Nonlocal Singular Problems and Applications to MEMS

We consider fourth order nonlinear problems which describe electrostatic actuation in MicroElectroMechanicalSystems (MEMS) both in the stationary case and in the evolution case; we prove existence, uniqueness and regularity theorems by exploiting the Near Operators Theory

Next generation main battle tank. Part II: Converting old MBTS into unmanned MBTS (UMBT)

Modern MBTs (Main Battle Tank) are extremely expensive. Many outdated MBTs and other armored vehicles, often lacking the required armor protection, are still kept in depots. It is now convenient to upgrade them to optionally unmanned weapons by adding a humanoid driver, and a robotic arm as a loader. Sensors, an optional automatic driving system, a control and communication suite would complete the transformation. The main armament and secondary armament may be also changed or upgraded. The off-the-shelf huge electronic equipment can be installed wireless inside the hull. The old crew compartment may be spoiled of all the human related parts. Only the driver seat may be kept in order to leave the capability to remove the humanoid, robotized driver and reinstate the human one. This upgrade should also include a diagnostic system for the vehicle, the sensors and the additional systems to reduce the maintenance burden. An additional, specialized, lightweight armor suite should be focused to protect the mobilization system, the robots, the control and the communication system. This second part of the paper introduces a few options to convert the Leopard 1 MBT to an optionally piloted UMBT (Unmanned Main Battle Tank). A first, minimal step, is just the automation of the original tank. In a second step, the weight is reduced by installing a smaller 60mm cannon with a lighter, but more numerous ammunition storage. A third step increases the firepower by installing on the main turret an automated turret with a 12.7 or 30mm cannon with an optional additional 7.62 machinegun. It is also highly advisable to add an APU (Auxiliary Power Unit) and a battery to reduce IR (infrared) signature, improve main engine life and reduce maintenance

Mobility improvement of heavy tracked vehicles: The "pan" tank experience

This paper shows that the sinkage of the tracked vehicle is the most important parameter in its mobility. Power and fuel consumption follow cubic power law with sinkage. So the usual strategy to increase power is not the more convenient way to improve vehicle off road performance. The Ground Pressure (GP) is the critical parameter. Power requirement goes with the cubic power of sinkage. GP above 0.9 daN/cm2 should be avoided at all costs. The best way to obtain this result on an existing design is to increase track length. However it is easier to work on track width. The easiest modification is to add "Duckbill extensions" in the outer part of the shoe. This system was used on the Sherman Tank when additional armor was added. With modern technology it is perfectly possible to perform experimental tests with new shoes. This can be done by manufacturing prototypes of high stress nitrided steel shoes, usually with 300M high strength steel. Comparative fuel consumption is a good index of vehicle performance. Also wheel diameter and width can be increased to improve off-road performance. Specialized tracks for different terrains should also be designed. The gravity center should be kept slightly rearward. This attitude should not be excessive to keep the pressure value more even possible along the track. In any case the vehicle naturally assumes the backward inclination due to terrain compression. Another important improvement is the addition of computer controlled directional control to improve the accuracy of trajectories. This is particularly important for tracked vehicles where turning involves extremely high energy consumption

Constructing Lifshitz solutions from AdS

Under general assumptions, we show that a gravitational theory in d+1 dimensions admitting an AdS solution can be reduced to a d-dimensional theory containing a Lifshitz solution with dynamical exponent z=2. Working in a d=4, N=2 supergravity setup, we prove that if the AdS background is N=2 supersymmetric, then the Lifshitz geometry preserves 1/4 of the supercharges, and we construct the corresponding Killing spinors. We illustrate these results in examples from supersymmetric consistent truncations of type IIB supergravity, enhancing the class of known 4-dimensional Lifshitz solutions of string theory. As a byproduct, we find a new AdS4 x S1 x T(1,1) solution of type IIB.Comment: 29 pages, no figures; v2 minor corrections, a reference adde

The Controversy of Myopia as a Risk Factor for Glaucoma: a Mathematical Approach

poster abstractPurpose: to quantify how individual variations in anatomical parameters often associated with myopia (e.g. longer ocular axial length (OAL), reduced scleral thickness (ST), lamina cribrosa diameter (LCD) and thickness (LCT)) affect retinal blood flow (RBF) and its sensitivity to ocular perfusion pressure (OPP). Methods: A mathematical model is used to calculate RBF through central retinal artery (CRA), arterioles, capillaries, venules, and central retinal vein (CRV). The flow is time-dependent, driven by systemic pressure and regulated by variable resistances to account for nonlinear effects due to (1) autoregulation (AR), and (2) lamina cribrosa effect on CRA and CRV. The latter is a nonlinear function of intraocular pressure (IOP), cerebrospinal fluid pressure (CSF) and OAL, ST, LCD, and LCT. RBF is computed as the solution of a system of five non-linear ordinary differential equations. The system is solved for different OPP values, obtained by varying independently IOP and mean arterial pressure (MAP), with and without AR. Results: Four representative eyes are compared: Eye 1 (OAL=24mm, ST=1mm, LCD=3mm, LCT=0.4mm), Eye 2 (OAL=28mm, ST=1mm, LCD=3mm, LCT=0.4mm), Eye 3 (OAL=24mm, ST=0.7mm, LCD=2mm, LCT=0.2mm), Eye 4 (OAL=28mm, ST=0.7mm, LCD=2mm, LCT=0.2mm). The model predicts that the cardiac cycle RBF average (RBFav) for eyes with smaller LCD and LCT is notably less than in normal eyes when IOP is elevated and without AR (c). Without AR and reduced MAP, the four eyes show similar RBFav reductions (d). With AR, anatomical changes do not induce notable changes in RBFav, (a) and (b). Conclusions: Reduced LCD and LCT, often associated with myopia, seem to affect RBFav more than elevated OAL. RBFav reductions magnify when AR is impaired, and this might reduce IOP safe levels for eyes with reduced LCD and LCT. These findings suggest that a combination of anatomical and vascular factors might cause certain myopic eyes to be at higher risk for glaucomatous damage than others

de Sitter Supersymmetry Revisited

We present the basic $\mathcal{N} =1$ superconformal field theories in four-dimensional de Sitter space-time, namely the non-abelian super Yang-Mills theory and the chiral multiplet theory with gauge interactions or cubic superpotential. These theories have eight supercharges and are invariant under the full $SO(4,2)$ group of conformal symmetries, which includes the de Sitter isometry group $SO(4,1)$ as a subgroup. The theories are ghost-free and the anti-commutator $\sum_\alpha\{Q_\alpha, Q^{\alpha\dagger}\}$ is positive. SUSY Ward identities uniquely select the Bunch-Davies vacuum state. This vacuum state is invariant under superconformal transformations, despite the fact that de Sitter space has non-zero Hawking temperature. The $\mathcal{N}=1$ theories are classically invariant under the $SU(2,2|1)$ superconformal group, but this symmetry is broken by radiative corrections. However, no such difficulty is expected in the $\mathcal{N}=4$ theory, which is presented in appendix B.Comment: 21 pages, 2 figure

A special road to AdS vacua

We apply the techniques of special Kaehler geometry to investigate AdS_4 vacua of general N=2 gauged supergravities underlying flux compactifications of type II theories. We formulate the scalar potential and its extremization conditions in terms of a triplet of prepotentials P_x and their special Kaehler covariant derivatives only, in a form that recalls the potential and the attractor equations of N=2 black holes. We propose a system of first order equations for the P_x which generalize the supersymmetry conditions and yield non-supersymmetric vacua. Special geometry allows us to recast these equations in algebraic form, and we find an infinite class of new N=0 and N=1 AdS_4 solutions, displaying a rich pattern of non-trivial charges associated with NSNS and RR fluxes. Finally, by explicit evaluation of the entropy function on the solutions, we derive a U-duality invariant expression for the cosmological constant and the central charges of the dual CFT's.Comment: 41 pages; v2, v3: minor improvements, references added, published versio

Holographic renormalization and supersymmetry

Holographic renormalization is a systematic procedure for regulating divergences in observables in asymptotically locally AdS spacetimes. For dual boundary field theories which are supersymmetric it is natural to ask whether this defines a supersymmetric renormalization scheme. Recent results in localization have brought this question into sharp focus: rigid supersymmetry on a curved boundary requires specific geometric structures, and general arguments imply that BPS observables, such as the partition function, are invariant under certain deformations of these structures. One can then ask if the dual holographic observables are similarly invariant. We study this question in minimal N = 2 gauged supergravity in four and five dimensions. In four dimensions we show that holographic renormalization precisely reproduces the expected field theory results. In five dimensions we find that no choice of standard holographic counterterms is compatible with supersymmetry, which leads us to introduce novel finite boundary terms. For a class of solutions satisfying certain topological assumptions we provide some independent tests of these new boundary terms, in particular showing that they reproduce the expected VEVs of conserved charges.Comment: 70 pages; corrected typo

Heterotic Flux Attractors

We find attractor equations describing moduli stabilization for heterotic compactifications with generic SU(3)-structure. Complex structure and K\"ahler moduli are treated on equal footing by using SU(3)xSU(3)-structure at intermediate steps. All independent vacuum data, including VEVs of the stabilized moduli, is encoded in a pair of generating functions that depend on fluxes alone. We work out an explicit example that illustrates our methods.Comment: 37 pages, references and clarifications adde