Catálogo de publicaciones - revistas

<jats:p>We discuss contemporary ideas in Monte Carlo algorithms in the simplified setting of the one-dimensional anharmonic oscillator. After reviewing the connection between molecular dynamics and Monte Carlo, we introduce the Metropolis and the factorized Metropolis algorithms and lifted non-reversible Markov chains. We, furthermore, illustrate the concept of thinning, where moves are accepted by simple bounding potentials rather than the harmonic and quartic contributions to the anharmonic oscillator. We point out the multiple connections of our example algorithms with real-world sampling problems. This paper is self-contained, and Python implementations are provided.</jats:p>

<jats:p>The bound states of a particle confined in a one-dimensional finite square well cannot be solved analytically, since the eigen-energies are determined by transcendental equations. Here, we numerically calculate the bound states and show their non-classical properties, using Wigner's quasi-probability distribution (also called the Wigner functions) in the phase space (x, p). In contrast to the infinite-well case, we find that the Wigner functions spread over the space dimension x, get squeezed along the momentum dimension p, and show negativity outside the well. Negativity in a Wigner function indicates non-classical properties of the bound states.</jats:p>

<jats:p>We describe the physics of the “Windkessel effect” and its role in smoothing the output of water produced by piston-driven pumps found in early fire engines and modern residential well houses. We also construct a simple, analytical model of its operation and apply this model to the Windkessel in Richard Newsham's 1725 fire engine. We find that Newsham's Windkessel reduces the variations in the pump output stream from a high of 80% to a low of 16%.</jats:p>

<jats:p>A simple, intuitive, and low-cost setup for generating and measuring capillary waves is presented enabling a precise determination of the dispersion relation for a cylindrical water jet. By setting the phase velocity and measuring the wavelength of capillary waves directly, this method provides an intuitive way for students to understand the dispersion relation of a cylindrical water jet. The setup produced measurements of wavelength versus phase velocity over a broader range of values than earlier work. The resulting data are generally consistent with earlier results but show an error of up to 15% at both the higher and lower end of the measured range of wavelengths compared to the theoretical dispersion relation of cylindrical water jets. For the shorter wavelengths, the deviation is in the opposite direction from that of earlier work.</jats:p>

<jats:p>We experimentally investigate the motion of a pendulum on a turntable. The dynamics of this conical pendulum experiment are very rich and can be studied both at the undergraduate and graduate levels. At low rotational frequency of the turntable, we measure the Coriolis acceleration. Increasing the rotational frequency, we experimentally demonstrate a supercritical pitchfork bifurcation: above a critical rotational frequency, the pendulum arm spontaneously rises up. Beyond the characterization of the equilibrium pendulum angle, we evidence the so-called critical slowing down corresponding to the increase in the pendulum period when approaching the critical rotational frequency. Bifurcation and critical slowing down are key concepts in the study of critical phenomena that are seldom illustrated experimentally. All our experimental measurements are in excellent quantitative agreement with the theory we provide.</jats:p>

<jats:p>We present a theoretical study of a periodic vibrating string composed of a finite sequence of string segments connected periodically, with each segment characterized by a constant linear mass density. The main purpose is to provide a model that can mimic the properties of photonic or phononic crystals. This system displays frequency intervals for which wave propagation is not allowed (frequency bandgaps), in close analogy to photonic and phononic crystals. We discuss the behavior of these bandgaps when varying physical parameters, such as the values of the linear mass densities, the oscillation frequency, and the number of string segments constituting the entire system.</jats:p>

<jats:p>“Can one hear the shape of a drum?” was a question posed (and made famous) by mathematician Mark Kac in the mid-1960s. It addresses whether a deeper connection exists between the resonance modes (eigenmodes) of a drum and its shape. Here, we propose a numerical experiment, suitable for advanced undergraduate physics students, on the calculation of the eigenmodes of a square Koch fractal drum, for which experimental results do exist. This exercise is designed to develop the students' understanding of the vibrations of fractal drums, their eigenmodes, and potentially their integrated density of states. The students calculate the lowest order eigenmodes of the fractal drum, visualize these modes, and study their symmetry properties. As an extension, the students may investigate the integrated density of states of the fractal drum and compare their findings to the Weyl–Berry conjecture.</jats:p>

<jats:p>We offer two Excel modules that students can use to view the real-time spatial evolution of a diatomic molecule's nuclei when two different potential energy curves governing the nucleus motion spatially cross one another or are coupled by a light field. Module 1 comprises three spreadsheets that can be used to view non-adiabatic nuclear dynamics on two crossing nuclear potential energy curves. These curves cross because there is a value of the spatial coordinate where the two curves have the same energy, which results in a non-zero probability of the probability density crossing from one potential curve to the other. Students can view non-adiabatic nuclear dynamics involving two unbounded nuclear potential curves, pre-dissociation with a bound “ionic state” to an unbound covalent state, and quantum tunneling dynamics between two bounded potential curves. Module 2 comprises two spreadsheets that can be used to view the dynamics of the photo-excitation process, i.e., where the absorption of light leads to transitions between two nuclear potentials. Students can model the light-induced transitions between nuclear potentials when the light is provided by both a continuous wave laser and a pulsed laser. These modules are included as the supplementary material and can be run on any computer that supports Excel.</jats:p>

<jats:p>We derive the “complete” or “strong” version of Wien's displacement law from two adiabatic invariants: one of a thermodynamic system composed of a finite-sized segment of frequencies taken from the spectrum of blackbody radiation and one of the individual electromagnetic waves that compose this system. By exploiting the algebra of these invariants, we shift the calculational burden of deriving Wien's displacement law toward the methods of classical thermodynamics. These methods also produce a class of displacement laws that constrain both the particles of a classical ideal gas and the acoustic waves of the Debye model of a solid.</jats:p>