%. In the remaining part of the thesis we look at global optimization of cubic polynomial problems with non-negative bounded variables via branch and bound. A theoretical study on the properties of convex underestimators for non-linear terms which are quadratic in one of the variables and linear on the other variable is presented. A new underestimator is introduced for this class of terms. The final part of the thesis describes the numerical testing of the previously mentioned underestimators together with approximations obtained by considering lifted approximations of the convex hull of the (x x y) terms. Two sets of instances are generated for this test and the descriptions of the procedures to generate the instances are detailed here. By analyzing the numerical results we can conclude that our proposed underestimator has the best behavior in the family of instances where the only non-linear terms present are of the form (x x y). Problems originating from least squares are much harder to solve than the other class of problems. In this class of problems the efficiency of linear programming solvers plays a big role and on average the methods that use these solvers perform better than the others.

Let S be a smooth n-dimensional cubic variety over a field K and suppose that K is finitely generated over its prime subfield. It is a well-known fact that whenever we have a set of K-points on S, we may obtain new ones, using secant and tangent constructions. A Mordell-Weil generating set B ⊆ S(K) is a subset of minimal cardinality that generates S(K) via these operations; we define the Mordell-Weil rank as r(S,K) = #B. The Mordell-Weil theorem asserts that in the case of an elliptic curve E defined over a number field K, we have that r(E,K) < 1. Manin [11] asked whether this is true or not for surfaces. Our goal is to settle this question for higher dimensions, and for as many fields as possible. We prove that when the dimension of the cubic hypersurface is big enough, if a point can generate another point, then it can generate all the points in the hypersurface that lie in its tangent plane. This gives us a powerful tool, yet a simple one, for generating sets of points starting with a single one. Furthermore, we use this result to prove that if K is a finite field and the dimension of the hypersurface is at least 5, then r(S,K) = 1. On the other hand, it is natural to ask whether r(S,K) can be bounded by a constant, depending only on the dimension of S. It is conjectured that such a constant does not exist for the elliptic curves (the unboundedness of ranks conjecture for elliptic curves). In the case of cubic surfaces, Siksek [16] has proven that such a constant does not exist when K = Q. Our goal is to generalise this for cubic threefolds. This is achieved via an abelian group HS(K), which holds enough information about the Mordell-Weil rank r(S,K) in the following manner; if HS(K) becomes large, so does r(S,K). Then, by using a family of cubic surfaces that is known to have an unbounded number of Mordell-Weil generators over Q, we prove that the number of Mordell-Weil generators is unbounded in the case of threefolds too.

Electrochemical Impedance Spectroscopy (EIS) was used to develop a novel methodology for studying ionic interaction with lipids arranged in a lipid cubic phase (LCP). Studying different types of ions, both cations and anions, validated the method. A free-standing LCP membrane was formed between two cell compartments and impedance experiments were carried out in a 2-electrode setup to estimate dielectric properties of the membrane, exposed to the following electrolyte solutions at different concentrations: KCl, CsBr, CaCl2, MgCl2, CsCl, NaCl, NaOAc and NaTryptophan. Two different LCP were used in this setup, i.e: Monoloein/water and the ternary system of monoolein/dioleoylphosphatidylcholine/water (MO/DOPC/H2O). SAXRD measurements were performed to determine the space group of the cubic phase and confirm the stability of the LCP during measurements. Membrane resistances and capacitances were found from equivalent circuit fitting to the impedance data. The membrane resistance was shown to be related to ionic interaction with the lipid head group in the water channels of the LCP. Membrane capacitance were correlating to condensing and swelling effect of LCP due to the exposure of ions. The results correlated well with the SAXRD results and earlier published data. The results also indicate that these membranes become less permeable to ions as they increase in size as well as in charge or polarity.  Cyclic voltammetry was used to study the applications of a LCP for modification of the bioanode in a biofuel cell. The monoolein cubic phase was used to host Glucose oxidase (GOx) and a freely diffusing ferrocene carboxylate was used as mediator. The supported cubic phase had an intrinsic resistance in the same order of magnitude as the freestanding MO-LCP membrane as measured with EIS.
Elektrokemisk impedans spektroskopi har använts för att utveckla en ny metod för att studera joners växelverkan med lipider som bildat en kubisk fas. Olika typer av joner, både positiva och negativa, användes för att validera metoden. Ett fristående membran uppbyggt av en kubisk fas separerade två avdelningar i en elektrokemisk cell. Cellen fylldes med elektrolyt-lösningar och impedansmätningar kunde utföras mellan två platina elektroder placerade i vardera avdelning. Membranet exponerades för följande elektrolytlösningar av olika koncentration: KCl, CsBr, CaCl2, MgCl2, CsCl, NaCl, NaOAc and NaTryptofan. Två olika kubiska faser användes i denna uppställning, dvs: Monoloein/vatten och det ternära systemet monoolein/dioleoylfosfatidylkolin/vatten(MO/DOPC/H2O). Med hjälp av SAXRD kunde den kubiska fasens kristallstruktur bestämmas och dess stabilitet under mätningarna bekräftas. De dielektriska egenskaperna hos membranet bestämdes genom att anpassa impedansspektrat till en ekvivalent krets bestående av resistanser, kapacitanser och konstant-faselement. Membranresistansen visade sig vara relaterad till jonernas växelverkan med lipidhuvudgruppen i vattenkanalerna i kubiska fasen. Ju starkare växelverkan desto högre var resistansen. Membrankapacitansen kunde korreleras med kondenserande och uppsvällande effekter på kubiska fasen förorsakade av exponeringen till joner. Resultaten bekräftades av SAXRD mätningar och även tidigare publicerade data. Resultaten indikerar också tydligt att permeabiliteten hos membranet minskar med ökad jonstorlek, jonladdningoch polaritet hos jonen. Cyklisk voltammetri användes för att studera en tillämpning av kubiska fasen i en tänkt applikation som bioanod i en biobränslecell. Elektroden modifierades med en kubisk fas innehållande GOx och tillsammans med en fritt diffunderande ferrocen karboxylat som mediator, där oxidation av glukos studeras. Det visade sig att den kubiska fasen hade en resistans av samma storleksordning som det fristående membranet uppmätt med impedansspektroskopi.

The cubic lattice is a graph in Â3 where the vertices are points with integer coordinates and edges are unit length line segments parallel to the x-, y-, or z-axis. A step is a line segment that connects one vertex to a neighboring vertex one unit away in the x-, y-, or z-direction. This thesis will show that the Whitehead Link needs at least 34 steps to be embedded on the cubic lattice.

The Lielmezs-Merriman equation of state has been modified in such a way that it can be applied over the entire PVT surface except along the critical isotherm. The dimensionless T* coordinate has been defined according to the two regions on the PVT surface as: [Formula Omitted] The two substance-dependent constants p and q are generated from the vapor pressure data. The applicability of the proposed modification has been tested by comparing its predictions of various pure compound physical and thermodynamic properties with known experimental data and with predictions from the Soave-Redlich-Kwong and Peng-Robinson equations of state. The proposed equation is the most accurate equation of state for calculating vapor pressure, and saturated vapor and liquid volumes. The Peng-Robinson equation is the best for enthalpy and entropy of vaporization estimations. The Soave-Redlich-Kwong equation is the least accurate equation for pressure and volume predictions in the single phase regions. For temperature prediction, all three equations of state give similar results in the subcritical and supercritical regions. None of the three equations is capable of representing all departure functions accurately. The Peng-Robinson equation and the proposed equation are very similar in accuracy except in the region where the temperature is near the critical. That is, between 0.95 ≤ Tr ≤ 1.05, the proposed equation gives rather poor results. For isobaric heat capacity calculation, both Soave-Redlich-Kwong and Peng-Robinson equations are adequate. The Soave-Redlich-Kwong equation gives the lowest overall average RMS % error for Joule-Thomson coefficient estimation. The Soave-Redlich-Kwong equation also provides the most reliable prediction for the Joule-Thomson inversion curve right up to the maximum inversion pressure. None of the cubic equations of state studied in this work is recommended for second virial coefficient calculation below Tr = 0.8. An α-function specifically designed for the calculation of second virial coefficient has been included in this work. The estimation from the proposed function gives equal, if not better, accuracy than the Tsonopoulos correlation.
Applied Science, Faculty of
Chemical and Biological Engineering, Department of
Graduate

Understanding the mechanical properties and deformation characteristics of nanoscale metallic nanopillars and wires is a significant concern for designing reliable small devices that must resist loads in service. This thesis aims to extend understanding of the size dependent behaviour of nanopillars and wires in compression and tension by investigating their mechanical properties and deformation characteristics. Single crystal bcc pillars were fabricated by focussed ion beam (FIB) machining from Fe, Nb, V, Ta, Mo, W and Cr, as well as the ferrite (bcc) and austenite (fcc) components of a duplex stainless steel (DSS). These were tested in compression over a range of test temperatures from 193 K to 393 K using various types of nanomechanical devices. The effect of sample size (pillar diameter) on the strength was investigated and found to increase with decreasing pillar size. In bcc metals, the yield or flow stress, 􀀂􀀖, is inversely proportional with some power of the pillar diameter, d. In bcc metals tested, the power-law exponent, n, were found in the range of between -0.23 to -0.63, showing a less pronounced size effect than found for fcc pillars. The power-law exponent for bcc pillar deformation is also temperature dependent and was found to scale with the ratio of test temperature, Ttest to the critical temperature for screw dislocation mobility, Tc, of the bcc metal (T*= Ttest / Tc). It is notable that the size effect exponent weakens (approaches 0) as T* decreases. However, when the experiments are carried out at temperatures close to or just above Tc, the power-law exponents approaches the value reported in the literature for a range of fcc metals (-1 < n < -0.6). The variation in the power-law exponent observed for bcc metals can be explained by the change in mobility of thermally activated screw dislocations. Their mobility can be modelled by a threshold or lattice friction stress. If this friction stress is introduced into the empirical equation that relates the strength of fcc metal pillars to their diameter, a strong correlation between size effect exponent, the normalised test temperature (T*) and friction stress is obtained. It was found that the friction stress values (Fe, Nb and V) increase as Ttest decreases from 296 to 193 K. When the pillar diameter decreases, the friction stress would be more easily overcome due to the increase in surface-to-volume ratio. The contribution of lattice friction stress on the strength is higher at larger pillars than those for nanopillars. Thus, the divergence between best fit lines has become more apparent at micron-sized pillars, resulting in weaker size effects. Furthermore, the transition in deformation morphology from localized to wavy deformation was only found in Fe pillars, as the Ttest decreased from 296 to 193 K, further revealing that temperature has also strong influence on deformation behaviours of bcc pillars.

The properties of cubic nitrides grown by molecular beam epitaxy (MBE) on GaAs (001) have been studied using optical and electrical techniques. The aim of these studies was the improvement of the growth techniques in order to improve the quality of grown nitrides intended for bulk substrate and optoelectronic device applications. We have also characterised hexagonal nanocolumn structures incorporating indium. Firstly, bulk films of cubic AlxGa1-xN with aluminium fractions (x) spanning the entire composition range were tested using time-integrated and time-resolved photoluminescence (PL) plus reflectivity measurements. Strong PL emission was recorded from the samples, with improved intensity for higher aluminium concentrations. Temperature dependent and time-resolved PL showed the increasing role of carrier localisation at larger AlN fractions. The reflectivity results showed a near-steady increase in the bandgap energy with increasing AlN content. Alternative interpretations that did and did not involve a transition from direct-gap to indirect-gap behaviour in cubic AlxGa1-xN were considered. We next looked at cubic AlxGa1-xN/GaN/AlxGa1-xN single quantum well (QW) structures with varying AlN content in the barrier regions. The PL studies indicated that carrier escape from the QWs and non-radiative recombination at layer interfaces were limiting factors for strong well emission. Higher AlN concentration in the barriers appeared to exacerbate these problems. The doping of cubic GaN with silicon (n-type) and magnesium (p-type) was also studied. For Mg-doped GaN, a strong blue band emission was noted in the PL spectrum, which became more intense at higher doping levels. The Mg-doped GaN layers had low conductivity and their mobility could not be measured due to strong compensation effects. The cubic film had similar time-resolved PL properties for the blue band emission compared to hexagonal Mg:GaN. These results suggested that the blue band was the result of recombination between a shallow Mg acceptor and deep donor, believed to be a complex including a nitrogen vacancy and an Mg atom. This complex was also associated with the compensation effect seen in the electrical measurements. With the Si-doped cubic GaN, we observed PL spectra that were consistent with other sources. Thicker layers of GaN:Si did not have measurable mobility. This was likely caused by the rough surface structure that was imaged using a scanning electron microscope. The thin layer had a very smooth surface in comparison. The mobility of sub-micron thickness layers with a carrier concentrations of n = 2.0×1018cm-3 and n = 9.0×1017cm-3 were μ = 3.9cm2/Vs and μ = 9.5cm2/Vs respectively. The mobility values and structural issues indicated that growth improvements were needed to reduce scattering defects. In addition to cubic structures, we have considered nanocolumn growth of InGaN and InN. InxGa1-xN nanocolumns were grown on Si (111) by MBE with a nominal indium concentration of x = 0.5. PL emission was obtained from samples grown at higher temperature, but overall intensity was low. A second set of samples, where nanocolumn growth was followed by growth of a continuous coalesced film exhibited much stronger PL emission, which was attributed to the elimination of a phase separated core-shell structure in the nanocolumns. Next, a coalesced InxGa1-xN structure with vertically varying indium fraction was characterised. PL readings showed evidence of successful concentration grading. Finally, the PL spectra of coalesced InN layers were recorded, for which a specialised infrared PL system needed to be used. The results highlighted how increased growth temperature and indium flux can improve PL properties. For the binary alloy however, coalescence growth can decrease PL intensity compared to the nanocolumns stage.

Philosophiae Doctor - PhD
The history of the pursuit of uncolourable cubic graphs dates back more than a century. This pursuit has evolved from the slow discovery of individual uncolourable cubic graphs such as the famous Petersen graph and the Blanusa snarks, to discovering in nite classes of uncolourable cubic graphs such as the Louphekine and Goldberg snarks, to investigating parameters which measure the uncolourability of cubic graphs. These parameters include resistance, oddness and weak oddness, ow resistance, among others. In this thesis, we consider current ideas and problems regarding the uncolourability of cubic graphs, centering around these parameters. We introduce new ideas regarding the structural complexity of these graphs in question. In particular, we consider their 3-critical subgraphs, speci cally in relation to resistance. We further introduce new parameters which measure the uncolourability of cubic graphs, speci cally relating to their 3-critical subgraphs and various types of cubic graph reductions. This is also done with a view to identifying further problems of interest. This thesis also presents solutions and partial solutions to long-standing open conjectures relating in particular to oddness, weak oddness and resistance.

We develop a method that is capable of proving lower bounds that are consistent with Manin's conjecture for the number of rational points of bounded height on Fano varieties for which establishing Manin's conjecture is far out of reach with current technology. More specifically we develop the fibration method from the perspective of analytic number theory and as an application we provide correct lower bounds for families of smooth cubic surfaces with a rational line. The key ingredient of our approach is an asymptotic formula with a precise error term for Manin's conjecture for general smooth conics. Using the geometry of conic bundles we transform the average of the Peyre constants of the fibers into divisor sums over values of quintic binary forms. The underlying divisor functions include Dirichlet convolutions of quadratic characters whose modulus is unbounded, an element which is new in the large body of work on divisors sums. In the concluding chapter we combine the fibration method with sieve techniques to attack the saturation number problem. We show that rational points with at most 22 prime factors counted with multiplicity form a Zariski dense subset of each smooth cubic surface with two rational skew lines. This chapter is part of joint work with Yuchao Wang.

Thesis (Ph.D.)--Indiana University, Dept. of Mathematics, 2008.
Title from PDF t.p. (viewed on Jul 27, 2009). Source: Dissertation Abstracts International, Volume: 69-11, Section: B, page: 6843. Adviser: Darrell Haile.

Thesis (M. S.)--Computing, Georgia Institute of Technology, 2009.
Committee Chair: Prof. Richard Lipton; Committee Member: Prof. Dana Randall; Committee Member: Prof. H. Venkateswaran. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Maximal unramified extensions of quadratic number fields have been well studied. This thesis focuses on maximal unramified extensions of cyclic cubic fields. We use the unconditional discriminant bounds of Moreno to determine cyclic cubic fields having no non-solvable unramified extensions. We also use a theorem of Roquette, developed from the method of Golod-Shafarevich, and some results by Cohen to construct cyclic cubic fields in which the unramified extension is of infinite degree.

I lipidi esibiscono un comportamento ricco di diverse fasi liotropiche e termotropiche, a causa del loro carattere antipatiche: questo è un punto molto importante, infatti ogni variazione dei parametri fisicochimici della componente lipidica può portare in gran parte a modificare lo stato di membrana e quindi influenzare l’attività delle proteine presenti.Il comportamento di fase e le proprietà strutturali del monoacilglicerolo (monoleina) è stato investigato da lungo tempo in quanto esibisce un vasto polimorfismo. In particolare la monoleina in acqua mostra diverse mesofasi caratterizzate da un alto grado di disordine conformazionale delle catene idrocarburiche. Variando la concentrazione di acqua si passa da una fase lamellare (L-alfa) ad un’esagonale inversa (H II) a due fasi cubiche bi continue inverse : Ia3d (Q230) e Pn3m (Q224). Le fasi cubiche sono uniche nella loro capacità di inglobare proteine al loro interno, comparare con altre fasi lipidiche. Una grande varietà di proteine globulari con un peso molecolare di circa 5000- 15000 sono intimamente legate alle fasi lipidiche e in alcuni casi ne promuovono la transizione di fase. Solo pochi diagrammi di fase lipide-proteina-acqua sono stati completamente determinati, ma il ruolo della proteina nella transizione di fase non è ancora chiaro. In questa tesi è stato studiato in particolare il sistema monoleina-citocromo c –acqua. In questo sistema avviene una transizione fase cubica- fase cubica quando la monoleina è in equilibrio per alcuni giorni con un eccesso di soluzione di citocromo c. questa proteina ha l’effetto di promuovere la transizione di fase da Pn3m a Im3m (Q229).La monoleina forma la Pn3m in eccesso d’acqua mentre forma Im3m in eccesso di soluzione di citocromo c. In questa tesi lo studio delle variazioni strutturali sono stati condotti variando la concentrazione di proteina e valutando gli effetti della variazione di temperatura e di pressione nella transizione di fase Pn3m a Im3m usando le tecniche del SAXS (Small Angle X Ray Scattering ) e la spettroscopia elettronica di assorbimento (EAS).Gli esperimenti sono stati fatti usando il diffrattometro in dotazione presso il nostro laboratorio e quello del dipartimento di fisica dell’università di San Paolo e la luce di sincrotrone di Grenoble (ESRF), Amburgo (DESY), Campinas (San Paolo-Brasile ). I campioni sono formati da 50 mg/ml di monoleina e diverse concentrazioni di citocromo (1-5-10-25- 50 e 100 mg/ml).In primo luogo, abbiamo studiato l'influenza della concentrazione Cytocrome-C sulla transizione di fase cubica Pn3m formata dalla monoleina.. Abbiamo iniziato con 25 mg / ml di lipide, ma la concentrazione non era sufficiente per effettuare tutti gli esperimenti necessari. Così abbiamo deciso di utilizzare 50 mg / ml (MO Cv = 0,614) e le concentrazioni di citocromo c (1, 5, 10, 25, 50, 100 mg / ml).Tutte le misure sono state eseguite dal primo fino al ventunesimo giorno dopo la preparazione del campione, al fine di indagare la cinetica di tale transizione. È interessante notare che, la concentrazione di proteina gioca un ruolo importante nella transizione di fase monoleina. Tutti gli esperimenti SAXS sono stati effettuati in Brasile, presso l'Istituto di Fisica dell'Università di San Paolo, sotto la supervisione del Prof. Rosangela Itri. Il secondo passo è stato quello di valutare l'influenza della temperatura sul sistema monoleina-acquacitocromo, e osservare la differenza con il diagramma di fase tradizionale della monoleina. Il comportamento strutturale termo tropico del sistema MO / citocromo è stata studiato tramite diffrazione con un range che va dai 25 ai 90 ° C; tale analisi è stata effettuata presso il sincrotrone DESY di Amburgo (Germania) in diversi giorni della preparazione dei campioni, dal primo fino al giorno tredici. L'analisi della temperatura è interessante perché permette di il comportamento della componente lipidica temperature che vanno oltre il suo status di denaturazione delle proteina. In questa tesi,alta pressione è utilizzata per ottenere alcuni contributi sulla comprensione della struttura di sistemi biologicamente interessanti come monoleina e citocromo c.L'analisi è stata effettuata nei laboratori dell’ ESRF di Grenoble (Francia) a diversi giorni dalla preparazione del campione, a 2 e 8 giorni. Sistemi di monoleina e acqua sono stati poi usati per la nuova tecnica del drug delivery per la cura di particolari patologia come il morbo di Parkinson usando dispersioni in acqua di monoleina sotto forma di cubosomi o Solid Lipid Nanoparticules. Infine all’interno dei canali formanti dalla monoleina sono stati introdotti oltre che proteine anche nucleotidi per testare la loro influenza sulle transizioni di fase.
The lipids exhibit a rich lyotropic and thermotropic phase behaviour, due to their amphipatic character : this is a very important point, in fact any variation oh the physico-chemical properties of the lipid component will largely modify the state ad function of the membrane, for example influencing the protein activity. Phase behaviour and structural properties of monoacylglyceride (monoolein) in water have been investigate for a long time, because exhibit an extended polymorphism. In particular, monoolein in water shows several mesophases, characterized by a highly disordered conformation of the hydrocarbon chain.Varying the water concentration a lamellar L-alfa, an inverted (type II) hexagonal phase H II and two bicontinuos inverted cubic phases with space group Pn3m (Q224) and Ia3d (Q230) have been identified. The cubic phases are also unique in their ability to accommodate proteins as compared with other lipid-water phases. A wide range of globular protein with molecular weight 5000-15000 is known to intimately mix in lipid cubic phases, even if in some cases, the protein causes phase transition to occur. Only few ternary lipid-protein-water phase diagram have been completely determined, but the role of protein on the phase transition remain unclear. We was in particular attracted by monoolein-cytochrome C-water, that was studies some time ago. In this system, a cubic-to cubic phase transition occurs when the monoolein is left to equilibrium for several day in excess of a cytochrome C solution: this protein has the unique effect to induce the transformation from the Pn3m to Im3m cubic phase. The monoolein forms the Pn3m cubic phase in excess water, while it forms the Im3m cubic phase in excess of cytochrome C solutions. In this thesis the result of the structural investigation of the monoolein- cytochrome C- water system under variation of concentration of protein, temperature and pressure are discusses. We take advantage of the structural properties of monoolein and cytochrome-c to extensively study the temperature, pressure and concentration of protein effects on the cubic transition from Pn3m to Im3m by means of small-angle X-ray scattering technique (SAXS) and electronic absorption spectroscopy (EAS).Experiments were performed at our laboratory and diffractometer at the synchrotron in Grenoble (ESRF), Hamburg (DESY), Campinas (LNLS) and the unity of physics at the University of São Paulo (Brazil). To do so, we made samples composed of monoolein (50 mg/ml) in the presence of 1,5, 10,25,50 and 100 mg/ml of cytochrome-c. First, we studied the influence of Cytocrome-c concentration on Monoolein phase transition . We started with 25 mg/ml but the concentration was not good enough to perform all the required experiments. So we decided to use 50 mg / ml (Cv mo = 0.614) and cytochrome c concentrations (1, 5, 10, 25, 50, 100 mg/ml). All the measurements were performed dairy from the first up to the twenty-first day after sample preparation, in order to investigate the kinetics of such transition. Interestingly, the protein concentration plays an important role on the monoolein phase transition. All SAXS experiments were performed in Brazil, in the Institute of Physics of the University of Sao Paulo, under the supervision of Prof. Rosangela Itri. The second step was to evaluate the influence of temperature on the system monooleinwater- cytochrome, and observe the difference with the traditional phase diagram of monoolein. The thermotropic structural behavior of the MO/cytochrome was investigated by diffraction temperature scan between 25 and 90°C and this analysis was mad in the Hamburg Synchrotron DESY (Germany) at different days of sample preparation, from the first up to the thirteen day. The temperature analysis is interesting because it provides outline the lipid part and the cytochrome behaviour at room –temperature up to temperature that go over its denaturation status. .In this thesis, high-pressure is used to obtain some contributions to our understanding of biologically relevant molecular structure, in this case monoolein and cytochrome c. This analysis was made in the Grenoble ESRF (France) at different days of sample preparation, at 2 and 8 days. Monoolein- water systems were then used for the new drug delivery technique for treating specific disorders such as Parkinson's disease using monoolein dispersions in water or in the form of Solid Lipid Nanoparticule and cubosomes .Finally, within the channels forming the monoleina were introduced as well as proteins nucleotides also to test their influence on phase transitions.

In this work growth of cubic GaN in the selective area (SA) MOVPE process is

simulated. The simulations are restricted to small pattern SA MOVPE growth.

In this case the traditional MOVPE growth and the enhanced growth caused by

surface diffusion are important growth factors. The lateral vapor phase diffusion

is ignored while this process only has a small impact on the enhanced growth in

the small pattern SA growth. The model is build for simulation of anisotropic

growth. It has been shown that different type of anisotropic growth occurs when

the mask pattern are orientated in different directions on the substrate. While

the anisotropic growth is not well understood two different models are studied in

this work.

The simulation is restricted to the geometrical growth characteristics such

as mask and crystal width, mask alignment and surface diffusion on the crystal.

The reactor geometry, pressure and growth temperature are not investigated that

closely and are only treated as constants in the model.

The model used in this simulation gives good results for short time simulations

for some certain cases. The model shows that the fill factor has a greater

impact on the grown shapes than the individual mask and crystal width. But

there are problems with the anisotropic and flux from mask modeling while some

facets do not appear and the lateral growth along the mask show doubtful results.

The model show good results in short time growth and predict some important

characteristics in SA MOVPE.

Silicon carbide (SiC) is a wide band gap semiconductor satisfying requirements to replace silicon in devices operating at high power and high frequency at high temperature, and in harsh environments. Hexagonal polytypes of SiC, such as 6H-SiC and 4H-SiC are available on the power device markets. However, the cubic SiC (3C-SiC) polytype is still not industrially used, essentially due to the lack of 3CSiC substrates. This is mainly because of a high density of defects appearing in the  crystals. Thus, it is critical to understand material growth and defect formation, and learn to control their appearance. Ensuring, that growth methods capable of large scale industrial production can be applied. The aim of this work was to develop operation conditions for fabrication of 3C-SiC crystals via understanding fundamentals of the growth process and to explore structural and electrical properties of the grown material, including its suitability for substrate applications. The physical vapor transport or sublimation process has already shown a capability to produce substantial quantities of large area and high quality hexagonal SiC substrates. In the present study a similar growth principle, but in a different geometry, namely sublimation epitaxy, was applied. Using this method very high growth rates (up to 1 mm/h) can be achieved for hexagonal polytypes while maintaining high material quality. Additionally, the growth process does not require expensive or hazardous materials, thus making the method very attractive for industrial use. When growing 3C-SiC directly on 6H-SiC, the substrate roughness does not have significant influence on the yield and quality of 3C-SiC. This is mostly due to the growth of homoepitaxial 6H-SiC which appears before the 3C-SiC. Structural characterization showed that 3C-SiC grown directly on 6HSiC exhibited the highest quality as compared with other substrate preparation, such as annealing or deposition of a 3C-SiC buffer layer. Thus, further investigation was devoted to the growth of 3C-SiC on 6H-SiC substrates. The parameter window for the growth of 3C-SiC is quite narrow. The temperature interval is from ~1675oC, where the material starts to nucleate, to ~1850oC, where an uncontrolled growth process begins. Si-rich conditions (high Si/C ratio) and high supersaturation are needed in the growth chamber for preferable 3C-SiC nucleation. Deviation from these parameters leads to the growth of homoepitaxial 6HSiC in spiral or 2D island mode along with cubic SiC with high defect density. Nucleation is the most important step in the growth process. The growth on 6H-SiC substrates commences from homoepitaxial 6H-SiC growth in spiral mode, which makes the surface perfect for 3CSiC nucleation. At temperature of ~1675oC the supersaturation is high enough and the 3C-SiC nucleation initiates in two-dimensional islands on the 6H-SiC spiral terraces. Control of the homoepitaxial 6H-SiC growth is a key element in the growth of 3C-SiC. SiC is a polar material having surfaces terminated by either silicon or carbon atoms, called Si- and C-face, respectively. The growth is different on both faces due to the different free surface energies. The lower surface free energy on the C-face causes more uniform nucleation of 3C-SiC and thereafter more uniform twinned domain distribution. Additionally, calculations showed that increase of growth temperature from 1675oC to 1775oC does not change the supersaturation ratio on the C-face due to a much higher surface diffusion length. This results in appearance of pits in the 3C-SiC layer with a 6H-SiC spiral. The pits were not observed on Si-face material as the supersaturation ratio was much higher. Pits formed in the early stages of growth were overgrown more effectively during the later stages. Characterization by transmission electron microscopy showed that transformation from 6H-SiC to 3C-SiC is not abrupt and can appear in two different modes. The first one is forming a few micrometers of polytypic transition zone consisting predominantly of 15R-, 6H- and 3C-SiC. The second one appears due to a competition between 3C-SiC and 6H-SiC resulting in a step-like intermixing zone between these polytypes. Four-fold twins were observed, which resulted in depressions at the surface of 3C-SiC. These defects expand proportionally to the layer thickness, thus drastically reducing usable area of thick layers. Electrical measurements revealed carrier mobility ~200 cm2/Vs at room temperature and the dominant charge carrier scattering is by neutral centers and phonons. The neutral centers originate from extended defects, such as 6H-SiC inclusions, stacking faults and twin boundaries. By growing 3C-SiC on atomically flat and vicinal substrates a preferential orientation of twin boundaries (TBs) was achieved. The mobility was higher in the material with twin boundaries parallel to the current flow, and lower when twin boundaries were perpendicular to the current flow. This was less pronounced at higher temperature as relatively fewer carriers have to overcome barriers created by TBs. Finally, the substrate capability of the 3C-SiC (111) was demonstrated by growth of a monolayer graphene, which was compared with graphene grown on hexagonal SiC poytypes. The quality of the graphene in terms of thickness uniformity and pit appearance was the best when grown on 3C-SiC. The lower quality on hexagonal substrates was attributed to a more difficult process control which is due to the more complex crystal structure.

L’objectif de ce travail est de proposer une étude de divers comportements non linéaires pour un système de deux équations de Schrödinger cubiques couplées. Selon le choix de l’espace des positions, nous mettons en évidence différents exemples de comportements non linéaires. Dans le premier chapitre, nous introduisons les notions et outils nécessaires à la compréhension de l’enjeu. En particulier, nous justifions ce choix de modèle par des résultats récents sur l’équation de Schrödinger non linéaire. Le second chapitre est dédié à l’étude de ce système sur le tore (une coordonnée périodique). Nous mettons en évidence un échange d’énergie en temps long (mais fini) entre différents modes de Fourier des solutions : c’est l’effet de battement (éventuellement décalé). Le troisième chapitre porte sur l’étude du système sur la droite réelle (une coordonnée euclidienne). Nous mettons en place un résultat de scattering modifié pour obtenir un comportement non linéaire en temps infini. Enfin, dans le quatrième chapitre, nous nous plaçons dans un espace produit (une coordonnée euclidienne et une coordonnée périodique). Nous exhibons alors le résultat principal de cette thèse : un échange d’énergie en temps infini via un résultat de scattering modifié
The aim of this work is to propose a study of various nonlinear behaviors for a system of two coupled cubic Schrödinger equations. Depending on the choice of the spatial domain, we highlight different examples of nonlinear behaviors. In the first chapter, we introduce the notions and tools needed to understand the issue. In particular, we justify this choice of model by recent results on the nonlinear Schrödinger equation. The second chapter is dedicated to the study of this system on the torus (one periodic coordinate). Here, we exhibit an energy exchange for long (but finite) times between different Fourier modes of the solutions: this is the (possibly shifted) beating effect. The third chapter deals with the study of the system on the real line (one Euclidean coordinate). We set up a modified scattering result to get a nonlinear behavior in infinite time. Finally, in the fourth chapter, we consider a product space (one Euclidean coordinate and one periodic coordinate). We obtain the main result of this thesis: an energy exchange in infinite time thanks to a modified scattering result

The properties of free-standing cubic silicon carbide for optoelectronic applications are explored in this work. The main focus of the work is on boron doped cubic silicon carbide, which is proposed as a highly useful material in several optoelectronic applications. The material is grown using sublimation epitaxy and the doped material is grown homoepitaxially on nominally undoped seeds. It is characterized using the experimental setups of photoluminescence spectroscopy, Nomarski interference spectroscopy and absorption spectroscopy. I have studied seed growth of nominally undoped cubic material on hexagonal (4H) substrates, and the influence on the grown material from the different faces of the substrate. It is found that it is not possible under the explored conditions to completely cover the growth area with the cubic polytype on the carbon face, but it can be done reproducibly on the silicon face. Reasons for this are discussed. Different doping setups are also explored. The influence on the material properties from growth conditions is explored. It is shown from absorption measurements that it is possible to grow boron doped cubic silicon carbide using this growth method, whereas optical microscopy studies show that the sample quality degrades with high doping concentrations. I have explored the luminescence properties of the material. No boron related emission is found with either room temperature or low temperature photoluminescence spectroscopy. Reasons for this are discussed using results from absorption measurements and optical microscopy.

A method is described for least squares filling an ordered set of data in the plane with a free-form curve with no specific function or parameterization given for the data. The method is shown to be effective and uses some techniques from the field of Computer Aided Geometric Design (CAGD). We construct a piecewise G cubic Bezier curve from cubic curve segments which have as their initial end points, or knot points, some of the data points. The parameters for the curve are: the knot points, the angles of the tangent vectors at the knot points, and the distances from each knot point to the adjacent control points. The algorithm is developed and three solution curves are presented: Globally Optimized Only (GOO), Segmentally Optimized Only (SOO), and Segmentally then Globally Optimized (SGO).

Thesis (S.M.)--Massachusetts Institute of Technology, School of Architecture and Planning, Program in Media Arts and Sciences, 2012.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 91-95).
This thesis details the design, execution and evaluation of a new type of display technology, known as Display Blocks. Display Blocks are a response to two major limitations of current displays: visualization and interaction. Each device consist of six organic light emitting diode screens, arranged in a cubic form factor. I explore the possibilities that this type of display holds for data visualization, manipulation and exploration. To this end, I also propose a series of accompanying applications that leverage the design of the displays. To begin assessing the potential of this platform and to define future directions in which to expand this research, I report on a series of interviews I conducted regarding the potential of Display Blocks with relevant technologists, interaction designers, data visualizers and educators. The work encompassed in this thesis shows the promise of display technologies which use their form factor as a cue to understanding their content.
by Pol Pla i Conesa.
S.M.

Cubic carbides (titanium, tantalum, niobium, and zirconium carbides) can constitute a significant proportion of so-called cubic and cermet grades, where it is added to substitute a portion of tungsten carbide. It is thus critical to understand and be able to thermodynamically model the cubic carbide systems. In order to do this, the thermodynamic descriptions of lower order systems, such as the Ti-Cr-C system, need to be well studied. To approach this goal, an extensive literature survey of thermodynamic data and phase diagram information on the Ti-Cr-C system, the Ta-Cr-C system, the Nb-Cr-C system and the Zr-Cr-C is presented in this work. Experiments are performed in the Ti-Cr-C system using powder metallurgy and heat treatments. The solubility of Cr in FCC_TiC phase was experimentally measured at 1773K and compared with previous studies showing that the solubility reported earlier is too large. Thereafter, a re-optimization of FCC_TiC and liquid interaction parameters of the Ti-Cr-C system was performed taking into account the experimental data obtained both from previous studies and this work. The Gibbs energy descriptions of the Cr-carbide end members were compared between the one from the in-house database [SandvikTDB] and from other studies. With the new description, the solubility of Cr in FCC_TiC is better described.

Master of Science
Department of Chemical Engineering
J. H. Edgar
Boron phosphide, BP, is a III-V compound semiconductor with a wide band gap of 2.0 eV that is potentially useful in solid state neutron detectors because of the large thermal neutron capture cross-section of the boron-10 isotope (3840 barns). In this study, cubic BP crystals were grown by crystallizing dissolved boron and phosphorus from a nickel solvent in a sealed (previously evacuated) quartz tube. The boron - nickel solution was located at one end of the tube and held at 1150°C. Phosphorus, initially at the opposite end of the tube at a temperature of 430°C, vaporized, filling the tube to a pressure of 1–5 atmospheres. The phosphorus then dissolved into solution, producing BP. Transparent red crystals up to 4 mm in the largest dimension with mostly hexagonal shape were obtained with a cooling rate of 3°C per hour. The crystal size decreased as the cooling rate increased, and also as growth time decreased. The characterization with x-ray diffraction (XRD) and Raman spectroscopy established that the BP produced through this method were highly crystalline. The lattice constant of the crystals was 4.534 Ǻ, as measured by x-ray diffraction. Intense, sharp Raman phonon peaks were located at 800 cm[superscript]-1 and 830 cm[superscript]-1, in agreement with the values reported in the literature. The FWHM for XRD and Raman spectra were 0.275° and 4 cm[superscript]-1 which are the narrowest ever reported and demonstrates the high quality of the produced crystals. Energy dispersive x-ray spectroscopy (EDS) and scanning electron microscope (SEM) also confirmed the synthesized crystals were cubic BP crystals, with a boron to phosphorus atomic ratio of 1:1. Defect selective etching of BP at 300ºC for two minutes with molten KOH/NaOH revealed triangular and striated etch pits with low densities of defects of ~4 x 10[superscript]7 cm[superscript]-2 and 9.2 x 10[superscript]7 cm[superscript]-2 respectively. The BP crystals were n-type, and an electron mobility of ~39.8 cm[superscript]2/V*s was measured. This is favorable for application in neutron detection. Scaling to larger sizes is the next step through gradient freezing and employing a larger crucible.

Le but de ce travail était l’analyse de la capacité de carbure de silicium cubique à servir de matériau d’anode pour le fractionnement de l’eau photo-électrochimique direct. Les données récoltées (principalement la spectroscopie photo-électronique, électrochimie, Raman et spectroscopie UV-Vis) permettaient de ramener la faible efficacité de carbure de silicium cubique dopé n pour le dégagement d’oxygéne à des problèmes fondamentaux.Principalement le courant photoélectrique réalisable est limité par le flux des trous générés par photo à la surface de semi-conducteur. Comme carbure de silicium cubique est un semi-conducteur indirect, le faible coefficient d’absorption en combinaison avec une dotation élevée et une petite longueur de diffusion de trou ont été déterminés comme les facteurs limitant. Un film épitaxial additionnel de carbure de silicium n-cubique a entraîné une augmentation signifiante du courant photoélectrique maximal.La tension photoélectrique réalisable et les pertes dues aux recombinaisons dépendent principalement des propriétés de surface. L’utilisation des minces couches de catalyseur s’est révélé prometteur pour améliorer les deux propriétés même si cette technique a besoin d'optimisation parce que des états défectueux à l’interface limitent la tension photoélectrique
The goal of this work was to investigate cubic silicon carbide as anode material for direct photoelectrochemical water splitting. From the performed measurements (mostly photoelectron spectroscopy, electrochemical measurements, Raman and UV-Vis spectroscopy) n-type cubic silicon carbide’s low oxygen evolution efficiency could be related to some fundamental problems.Primarily, the attainable photocurrent is limited by the flux of photo generated holes to the semiconductor surface. As cubic silicon carbide is a indirect semiconductor, the low absorption coefficient in combination with a high doping concentration and low hole diffusion length were determined as limiting factors. An additional epitaxial n- cubic silicon carbide film resulted in a significant improvement of the photocurrent.The obtainable photovoltage and recombination losses are mostly dependent on the surface properties. While a buried junction between the silicon carbide and a thin catalyst layer has proven to be promising for improving both properties, it still needs optimization, as Fermi level pinning from interface defect states drastically reduces the photovoltage

Vibration isolators are often assumed to possess linear viscous damping which has well known consequences for their performance. However, damping may be designed to be or prove to be nonlinear. This study investigates the effect of cubic damping, as an example of damping nonlinearity, in a single degree of freedom (SDOF) vibration isolation system. The response behaviour due to two excitation types, namely harmonic and broadband excitations, was examined. For harmonic excitation, the Harmonic Balance Method (HBM) was applied to yield approximate closed form solutions and simplified analytical expressions implicitly show the influence of cubic damping for particular frequency regions. The HBM solutions were verified using direct numerical integration. The presence of cubic damping proves to be beneficial for the force excited case. It reduces response amplitude around the resonance frequency and has similar response to an undamped system in the isolation region. In contrast, for base excitation, the cubic damping is detrimental at high excitation frequencies as the base excitation and isolated mass move almost together. The effect becomes more pronounced for larger excitation amplitudes. The case of base excitation was then considered for broadband excitation. The responses using direct numerical integration were presented using power spectral densities. In contrast to harmonic excitation, the amplitude of the response does not appear to approach that of the input. Instead, a higher effective cubic damping results in a higher vibration level of the isolated mass at frequencies below the resonance frequency. It also does not reduce explicitly the response amplitude around the resonance frequency unlike the linear viscous damping. For a constant displacement amplitude random excitation, the excitation frequency bandwidth is found to be a significant factor in the level of effective cubic damping. A broader excitation bandwidth results in a higher level of cubic damping force. The theoretical and numerical results for both harmonic and broadband excitation were validated experimentally. The experimental investigation was performed using a SDOF base excited vibration isolation system possessing a simple velocity feedback control active damper to reproduce the nonlinear damping force. The predictions were shown to be in good agreement with measurements thereby verifying the effects of cubic damping on a SDOF system undergoing harmonic and broadband base excitation.

Ce projet de thèse s'inscrit dans un large contexte : l'étude des théories de la gravitation, notamment par la modélisation d'objets compacts tels que les trous noirs. Le but ultime de cette démarche est de déterminer toutes les théories incompatibles avec les observations, ou présentant des pathologies théoriques. En conséquence, la première partie de ce manuscrit présente les concepts et principes essentiels communs à toutes ces théories, et introduit certaines d'entre elles entretenant un lien avec le projet. La deuxième partie expose les résultats propres au projet : une comparaison entre une famille de trous noirs en rotation issue de la théorie du Galileon cubique, et les trous noirs de Kerr de la théorie de la relativité générale. Le Galileon cubique est une théorie très récente relativement à la relativité générale, développée par Albert Einstein il y a plus d'un siècle.Tout d'abord, ces trous noirs sont construits numériquement. Les orbites autour de ces trous noirs, notamment leur stabilité, sont ensuite étudiées. Enfin, les images produites par un modèle simple de disque d'accrétion en orbite autour de ces trous noirs sont simulées numériquement. Ces géodésiques et images sont directement liées aux observations réalisées par certains instruments en activité, tels que GRAVITY ou l'Event Horizon Telescope, qui sont dédiés à l'étude des trous noirs supermassifs. Ce projet permet ainsi d'identifier de possibles tensions entre les prédictions de la théorie du Galileon cubique et certaines observations liées aux trous noirs
The present project falls within the wide effort conducted to study theories of gravitation, notably by modelling the physics of compact objects like black holes. The long-term objective of this approach is to determine all theories that are either incompatible with observations, or theoretically inconsistent. The first part of the manuscript thus presents the essential concepts and principles that are common to all these theories, and introduces some of these theories which connect to the project. In the second part, the actual contribution of the project is exposed: comparing rotating black holes of the cubic Galileon theory with the Kerr family of the general theory of relativity. The latter was developed by Albert Einstein more than a century ago, while the cubic Galileon is a much more recent theory.First, the rotating black holes are constructed numerically. Then, the properties of the orbits around them are investigated, in particular their stability. Finally, the images of a simple model of accretion disk orbiting the black holes are simulated. Such orbits and images directly relate the observations realized by instruments like GRAVITY or the Event Horizon Telescope, which monitor supermassive black holes. The present project thus allows to identify possible tensions between the predictions of the cubic Galileon theory and observational data on black holes