ISEL - Matemática - Artigos
Permanent URI for this collection
Browse
Recent Submissions
- Fractal Laplace transform: analyzing fractal curvesPublication . Khalili Golmankhaneh, Alireza; Welch, Kerri; Serpa, Cristina; Rodríguez-Lopez, RosanaThe concept of Laplace transform has been extended to fractal curves, enabling the solution of fractal differential equations with constant coefficients. This extension, known as the fractal Laplace transform, is particularly useful for handling inhomogeneous differential equations that involve delta Dirac functions and step functions within the realm of fractal functions. A comprehensive table of essential formulas for the fractal Laplace transform has been compiled to facilitate its application in various scenarios. By utilizing this transformative approach, researchers can now delve into the study of fractal functions and address complex problems involving non-traditional geometries. To illustrate the practicality of the fractal Laplace transform, several examples are provided, showcasing its effectiveness in solving fractal differential equations. This advancement represents a significant augmentation of the classical Laplace transform, tailored to suit the distinctive characteristics of fractal systems and functions.
- a-fractal function with variable parameters: an explicit representationPublication . Priyanka, T. M. C.; Serpa, Cristina; Gowrisankar, A.In this paper, new results on the alpha-fractal function with variable parameters are presented. The Weyl-Marchaud variable order fractional derivative of an alpha-fractal function with variable parameters is examined by imposing certain conditions on the scaling factors. Following the investigation of fractional derivative, the definite integral of the alpha-fractal function with variable parameters is evaluated for various intervals in the prescribed domain. Finally, an explicit structure for the alpha-fractal function is provided using the base q representation of numbers.
- Velocity and energy of periodic travelling interfacial waves between two bounded fluidsPublication . Cal, Filipe; Dias, Gonçalo A. S.For a periodic travelling irrotational wave propagating at the interface between two homogeneous, incompressible and inviscid fluids bounded by horizontal planes, we generalise the Stokes definitions for the velocity of the wave propagation. Under certain conditions imposed on the horizontal velocity of the motion at the interface and supposing that the horizontal components of the velocity in each layer never reach the wave speed, we prove that the mean horizontal velocity of propagation of the wave is greater than the generalised mean horizontal velocity of the mass of the fluid. We show that, for interfacial waves of small amplitude, the excess kinetic and potential energy of the fluid have the same magnitude, but different signs, and for the nonlinear setting, we prove that the excess kinetic energy is negative.
- Automatic completion of data gaps applied to a system of water pumpsPublication . Enguiça, Ricardo; Soares, FilipaWe consider a time series with real data from a water lift station, equipped with three water pumps which are activated and deactivated depending on certain starting and halting thresholds. Given the water level and the number of active pumps, both read every 5 min, we aim to infer when each pump was activated or deactivated. To do so, we build an algorithm that sets a hierarchy of criteria based on the past and future of a given interval to identify which thresholds have been crossed during that interval. We then fill the gaps between the 5 min time steps, modeling the water level continuously with a piecewise linear function. This filling takes into account not only every water level reading and every previously identified change of status, but also the fact that activation and deactivation of a pump has no immediate effect on water level. This allows for the fulfillment of the ultimate objective of the problem in its real context, which is to provide the water management company an estimate of how long each pump has been working. Additionally, our estimates correct the errors contained in the time series regarding the number of active pumps.
- The modelling of urban running racesPublication . Enguiça, Ricardo; Lopes, Nuno D.In this paper, we model mass running urban races, taking into consideration several conditioning factors. The main goal is to find ideal configurations of the start of the race, splitting it into several waves, reducing the density of athletes and the overall time lost, when comparing the normal race results with a race without density constraints. This model takes into account distinct realistic runners' profiles, changes in slope and width on the race course and its influence on the running pace. Moreover, density levels, dynamics of the start of the race and time between the departure of waves are also considered.
- Multimodal optimization of piezoelectric patches number and placement for effective structural vibration reductionPublication . Magalhães, Pedro A.; Araújo, A. L.; Madeira, Jose Firmino AguilarThe presence of vibrations is a common phenomenon in many applications, with the potential to lead to structural issues. Therefore, control is crucial for reducing oscillation amplitudes, suppressing undesirable resonances, and preventing structural fatigue failures. In this context, the use of piezoelectric patches to act as controllers on plates has been implemented. However, an optimization challenge in this scenario precedes the dynamic study, which is the investigation of patch positioning. In this paper, we developed a model in ANSYS to optimize positioning conditions with the Global and Local Optimization using Direct Search (GLODS) and the Direct Multisearch (DMS) algorithms. The aim is to determine the optimal patch location based on the electromechanical coupling coefficient (EMCC), with GLODS optimizing individual modes and DMS optimizing multiple modes simultaneously. This approach enables the calculation of tuning values for resistances and inductances, effectively mitigating vibration issues.
- Highly porous NiFe nanofoams synthesized by dynamic hydrogen bubble template for hydrogen evolution in alkaline mediaPublication . Carvalho, Gabriel Garcia; do Nascimento, Ricardo Espingardas; Morais Silva, Teresa; Montemor, Maria de FátimaWhen coupled with renewable energy sources, alkaline electrolysis (AEL) is a clean technology to produce hydrogen. The conventional electrodes that have been established as the commercial standard for AEL are perforated nickel plates, which have low surface area and high mass loads of active material. The use of Ni has been associated with the adsorption of protons and their recombination into H2 molecules, assisting and enabling the hydrogen evolution reactions. Due to the rising Ni price, there is a demand for less expensive electrode materials with identical, or better, performance. Thus, this work explores new alternative electrode materials and combines Ni with a cheaper and also electroactive metal, iron. For this purpose, highly porous bimetallic nanofoams are produced through the dynamic hydrogen bubble template. NiFe electrodes of different compositions are characterized by scanning electron microscopy, energy-dispersive spectroscopy, linear sweep voltammetry, and chronopotentiometry analysis. The results allow obtaining key parameters that are essential for the optimization of the electrode's response considering overpotentials, Tafel slopes, and other electrochemically relevant parameters.
- Mixed Hodge structures on character varieties of nilpotent groupsPublication . A. A. Florentino, Carlos; Lawton, Sean; Silva, JaimeLet Hom0(Ƭ, G) be the connected component of the identity of the variety of representations of a finitely generated nilpotent group into a connected reductive complex affine algebraic group G. We determine the mixed Hodge structure on the representation variety Hom0(Ƭ, G) and on the character variety Hom0(Ƭ, G)//G. We obtain explicit formulae (both closed and recursive) for the mixed Hodge polynomial of these representation and character varieties.
- Periodic attractors of nonautonomous flat-topped tent systemsPublication . Silva, LuisIn this work we will consider a family of nonautonomous dynamical systems x(k)(+1) = f(k)(x(k), lambda), lambda is an element of [-1, 1] (N0), generated by a one-parameter family of flat-topped tent maps g(alpha) (x), i.e., f(k)(x, lambda) = g(lambda k) (x) for all k is an element of N-0. We will reinterpret the concept of attractive periodic orbit in this context, through the existence of some periodic, invariant and attractive nonautonomous sets and establish sufficient conditions over the parameter sequences for the existence of such periodic attractors.
- Fractal analysis and ferroelectric properties of Nd(Zn-1/Ti-2(1)/(2))O-3(NZT)Publication . Khamoushi, Kouros; Serpa, CristinaThe challenges in productivity of satellite mobile devices are growing rapidly to overcome the question of miniaturization. The intention is to supply the electrical and microwave properties of materials by discovering their outstanding electronic properties. Neodymium Zinc Titanate (NZT) can be a promising ferroelectric material due to its stable dielectric and microwave properties. The grain size and shape of NZT have a strong influence on overall material performances. Therefore, shape, reconstruction and property of the coming compound take an important part and can be predicted before being utilized in the devices. The significant of this research is to define ferroelectric properties of NZT and to characterize it by using Fractal Nature Analysis (FNA). FNA is a powerful mathematical technique that could be applied to improve the grain shape and interface reconstruction. The fractal structure is identified by its self-similarity. The self-similarity of an object means a repetition of shapes in smaller scales. A measure of this structure is computed using the Hausdorff dimension. It is for the first time in this investigation the Fractal analysis method is applied for the microwave materials microstructure reconstruction which makes this research an innovative work and will open the door for Curie-Weiss law fractal correction. In connection to our previous research for dielectric properties fractalization, we had some characterization and reconstruction data which include the Hausdorff dimension (HD).