Kompiuterinis geometrinis sklandytuvo Lak-17 modelis sugeneruotas programa AVL, kuri skirta orlaivių konfigūracijos ir skrydžio charakteristikų analizei. Imituojant realų skrydį programa suskaičiuotos įvairios šoninio stabilumo charakteristikos. Tirta, kaip šoninio stabilumo savyb÷ms, tokioms kaip krypties nestabilumas, spiralinis nestabilumas, „olandiškas žingsnis“, turi įtakos skersinio V kampo didinimas ar mažinimas, vertikalios uodegos plokštumos ploto keitimas. Pagal gautus rezultatus suformuluotos išvados kiekvienam šoninio nestabilumo atvejui. Darbą sudaro 3 dalys: įvadas, problemos analiz÷, AVL programos apžvalga, tyrimas, išvados, literatūros sąrašas. Darbo apimtis – 92 p. 65 p. teksto be priedų, 82 iliustr., 6 lent. Atskirai pridedami priedai. / Computer-based geometrical model of sailplane Lak-17 was generated with a program AVL (Athena Vortex Lattice), which is designed for analysis of characteristics of flight and rapid analysis of configuration of aircraft. Analysis was done how increasing and decreasing of wing dihedral and exchange of vertical tail area characteristics are influenced on lateral stability like directional divergence, spiral divergence and „dutch roll“. Simulating a real flight with the program various characteristics of stability and control were calculated. According results the conclusion was formulated for every case of lateral unstability. Structure: introduction, problem analysis, AVL overview, research, conclusions, references. Thesis consist of – 92 p. 65 p. text without appendixes, 82 pictures, 6 tables. Appendixes are included.

Kim, Straub, and Keyes introduced the statistical temperature molecular dynamics (STMD) algorithm to overcome broken ergodicity by sampling a non­-Boltzmann flat energy histogram as noted in Kim, Straub, and Keyes, Phys. Rev. Lett. 97: 050601 (2007). Canonical averages are calculated via reweighting to the desired temperature. While STMD is promising, its application has been almost entirely to simple or model systems. In this dissertation the implementation of STMD into the biosimulation package CHARMM is used to simulate the methionine enkephalin pentamer peptide with a methione terminal cap in a droplet of CHARMM TIP3P water molecules. Chain thermodynamics is analyzed from the novel perspective of the statistical temperature as a function of potential energy, $TS(U), automatically generated by STMD. Both the minimum in the slope of $TS(U), and the peak in the heat capacity as a function of temperature, calculated via reweighting, indicate a collapse transition at Tθ ≈ 253K. Distributions of dihedral angles are obtained as a function of temperature. Rotamer regions found in the literature are reproduced, along with unique regions not found previously, including with advanced algorithms, indicating the power of STMD enhanced sampling.

The subgroup commutativity degree sd(G) of a finite group G was introduced almost ten years ago and deals with the number of commuting subgroups in the subgroups lattice L(G) of G. The extremal case sd(G) = 1 detects a class of groups classified by Iwasawa in 1941 (in fact sd(G) represents a probabilistic measure which allows us to understand how far is G from the groups of Iwasawa). Among them we have sd(G) = 1 when L(G) is distributive, that is, when G is cyclic. The characterization of a cyclic group by the distributivity of its lattice of subgroups is due to a classical result of Ore in 1938. Therefore sd(G) is strongly related to structural properties of L(G). Here we introduce a new notion of probability gsd(G) in which two arbitrary sublattices S(G) and T(G) of L(G) are involved simultaneously. In case S(G) = T(G) = L(G), we find exactly sd(G). Upper and lower bounds in terms of gsd(G) and sd(G) are among our main contributions, when the condition S(G) = T(G) = L(G) is removed. Then we investigate the problem of counting the pairs of commuting subgroups via an appropriate graph. Looking at the literature, we noted that a similar problem motivated the permutability graph of non–normal subgroups ΓN (G) in 1995, that is, the graph where all proper non– normal subgroups of G form the vertex set of ΓN (G) and two vertices H and K are joined if HK = KH. The graph ΓN (G) has been recently generalized via the notion of permutability graph of subgroups Γ(G), extending the vertex set to all proper subgroups of G and keeping the same criterion to join two vertices. We use gsd(G), in order to introduce the non–permutability graph of subgroups ΓL(G) ; its vertices are now given by the set L(G) − CL(G)(L(G)), where CL(G)(L(G)) is the smallest sublattice of L(G) containing all permutable subgroups of G, and we join two vertices H, K of ΓL(G) if HK 6= KH. We finally study some classical invariants for ΓL(G) and find numerical relations between the number of edges of ΓL(G) and gsd(G).

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Unmanned aircraft systems (UAS) often encounter turbulent fields that perturb the aircraft from its desired target trajectory, or in a manner that increases the load factor. The aircraft's fixed dihedral angle, providing passive roll-stiffness, is often selected based on lateral-directional stability requirements for the vehicle. A study to predict the effect of an active dihedral system on lateral-directional stability and vertical gust rejection capability was conducted to assess the performance and feasibility of the system. Traditionally, the dihedral location begins at the root to maintain wing structural requirements, however, the active dihedral system was also evaluated for dynamic stability and gust rejection performance at alternative dihedral breakpoint locations. Simulations were completed using linear parameter-varying (LPV) models, derived from traditional Newtonian aircraft dynamics and associated kinematic equations, to improve the modeling of the nonlinear active dihedral system. The stability of the LPV system was evaluated using Lyapunov stability theory applied to switched linear systems, assessing bounds of operation for the dihedral angle and flapping rate. An ideal feedback controller was developed using a linear–quadratic regulator (LQR) for both a discrete gust model and a continuous gust model, and a gain scheduled LQR controller was implemented to show the benefits of gain scheduling with a parameter varying state and input model. Finally, a cost analysis was conducted to investigate the real-world benefit of altering the dihedral breakpoint location. The effects of the active dihedral system on battery capacity and consumption efficiency were observed and compared with the gust rejection authority. / Master of Science / Unmanned aircraft systems (UAS) often encounter wind disturbances that perturb the aircraft from its desired target trajectory, or in a manner that increases the force encountered on the vehicle. The aircraft's fixed dihedral angle, providing stiffness to roll rotations, is often selected based on stability and control requirements for the vehicle. A study to predict the effect of a flapping wing (active dihedral) system on the stability, control, and wind gust rejection capability is completed to assess the performance and feasibility of such a system. Traditionally, the dihedral location begins at the root to maintain wing structural requirements, however, the active dihedral system was also evaluated for stability and wind gust rejection performance at alternative locations along the wing where the dihedral could begin, with intention of finding the best location. Simulations were completed using a varying set of simplified models, obtained from traditional aircraft mechanics, to improve the modeling of the true complex active dihedral system. The stability of the system was evaluated using various theories applied to the linear systems in attempt to define a bounded operating region for the dihedral angle and flapping motion. An ideal controller for the system was developed using ideas from well documented linear control theory for both a single wind gust and a continuous wind gust model. A controller that varies with vehicle flapping motion was implemented to show the benefits of scheduling the controller with a parameter varying state and input model. Finally, a cost analysis was conducted to investigate the real-world benefit of altering the dihedral starting location. The effects of the active dihedral system on battery capacity and consumption efficiency were observed and compared with the total gust rejection capability.

This thesis investigates the mechanisms behind the control of a typical two line kite, where the lines are attached to the kite side by side. This arrangement gives the kite flyer the ability to apply a roll angle to the kite, which then results in a yawing motion. The reason for this yaw rotation has not been adequately described previously. The definitions of roll and yaw for a kite have been re-defined to match the real world behaviour of the kite-bridle-line system. Specifically, these are defined as rotations relative to the lines rather than the kite itself. This detail has been neglected in previous research, and has a significant effect on the turning behaviour of a kite. A static model of a kite represented by flat disks was created. This model allows the out of balance forces and moments to be found for a kite when it is held at any position. When the kite is held with a roll angle applied, the disk angles of attack become unequal. This causes a change in the magnitude, direction, and point of action of the aerodynamic forces on each disk, which can lead to a yaw moment. While this does not give a complete picture of how a kite turns, it does explain one of the two mechanisms that cause a kite to begin to yaw when a roll angle is applied. The other mechanism is due to the velocity of the roll rotation, and is out of the scope of this thesis since a dynamic analysis would be required. The static model showed that any variation to kite geometry or any parameter that affects the equilibrium position of the kite will affect turning response. The most important of these parameters for a simple kite represented by two disks is the dihedral angle. A minimum negative dihedral angle (or anhedral) is required for a kite to turn in the expected direction when a roll angle is applied. The value of the minimum anhedral angle required for this behaviour varies with other parameters, but is generally between 8° and 20°. Other parameters such as bridle geometry also affect the turning response of a kite, primarily because they alter the equilibrium positions of the kite and line. Altering these equilibrium positions has a strong effect on turning response, since it changes the initial disk angles of attack. Additionally, if the kite and line are not aligned perpendicular to each other (which is a rare condition for a kite) a roll angle further changes the disk angles of attack, since the roll angle is applied about an axis relative to the line rather than the kite. An investigation into the effect of varying wind velocity on turning response showed that it has an important effect. Some kites will reverse their response to a given roll angle at some wind velocities, which could make the kite very difficult to control. Additionally, some kites can alter their equilibrium positions sharply with wind velocity, again causing varying turning behaviour as the wind conditions change. Future work should examine the dynamic turning response of kites. A dynamic simulation could be used to examine how the turning response of a kite is influenced by the rate at which a control input is applied. Additionally, the behaviour of the kite once the initial turning movement has begun could be assessed.

Desde o início da década de 2010, o aumento do preço do combustível de aviação e a pressão da sociedade para redução da emissão de gases nocivos ao meio ambiente, junto com a necessidade de redução de ruído durante as fases de decolagem e pouso, levaram as companhias aéreas a buscar aeronaves mais eficientes. Para suprir essa demanda, os fabricantes de aviões comerciais solucionaram esse problema através do uso de motores de maior desempenho, que apresentam maior diâmetro que motores de gerações passadas. Desse modo, foi necessário projetar asas com maior diedro na região da raiz, possibilitando a instalação desses novos motores, e diedro menor após a seção do motor, adotando assim a solução de asa em gaivota. O presente trabalho visa analisar o impacto de diferentes tipos de asas em gaivota nos coeficientes aerodinâmicos de uma aeronave de configuração comercial típica. Para tanto, foi realizada uma revisão bibliográfica dos estudos envolvendo asas em gaivota. Numa primeira fase foi feito um estudo analítico das características aerodinâmicas de alguns modelos de aeronaves com asa em gaivota, e em uma segunda fase, foram empregadas ferramentas computacionais para analisar seus comportamentos aerodinâmicos. Posteriormente, em uma terceira fase, esses modelos foram ensaiados no túnel de vento do LAE (Laboratório de Aerodinâmica da EESC/USP), e os resultados das três fases foram comparados. / Since the beginning of the 2010s, the increasing price of aviation fuel and the pressure of society to reduce the emission of harmful gases into the environment, coupled with the need of noise reduction during the takeoff and landing, induce carrier companies to look for more efficient airplanes. To furnish this demand, the airplane manufacturers solved the problem using high performance engines, which present a larger diameter than the engines from previous generations. Thereby, it was necessary to project wing with higher dihedral on the root portion, enabling the installation of these new engines, and a lower dihedral after the engine section, thus adopting a gull wing solution. This research project aims at analyzing the impact of different types of gull wing on the aerodynamic coefficients of a typical commercial configuration airplane. For this purpose, a bibliographic review about the studies related to gull wings was performed. In a first phase, an analytical analysis of the aerodynamic characteristics of some airplane model with gull wings was done, and in a second phase, computational programs was used to study their aerodynamic behavior. Later, in a third phase, these models were tested in the wind tunnel of LAE (Laboratory of Aerodynamics of EESC/USP), and the results from the three phases were compared.

Based on Cohn and Umans’ group-theoretic method, we embed matrix multiplication into several group algebras, including those of cyclic groups, dihedral groups, special linear groups and Frobenius groups. We prove that SL2(Fp) and PSL2(Fp) can realize the matrix tensor ⟨p, p, p⟩, i.e. it is possible to encode p × p matrix multiplication in the group algebra of such a group. We also find the lower bound for the order of an abelian group realizing ⟨n, n, n⟩ is n3. For Frobenius groups of the form Cq Cp, where p and q are primes, we find that the smallest admissible value of q must be in the range p4/3 ≤ q ≤ p2 − 2p + 3. We also develop an algorithm to find the smallest q for a given prime p.