The method of fundamental solutions for the Oseen steady‐state viscous flow past obstacles of known or unknown shapes

In this paper, the steady‐state Oseen viscous flow equations past a known or unknown obstacle are solved numerically using the method of fundamental solutions (MFS), which is free of meshes, singularities, and numerical integrations. The direct problem is linear and well‐posed, whereas the inverse problem is nonlinear and ill‐posed. For the direct problem, the MFS computations of the fluid flow characteristics (velocity, pressure, drag, and lift coefficients) are in very good agreement with the previously published results obtained using other methods for the Oseen flow past circular and elliptic cylinders, as well as past two circular cylinders. In the inverse obstacle problem the boundary data and the internal measurement of the fluid velocity are minimized using the MATLAB© optimization toolbox lsqnonlin routine. Regularization was found necessary in the case the measured data are contaminated with noise. Numerical results show accurate and stable reconstructions of various star‐shaped obstacles of circular, bean, or peanut cross‐section

Revisiting the exercise heart rate-music tempo preference relationship

In the present study, we investigated a hypothesized quartic relationship (meaning three inflection points) between exercise heart rate (HR) and preferred music tempo. Initial theoretical predictions suggested a positive linear relationship (Iwanaga, 1995a, 1995b); however, recent experimental work has shown that as exercise HR increases, step changes and plateaus that punctuate the profile of music tempo preference may occur (Karageorghis, Jones, & Stuart, 2008). Tempi bands consisted of slow (95–100 bpm), medium (115–120 bpm), fast (135–140 bpm), and very fast (155–160 bpm) music. Twenty-eight active undergraduate students cycled at exercise intensities representing 40, 50, 60, 70, 80, and 90% of their maximal HR reserve while their music preference was assessed using a 10-point scale. The Exercise Intensity x Music Tempo interaction was significant, F(6.16, 160.05) = 7.08, p < .001, ηp 2 =.21, as was the test for both cubic and quartic trajectories in the exercise HR–preferred-music-tempo relationship (p < .001). Whereas slow tempo music was not preferred at any exercise intensity, preference for fast tempo increased, relative to medium and very fast tempo music, as exercise intensity increased. The implications for the prescription of music in exercise and physical activity contexts are discussed

Identification of obstacles immersed in a stationary Oseen fluid via boundary measurements

In this paper we consider the interior inverse problem of identifying a rigid boundary of an annular infinitely long cylinder within which there is a stationary Oseen viscous fluid, by measuring various quantities such as the fluid velocity, fluid traction (stress force) and/or the pressure gradient on portions of the outer accessible boundary of the annular geometry. The inverse problems are nonlinear with respect to the variable polar radius parameterizing the unknown star-shaped obstacle. Although for the type of boundary data that we are considering the obstacle can be uniquely identified based on the principle of analytic continuation, its reconstruction is still unstable with respect to small errors in the measured data. In order to deal with this instability, the nonlinear Tikhonov regularization is employed. Obstacles of various shapes are numerically reconstructed using the method of fundamental solutions for approximating the fluid velocity and pressure combined with the MATLAB©© toolbox routine lsqnonlin for minimizing the nonlinear Tikhonov's regularization functional subject to simple bounds on the variables

Improved Kansa RBF Method for the Solution of Nonlinear Boundary Value Problems

We apply the Kansa–radial basis function (RBF) collocation method to two-dimensional nonlinear boundary value problems. In it, the solution is approximated by a linear combination of RBFs and the governing equation and boundary conditions are satisfied in a collocation sense at interior and boundary points, respectively. The nonlinear system of equations resulting from the Kansa–RBF discretization for the unknown coefficients in the RBF approximation is solved by directly applying a standard nonlinear solver. In a natural way, the value of the shape parameter in the RBFs employed in the approximation may be included in the unknowns to be determined. The numerical results of several examples are presented and analyzed

The method of fundamental solutions for three-dimensional inverse geometric elasticity problems

We investigate the numerical reconstruction of smooth star-shaped voids (rigid inclusions and cavities) which are compactly contained in a three-dimensional isotropic linear elastic medium from a single set of Cauchy data (i.e. nondestructive boundary displacement and traction measurements) on the accessible outer boundary. This inverse geometric problem in three-dimensional elasticity is approximated using the method of fundamental solutions (MFS). The parameters describing the boundary of the unknown void, its centre, and the contraction and dilation factors employed for selecting the fictitious surfaces where the MFS sources are to be positioned, are taken as unknowns of the problem. In this way, the original inverse geometric problem is reduced to finding the minimum of a nonlinear least-squares functional that measures the difference between the given and computed data, penalized with respect to both the MFS constants and the derivative of the radial coordinates describing the position of the star-shaped void. The interior source points are anchored and move with the void during the iterative reconstruction procedure. The feasibility of this new method is illustrated in several numerical examples

Perceived importance of components of asynchronous music in circuit training

This study examined regular exercisers’ perceptions of specific components of music during circuit training. Twenty-four men (38.8 years, s = 11.8 years) and 31 women (32.4 years, s = 9.6 years) completed two questionnaires immediately after a circuit training class. Participants rated the importance of 13 components of music (rhythm, melody, etc.) in relation to exercise enjoyment, and each completed the Affect Intensity Measure (Larsen, 1984) to measure emotional reactivity. Independent t tests were used to evaluate gender differences in perceptions of musical importance. Pearson correlations were computed to evaluate the relationships between affect intensity, age and importance of musical components. Consistent with previous research and theoretical predictions, rhythm response components (rhythm, tempo, beat) were rated as most important. Women rated the importance of melody significantly higher than did men, while men gave more importance to music associated with sport. Affect intensity was found to be positively and significantly related to the perceived importance of melody, lyrical content, musical style, personal associations and emotional content. Results suggest that exercise leaders need to be sensitive to personal factors when choosing music to accompany exercise. Qualitative research that focuses on the personal meaning of music is encouraged

Simultaneous numerical determination of a corroded boundary and its admittance

In this paper, an inverse geometric problem for Laplace’s equation arising in boundary corrosion detection is considered. This problem, which consists of determining an unknown corroded portion of the boundary of a bounded domain and its admittance Robin coefficient from two pairs of boundary Cauchy data (boundary temperature and heat flux), is solved numerically using the meshless method of fundamental solutions. A non-linear minimization of the objective function is regularized, and the stability of the numerical results is investigated with respect to noise in the input data and various values of the regularization parameters involved

Tempo and intensity of pre-task music modulate neural activity during reactive task performance

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2013 The Authors.Research has shown that not only do young athletes purposively use music to manage their emotional state (Bishop, Karageorghis, & Loizou, 2007), but also that brief periods of music listening may facilitate their subsequent reactive performance (Bishop, Karageorghis, & Kinrade, 2009). We report an fMRI study in which young athletes lay in an MRI scanner and listened to a popular music track immediately prior to performance of a three-choice reaction time task; intensity and tempo were modified such that six excerpts (2 intensities × 3 tempi) were created. Neural activity was measured throughout. Faster tempi and higher intensity collectively yielded activation in structures integral to visual perception (inferior temporal gyrus), allocation of attention (cuneus, inferior parietal lobule, supramarginal gyrus), and motor control (putamen), during reactive performance. The implications for music listening as a pre-competition strategy in sport are discussed

Redesign and initial validation of an instrument to assess the motivational qualities of music in exercise: The Brunel Music Rating Inventory-2

In the present study, a measure to assess the motivational qualities of music in exercise was redesigned, extending previous research efforts (Karageorghis et al., 1999). The original measure, the Brunel Music Rating Inventory (BMRI), had shown limitations in its factor structure and its applicability to non-experts in music selection. Redesign of the BMRI used in-depth interviews with eight participants (mean age 31.9 years, s¼8.9 years) to establish the initial item pool, which was examined using a series of confirmatory factor analyses. A single-factor model provided a good fit across three musical selections with different motivational qualities (comparative fit index, CFI: 0.95 – 0.98; standardized root mean residual, SRMR: 0.03 – 0.05). The single-factor model also demonstrated acceptable fit across two independent samples and both sexes using one piece of music (CFI: 0.86 – 1.00; SRMR: 0.04 – 0.07). The BMRI was designed for experts in selecting music for exercise (e.g. dance aerobic instructors), whereas the BMRI-2 can be used both by exercise instructors and participants. The psychometric properties of the BMRI-2 are stronger than those of the BMRI and it is easier to use. The BMRI-2 provides a valid and internally consistent tool by which music can be selected to accompany a bout of exercise or a training session. Furthermore, the BMRI-2 enables researchers to standardize music in experimental protocols involving exercise-related tasks

Effects of music and music-video on core affect during exercise at the lactate threshold

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this recordThe objective of the present study was to examine the effects of music and music-video on core affect during and immediately after stationary cycling at the lactate threshold. A randomized, fully counterbalanced, crossover design with three conditions (music, music-video, and a no-music-video control) was adopted. Twenty-four participants exercised at lactate threshold while exposed to music, music-video, and control conditions. Affective valence and perceived activation were assessed every 2 min during a 20-min exercise bout and every 5 min post exercise over a 20-min period. Results indicated that there was a significant condition x time interaction for affective valence. The music-video condition elicited the highest levels of affective valence followed by the music condition and control. There was a main effect of condition for affective valence, wherein the experimental conditions facilitated significantly higher affective valence than control. Significant main effects of time emerged for both affective valence and perceived activation. Regardless of condition, affective valence decreased during the exercise bout and increased immediately post exercise. Conversely, perceived activation increased during exercise and decreased immediately post exercise. The present findings indicate that music and music-video can enhance core affect during exercise at the lactate threshold and the implications for exercise adherence are expounded