Hydrodynamic description of the adiabatic piston

<div class="section abstract"><div class="htmlview paragraph">The control and design optimization of a Free Piston Engine Generator (FPEG) has been found to be difficult as each independent variable changes the piston dynamics with respect to time. These dynamics, in turn, alter the generator and engine response to other governing variables. As a result, the FPEG system requires an energy balance control algorithm such that the cumulative energy delivered by the engine is equal to the cumulative energy taken by the generator for stable operation. The main objective of this control algorithm is to match the power generated by the engine to the power demanded by the generator. In a conventional crankshaft engine, this energy balance control is similar to the use of a governor and a flywheel to control the rotational speed. In general, if the generator consumes more energy in a cycle than the engine provides, the system moves towards a stall. If the generator consumes less energy, then the effective stroke, compression ratio and maximum translator velocity must rise steadily from cycle-to-cycle until the heat transfer losses stop the increase. Moreover, when stiff springs are added to the FPEG system, the dynamics becomes more sinusoidal and more consistent with increasing spring stiffness. To understand the behavior of proposed control and cycle-to-cycle variations, a comprehensive FPEG numerical model with a 1 kW target electric power was developed in MATLAB<sup>®</sup>/Simulink. An FPEG system corresponding to that numerical model has been operated in the laboratory. This MATLAB<sup>®</sup>/Simulink numerical model has been used to examine the sensitivity of FPEG dynamics and performance parameters to the changes in design and operating inputs. A difficulty during the modeling is associated with the cycle-to-cycle energy balance, and this difficulty is also reflected in the real-world FPEG control. Therefore, the authors have devised a control strategy similar to the real world intended control methodology. In this numerical model, two different feedback control methodologies were implemented and investigated. These control methodologies were applied to regulate the generator load with selected control or input variables, namely peak pressure, mid-stroke piston velocity, trapped compression ratio and dead center set points. The controllers with optimized coefficients demonstrated the feasibility of energy balance management during the transient operation. Based on the simulation results, the controllers with compression ratio, peak pressure and dead center clearance set points as control variables demonstrated stable FPEG operation whereas the mid-stroke velocity failed to achieve the steady-state operation due to deviation in the piston dynamics. The simulation results from this study will be used as the pathway for improving and optimizing the experimental FPEG design.</div></div>

We study the implications of a large value of the effective Majorana neutrino mass for a class of two-texture zero neutrino mass matrices in the flavour basis. We find that these textures predict near-maximal atmospheric neutrino mixing angle in the limit of large effective Majorana neutrino mass. We present the symmetry realization of these textures using the discrete cyclic group Z 3. It is found that the texture zeros realized in this work remain stable under the renormalization group running of the effective neutrino mass matrix at one-loop level.

Boson-fermion stars: going to larger boson masses

We complete the calculation of the wino-nucleon scattering cross section up to the next-to-leading order in $\alpha_s$. We assume that the other sparticles are decoupled and wino interacts with the Standard Model particles via the weak interaction. As a result, the uncertainties coming from the perturbative QCD are significantly reduced to be smaller than those from the nucleon matrix elements. The resultant scattering cross section is found to be larger than the leading-order one by about 70%, which is well above the neutrino background. In the limit of large wino mass the spin-independent scattering cross section with proton turns out $\sigma_{\text{SI}}^p = 2.3~{}^{+0.2}_{-0.3}~{}^{+0.5}_{-0.4}\times 10^{-47}~ \text{cm}^2$ (errors come from perturbative calculation and input parameters, respectively). The computation for a generic SU(2)$_L$ multiplet dark matter is also presented.

The implications of a large value of the effective Majorana neutrino mass for a class of two texture zero neutrino mass matrices have been studied in the flavor basis. It is found that these textures predict near maximal atmospheric neutrino mixing angle in the limit of large effective Majorana neutrino mass. It is noted that this prediction is independent of the values of solar and reactor neutrino mixing angles. We present the symmetry realization of these textures using the discrete cyclic group $Z_3$. It is found that the texture zeros realised in this work remain stable under renormalization group running of the neutrino mass matrix from the seesaw scale to the electroweak scale, at one loop level.

Classical solutions of the relativistic Vlasov–Maxwell system are considered, describing a collisionless plasma with two species of particles. ions and electrons. It is shown that as the ion mass m tends to infinity, the corresponding solution of the relativistic Vlasov–Maxwell system tends to the solution of a system, in which the ions are given by a fixed ion background and only the electrons move. The convergence is uniform on compact time intervals, with an asymptotic convergence rate of m−1.

We consider a massive inelastic piston, whose opposite faces have different coefficients of restitution, moving under the action of an infinitely dilute gas of hard disks maintained at a fixed temperature. The dynamics of the piston is Markovian and obeys a continuous Master Equation: however, the asymmetry of restitution coefficients induces a violation of detailed balance and a net drift of the piston, as in a Brownian ratchet. Numerical investigations of such non-equilibrium stationary state show that the velocity fluctuations of the piston are symmetric around the mean value only in the limit of large piston mass, while they are strongly asymmetric in the opposite limit. Only taking into account such an asymmetry, i.e. including a third parameter in addition to the mean and the variance of the velocity distribution, it is possible to obtain a satisfactory analytical prediction for the ratchet drift velocity.

First we give a short informal introduction to the theory behind the ’t Hooft equation. Then we consider numerical solutions to this equation in the limit of large fermion masses. It turns out that the spectrum of eigenvalues coincides with that of the Airy differential equation. Moreover when we take the Fourier transform of eigenfunctions, they look like the corresponding Airy functions with appropriate symmetry. It is known that these functions correspond to solutions of a one dimensional Schrodinger equation for a particle in a triangular potential well. So we find the analogy between this problem and the ’t Hooft equation. We also present a simple intuition behind these results.

We solve for the velocity fields of momentum-conserving supershells driven from galaxy centres by steady winds from supermassive black holes or nuclear star clusters (central massive objects: CMOs). We look for the critical CMO mass that allows such a shell to escape from its host galaxy. In the case that the host galaxy dark matter halo is a singular isothermal sphere, we find that the critical CMO mass derived by King, which scales with the halo velocity dispersion as M_crit \propto \sigma^4, is necessary, but not by itself sufficient, to drive shells to large radii in the halo. Furthermore, a CMO mass at least 3 times the King value is required to drive the shell to the escape speed of the halo. In the case of CMOs embedded in protogalaxies with non-isothermal dark matter haloes, which we treat here for the first time, we find a critical CMO mass that \textit{is sufficient} to drive \textit{any} shell (under a steady wind) to escape \textit{any} galaxy with a peaked circular speed profile. In the limit of large halo mass, relevant to real galaxies, this critical CMO mass depends only on the value of the peak circular speed of the halo, scaling as M_crit \propto V_c,pk^4. Our results therefore relate to observational scalings between black hole mass and asymptotic circular speed in galaxy spheroids. They also suggest a natural way of extending analyses of M-\sigma relations for black holes in massive bulges, to include similar relations for nuclear clusters in lower-mass and disc galaxies.

Based on the exact solution method, the ground state and quench dynamics properties of one-dimensional single-spin flipped Fermi gas with repulsion interaction are studied. With the Bethe wave function, the single-body correlation function and two-body correlation function of the ground state and those between different eigen-states can be reduced into a summation of simple functions, thereby greatly reducing the computational difficulty. For the system in the ground state, the single-body correlation functions and two-body correlation functions as well as momentum distributions for spin-up particles are investigated in real space with different interaction strengths. As the interaction strength increases, the number of nodes in the single-body correlation function remains unchanged, while the amplitude of oscillation decreases. Meanwhile, the number of peaks in the two-body correlation function increases by one due to interaction, indicating that the spin-down particle behaves as a spin-up particle. The momentum distribution becomes more smooth around Fermi surface with the interaction strength increasing. The interaction quench dynamics is investigated. The system is prepared in the ground state of ideal Fermi gas, and then the interaction strength is quenched to a finite positive value. The system evolves under time-dependent Schrödinger equation. The overlap between the initial state and eigen-state of post-quench interaction strength is expressed in the form of continued multiplication. The square of the modulus of this overlap, which represents the occupation probability, is calculated. We find that the occupation probabilities of the ground state and doubly degenerated excited state always have the first and the second largest value for an arbitrary interaction strength, respectively, which means that the difference in eigenenergy between these two states gives the primary period of oscillation. For relatively large particle number (<inline-formula><tex-math id="M2">\begin{document}$ N\geqslant10$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20231425_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20231425_M2.png"/></alternatives></inline-formula>), the primary period always does not change under different interaction strengths.It is found that in the case of interaction quenching, the momentum distribution and the correlation function show periodic oscillations. When the interaction strength is adjusted to a relatively small value, the oscillation periodicity is well-defined and the oscillation amplitude is small. The system can be approximated by a two-level model. When the interaction strength increases to a very large value, the oscillation periodicity worsens and the amplitude increases, but a primary period remains unchanged. Although the overall deviation is far from the initial state, it is very close to the initial state at time <inline-formula><tex-math id="M3">\begin{document}$ t=mL^2/(2\pi\hbar)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20231425_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20231425_M3.png"/></alternatives></inline-formula>. This is because the difference between most energy eigenvalues is almost an integral multiple of energy unit <inline-formula><tex-math id="M4">\begin{document}$ 2\times\left(2\pi/L\right)^{2}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20231425_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20231425_M4.png"/></alternatives></inline-formula>.

The state-to-state photodissociassion dynamics for the B band of D2O have been explored from quantum dynamical calculations including the electronic ̃X and ̃B states. The calculations were carried out using a Chebyshev real wave packet method. The calculated absorption spectra, product state distributions, and branching ratios from different initial vibrational states show different dynamic features, due to the different shapes of the vibrational wavefunctions. The initial bending mode (0,1,0) generates two lobes with a shallow minimum on the absorption spectrum and a slight inverted vibrational population of OD(̃X) product at high total energies. The rotational state distributions of OD(̃X, v=0) product are highly inverted and depend weakly on the initial state and total energy. On the other hand, the ro-vibrational distributions of OD(̃A) product strongly oscillate with the total energy, which are dominated by the long-living resonances and depend sensitively on the potential surfaces. The antisymmetric stretching mode (0,0,1) has large OD(̃A)/OD(̃X) branching ratios at high total energies, which indicates that the B band dissociation proceeds mainly via the adiabatic pathway in some cases.

Relaxation processes in thin (up to 125 μm) homeotropic layers of nematic liquid crystals (n-methoxybenzylidene-n-butylaniline), which were observed after switching off periodic shear oscillations with a low frequency (about 200 Hz), were experimentally studied. The foner method was used to excite vibrations in a liquid crystal sample. The amplitude of the oscillations was determined by inductive and optical methods. The cell with the sample was made in the form of a multi-layer structure. A liquid crystal was placed between the three glass plates. The middle plate floated in the liquid crystal and transmitted oscillatory movements to it. The dependences of the angle of deviation of the director from the normal to the cell on the time and relaxation times, the relaxation time on the shear amplitude and exposure time, as well as on the thickness of the liquid crystal layer; the time dependences of the optical signal at different exposure times and oscillation amplitudes; the dependences of the maximum values of the angle of rotation of the director in the XY plane on the shear amplitude and exposure time. It is found that after switching off the external perturbation, the relaxation processes of the liquid crystal director field depend on the exposure time, the thickness of the liquid crystal layer, and the oscillation amplitude. The relaxation dependences of the angle of inclination of the director after switching off the shift are described by an exponential dependence. Relaxation times are tens of seconds. The value of the relaxation time coincides with the relaxation time for the classical Fredericks effect and is about 30 s.

A study of the nature of the motion of a Holstein polaron in a homogeneous polynucleotide chain in a constant electric field, depending on the initial polaron state, was carried out. The calculations performed showed that the duration of the uniform motion of the polaron along the chain is finite and depends on the entire set of system parameters, including the characteristic size of the initial polaron state. It is shown that at a fixed value of the electric field intensity, an increase in the characteristic size of the initial polaron state leads to a decrease in the time of uniform motion of the polaron along the chain. The calculations carried out earlier showed that with the uniform movement of the polaron along the chain, low-density components of the polaron are formed immediately after the electric field is turned on. Moreover, the low-density components of the polaron have their own internal dynamics, which are different from the dynamics of the macro-part of the polaron. With uniform motion, the macro-part of the polaron moves at a constant velocity, maintaining its shape, while the low-density components of the polaron demonstrate such characteristics of Bloch oscillations as the period of Bloch oscillations and the maximum Bloch amplitude. It is also shown that a change in the shape of the initial polaron state exerts influence upon not only the duration of the uniform motion of the polaron along the chain, but also the characteristics of the low-density components of the polaron.

Experimental study of the head/medium magneto dynamics in perpendicular recording

Mass and energy rate (ER) data have been collected for a wide variety of (complex) systems from the biological, cultural, and cosmological realms. They range from the cytochrome oxidase protein (10-22 kg and 6x10-19 W) to the observable universe (1.5x1053 kg and 1048 W) and, thus, span 75 mass and 66 ER orders of magnitude. Many of these systems are relevant for the big history (BH) narrative, i.e., the development of complexity over “big time” from the Big Bang up to the human society on Earth of today. The purpose of this paper is not per se to describe their history though, but to explore a master plot of ER vs. mass. Notably, the development of systems over big time has followed a rather tortuous path criss-crossing over this ER vs. mass master plot. The true mass of the system as a whole is used (for example trees including the non-living wood, living organisms including their intrinsic water, and social systems including the built constructs), because these inactive parts are essential for the performance of the system and facilitate its ER. A double logarithmic master plot of all ER vs. mass data shows clusters of data points. To some extent, this provides quantitative support for the distinction between the (sub-)realms, which is based on a qualitative description of their material structure and energy processing. In the master plot, small systems with low mass and ER converge into larger systems with larger mass and ER, which is typically accompanied by a decrease of the energy rate density (ERD = ER/mass). Correlation of ER with mass for various groups of systems demonstrates both sub- and supra-linear scaling with the power law β constant varying between 0.5 and 4.0, showing that the mechanisms of self-organisation are quite different for the corresponding system groups. The combination of convergence and scaling with β always larger than zero explains why the ER & mass data points fall in a diagonal band with a width of 17 orders of magnitude.
 ER and mass have changed over wide ranges during the evolution of groups of systems, suggesting that evolution can be viewed as a process of systems exploring a larger ER vs. mass area until they run into ER and/or mass limitations. Indeed, there is a diagonal ER vs. mass limit for stable systems in all realms, corresponding to an ERD value of around 105 W/kg. Systems with ER & mass combinations above this limit, such as bombs, super-novae and cosmological transients, are unstable and “explosive”. This raises the interesting question of whether such an ERD maximum puts a limit on the development of complexity over big time. It seems that the low, right side of the master plot is empty. However, it is argued here that it is full of systems with low ER, such as dormant, living organisms, technological systems with their power adjusted or even switched off, as well as cooling, cosmological objects. Such systems are typically considered of less interest in a BH context, but they are viewed here as simple, complex systems which are out of equilibrium with matter, energy and information stored in their structure. While ERD appears to increase with the ‘advancement’ of systems over big time [5,51,52], there are quite some confounding factors regarding the efficacy of ERD as a metric for complexity in BH. For example, ERD decreases during the lifetime of a human and the human society (the mass of human-made constructs has grown faster than the global energy consumption), as well as during the evolution of living organisms and stars, whereas complexity is considered to increase. High ERD values of system parts may be illustrative for the complexity of the larger system, but are not representative for ERD of the system itself. Machines with an increased efficiency of energy conversion have a lower ERD, but could be considered more complex. The smallest and largest ERD values observed for the various realms appear to correlate with activity level and reciprocally with size, which do not per se reflect complexity. It is hoped that the raw data collected and the major trends observed in this paper will offer new insights into various aspects of the evolution of the universe over big time, and serve as an important resource for other related studies.