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Michael A. Slawinski

Publications and source records attributed to Michael A. Slawinski.

At least 19 recordsLinked to original sources
arXiv2026

On the brachistochrone problem for cycling ascents

VAM ({\it velocità ascensionale media}) is a measurement that quantifies a cyclist's climbing ability. We show that to minimize the time to attain a given height gain\, -- \,which is tantamount to maximizing VAM\, -- \,a cyclist should climb as steep a constant-grade hill as possible. Apart from the power-to-weight ratio, the limit of steepness is imposed by such factors as the efficiency of pedalling, which is related to feasible cadence, maintaining balance, preventing lifting of the front, and skidding of the rear, wheel. In an appendix, we discuss steepness constraints due to pedalling efficiency. The article itself is focused on consequences of the power available to the cyclist, which can be viewed as a necessary condition to examine other aspects of climbing strategy. We show that\, -- \,for given start and end points, and for any fixed average-power constraint\, -- \,the brachistochrone, which is the trajectory of minimum ascent time, is the straight line connecting these points, covered with a constant speed, which along such a line is equivalent to a constant power. This is in contrast to the classical solution of a descent brachistochrone under gravity, which is a cycloid along which the speed is not constant.

physics.pop-ph↗
arXiv2025

On minimizing cyclists' ascent times: Part II

We formulate an optimization of a bicycle ascent time under the constraints of the average, maximum, and minimum powers. In contrast to the first part of this study, we do not restrict the departure to flying starts with an initial speed determined by the model and its optimization. We allow for various initial speeds, from a standstill to a launched start. We accomplish this by generalizing the discontinuous piecewise constant speed model to a continuous piecewise linear speed model. Regardless of the initial speed, steepness or profile of the ascent the optimal strategy tends to a constant ground speed, in agreement with the conclusion of the previous, more restricted, formulation. This new formulation allows us to compare various initial-speed strategies and, hence, has a direct application to competitive cycling. Notably, in timetrials composed of flat and steep sections, it helps one decide whether or not to change bicycle, which requires stopping and restarting, from one that is more appropriate for flats to one that is more appropriate for uphills.

physics.class-ph↗
arXiv2025

On minimizing cyclists' ascent times

We prove that, given an average power, the ascent time is minimized if a cyclist maintains a constant ground speed regardless of the slope. Herein, minimizing the time is equivalent to maximizing -- for a given uphill -- the corresponding mean ascent velocity (VAM: velocità ascensionale media), which is a common training metric. We illustrate the proof with numerical examples, and show that, in general, maintaining a constant instantaneous power results in longer ascent times; both strategies result in the same time if the slope is constant. To remain within the athlete's capacity, we examine the effect of complementing the average-power constraint with a maximum-power constraint. Even with this additional constraint, the ascent time is the shortest with a modified constant-speed -- not constant-power -- strategy; as expected, both strategies result in the same time if the maximum and average powers are equal to one another. Given standard available information -- including level of fitness, quantified by the power output, and ascent profile -- our results allow to formulate reliable and convenient strategies of uphill timetrials.

physics.class-ph↗
arXiv2023

Modelling of a cyclist's power for time trials on a velodrome

We formulate a phenomenological model to study the power applied by a cyclist on a velodrome\, -- \,for individual timetrials\, -- \,taking into account the straights, circular arcs, connecting transition curves and banking. The dissipative forces we consider are air resistance, rolling resistance, lateral friction and drivetrain resistance. Also, power can be used to increase the kinetic and gravitational potential energy. Herein, to model a steady ride\, -- \,as expected for individual timetrials\, -- \,we assume a constant centre-of-mass speed, while allowing the cadence and power to vary during a lap. Hence, the kinetic energy is constant and the only mechanical energy whose change we need to consider is the increase of gravitational potential energy due to raising the centre of mass upon exiting each curve. The effect of dissipative forces is examined at each point of the lap; the effect of conservative forces is examined as an average. The latter is a small\, -- \,albeit not negligible\, -- \,part of the total power, and its inclusion within a model is a novelty presented herein. It increases the model's empirical adequacy. Following derivations and justifications of expressions that constitute this mathematical model, we present a numerical example. We show that the cadence and power vary slightly during a steady ride. In other words, a constant centre-of-mass speed entails nearly constant cadence and power, as expected for a steady ride and as supported by measurements. Also, we examine changes in the required power due to changes of various quantities, such as air density at a velodrome, laptime and several others, as well as the model sensitivity to input errors. Furthermore, we examine the effects on the required power of slight and gradual changes in speed, which are pertinent to individual time trials.

physics.class-ph↗
arXiv2021

Modelling of cyclist's power to overcome dissipative forces on a velodrome

We model the instantaneous power applied by a cyclist on a velodrome -- for individual pursuits and other individual time trials -- taking into account its straights, circular arcs, and connecting transition curves. The forces opposing the motion are air resistance, rolling resistance, lateral friction and drivetrain resistance. We examine the constant-cadence and constant-power cases, and discuss their results, including an examination of empirical adequacy of the model.

physics.pop-ph↗
arXiv2021

On maximizing VAM for a given power: Slope, cadence, force and gear-ratio considerations

The velocità ascensionale media (VAM) is measurement that quantifies a cyclist's climbing ability. It depends on both the ground speed of a bicycle-cyclist system and the slope of an incline. To maximize the ascent speed, the solution to the brachistochrone problem determines that the optimal curve for the incline is a straight line, which is a hill with a constant slope. The maximum obtainable VAM value by a cyclist increases monotonically with the slope of the incline, but is limited by the maximum sustainable power. These properties -- which are theorems stemming from a standard mathematical model to account for the power required to propel a bicycle -- constitute a mathematical-physics background upon which various strategies for the VAM maximization can be examined in the context of the maximum sustainable power as a function of both the gear ratio and cadence. Recently established records provide an empirical support for these analytical results, which are based on theoretical considerations.

physics.pop-ph↗
arXiv2021

On modelling bicycle power-meter measurements

We combine power-meter measurements with GPS measurements to study the model that accounts for the use of power by a cyclist. The model takes into account the change in elevation and speed along with adverse effects of air, rolling and drivetrain resistance. The focus is on estimating the resistance coefficients using numerical optimization techniques to maintain an agreement between modelled and measured power-meter values, which accounts for the associated uncertainties. The estimation of coefficients is performed for two typical scenarios of road cycling under windless conditions, along a course that is mainly flat as well as a course of near constant inclination. Also, we discuss relations between different combinations of two model parameters, where other quantities are constant, by the implicit function theorem. Using the obtained estimates of resistance coefficients for the two courses, we use the mathematical relations to make inferences on the model and physical conditions. Along with a discussion of results, we provide two appendices. In the first appendix, we illustrate the importance of instantaneous cadence measurements. In the second, we consider the model in constrained optimization using Lagrange multipliers.

physics.pop-ph↗
arXiv2021

On modelling bicycle power for velodromes: Part II Formulation for individual pursuits

We model the instantaneous power on a velodrome--as applied to individual pursuits and other individual time trials--taking into account its straights, circular arcs, and connecting transition curves. The forces opposing the motion are air resistance, rolling resistance, lateral friction and drivetrain resistance. We examine the constant-cadence and constant-power cases, and discuss their results, including an examination of an empirical adequacy of the model. We also examine changes in the kinetic and potential energy.

physics.pop-ph↗
arXiv2020

On modelling bicycle power-meter measurements: Part II. Relations between rates of change of model quantities

Power-meter measurements are used to study a model that accounts for the use of power by a cyclist. The focus is on relations between rates of change of model quantities, such as power and speed, both in the context of partial derivatives, where other quantities are constant, and Lagrange multipliers, where other quantities vary to maintain the imposed constraints.

physics.pop-ph↗
arXiv2020

Selecting velocity models using Bayesian Information Criterion

We present a strategy for selecting the values of elasticity parameters by comparing walk-away vertical seismic profiling data with a multilayered model in the context of Bayesian Information Criterion. We consider $P$-wave traveltimes and assume elliptical velocity dependence. The Bayesian Information Criterion approach requires two steps of optimization. In the first step, we find the signal trajectory and, in the second step, we find media parameters by minimizing the misfit between the model and data.

physics.geo-ph↗
arXiv2020

On effects of inhomogeneity on anisotropy in Backus average

In general, the Backus average of an inhomogeneous stack of isotropic layers is a transversely isotropic medium. Herein, we examine a relation between this inhomogeneity and the strength of resulting anisotropy, and show that, in general, they are proportional to one another. There is an important case, however, in which the Backus average of isotropic layers results in an isotropic -- as opposed to a transversely isotropic -- medium. We show that it is a consequence of the same rigidity of layers, regardless of their compressibility. Thus, in general, the strength of anisotropy of the Backus average increases with the degree of inhomogeneity among layers, except for the case in which all layers exhibit the same rigidity.

physics.geo-ph↗
arXiv2020

On modelling bicycle power for velodromes: Part I: Formulation for individual pursuits

For a moving bicycle, the power can be modelled as a response to the propulsion of the centre of mass of the bicycle-cyclist system. On a velodrome, an accurate modelling of power requires a distinction between the trajectory of the wheels and the trajectory of the centre of mass. We formulate and examine an individual-pursuit model that takes into account the aforementioned distinction. In doing so, we provide details of the invoked physical principles and mathematical derivations, with an emphasis on their limitations. We assume that a velodrome consists of two parallel straights and two semicircular arcs. We neglect the effects of the track inclination along the straights and assume the track inclination along the curves to be constant. For either segment, we consider two distinct black-line speeds. For the latter, the lean-angle expression is derived based on a noninertial frame of the cyclist. Among conclusions quantified by this model is the fact that a constant-cadence approach to an individual pursuit does not minimize the required power.

physics.pop-ph↗
arXiv2019

Applications of Graph Integration to Function Comparison and Malware Classification

We classify .NET files as either benign or malicious by examining directed graphs derived from the set of functions comprising the given file. Each graph is viewed probabilistically as a Markov chain where each node represents a code block of the corresponding function, and by computing the PageRank vector (Perron vector with transport), a probability measure can be defined over the nodes of the given graph. Each graph is vectorized by computing Lebesgue antiderivatives of hand-engineered functions defined on the vertex set of the given graph against the PageRank measure. Files are subsequently vectorized by aggregating the set of vectors corresponding to the set of graphs resulting from decompiling the given file. The result is a fast, intuitive, and easy-to-compute glass-box vectorization scheme, which can be leveraged for training a standalone classifier or to augment an existing feature space. We refer to this vectorization technique as PageRank Measure Integration Vectorization (PMIV). We demonstrate the efficacy of PMIV by training a vanilla random forest on 2.5 million samples of decompiled .NET, evenly split between benign and malicious, from our in-house corpus and compare this model to a baseline model which leverages a text-only feature space. The median time needed for decompilation and scoring was 24ms.

cs.AI↗
arXiv2019

Guided waves as superposition of body waves

We illustrate properties of guided waves in terms of a superposition of body waves. In particular, we consider the Love and SH waves. Body-wave propagation at postcritical angles--required for a total reflection--results in the speed of the Love wave being between the speeds of the SH waves in the layer and in the halfspace. A finite wavelength of the SH waves--required for constructive interference--results in a limited number of modes of the Love wave. Each mode exhibits a discrete frequency and propagation speed; the fundamental mode has the lowest frequency and the highest speed.

physics.class-ph↗
arXiv2019

On Christoffel roots for nondetached slowness surfaces

The only restriction on the values of the elasticity parameters is the stability condition. Within this condition, we examine Christoffel equation for nondetached $qP$ slowness surfaces in transversely isotropic media. If the $qP$ slowness surface is detached, each root of the solubility condition corresponds to a distinct smooth wavefront. If the $qP$ slowness surface is nondetached, the roots are elliptical but do not correspond to distinct wavefronts; also, the $qP$ and $qSV$ slowness surfaces are not smooth.

physics.geo-ph↗
arXiv2019

On orthogonal transformations of Christoffel equations

The purpose of this paper is to prove the equivalence$-$under rotations of distinct terms$-$of different forms of a determinantal equation that appears in the studies of wave propagation in Hookean solids, in the context of the Christoffel equations. To do so, we prove a general proposition that is not limited to ${\mathbb R}^3$, nor is it limited to the elasticity tensor with its index symmetries. Furthermore, the proposition is valid for orthogonal transformations, not only for rotations. The sought equivalence is a corollary of that proposition.

physics.geo-ph↗
arXiv2018

Statistical and numerical considerations of Backus-average product approximation

In this paper, we examine the applicability of the approximation, $\overline{f\,g}\approx \overline f\,\overline g\,$, within Backus (1962) averaging. This approximation is a crucial step in the method proposed by Backus (1962), which is widely used in studying wave propagation in layered Hookean solids. According to this approximation, the average of the product of a rapidly varying function and a slowly varying function is approximately equal to the product of the averages of those two functions. Considering that the rapidly varying function represents the mechanical properties of layers, we express it as a step function. The slowly varying function is continuous, since it represents the components of the stress or strain tensors. In this paper, beyond the upper bound of the error for that approximation, which is formulated by Bos et al. (2017), we provide a statistical analysis of the approximation by allowing the function values to be sampled from general distributions. Even though, according to the upper bound, Backus (1962) averaging might not appear as a viable approach, we show that$-$for cases representative of physical scenarios modelled by such an averaging$-$the approximation is typically quite good. We identify the cases for which there can be a deterioration in its efficacy. In particular, we examine a special case for which the approximation results in spurious values. However, such a case$-$though physically realizable$-$is not likely to appear in seismology, where Backus (1962) averaging is commonly used. Yet, such values might occur in material sciences, in general, for which Backus (1962) averaging is also considered.

physics.geo-ph↗