Temperature and entropy in molecular system

The irreversibility, temperature, and entropy are identified for an atomic system of solid material. Thermodynamics second law is automatically satisfied in the time evolution of molecular dynamics (MD). The irreversibility caused by an atom spontaneously moves from a non-stable equilibrium position to a stable equilibrium position. The process is dynamic in nature associated with the conversion of potential energy to kinetic energy and the dissipation of kinetic energy to the entire system. The forward process is less sensitive to small variation of boundary condition than reverse process, causing the time symmetry to break. Different methods to define temperature in molecular system are revisited with paradox examples. It is seen that the temperature can only be rigorously defined on an atom knowing its time history of velocity vector. The velocity vector of an atom is the summation of the mechanical part and the thermal part, the mechanical velocity is related to the global motion (translation, rotation, acceleration, vibration, etc.), the thermal velocity is related to temperature and is assumed to follow the identical random Gaussian distribution for all of its [Formula: see text], [Formula: see text] and [Formula: see text] component. The [Formula: see text]-velocity (same for [Formula: see text] or [Formula: see text]) versus time obtained from MD simulation is treated as a signal (mechanical motion) corrupted with random Gaussian distribution noise (thermal motion). The noise is separated from signal with wavelet filter and used as the randomness measurement. The temperature is thus defined as the variance of the thermal velocity multiply the atom mass and divided by Boltzmann constant. The new definition is equivalent to the Nose–Hover thermostat for a stationary system. For system with macroscopic acceleration, rotation, vibration, etc., the new definition can predict the same temperature as the stationary system, while Nose–Hover thermostat predicts a much higher temperature. It is seen that the new definition of temperature is not influenced by the global motion, i.e., translation, rotation, acceleration, vibration, etc., of the system. The Gibbs entropy is calculated for each atom by knowing normal distribution as the probability density function. The relationship between entropy and temperature is established for solid material.

Quasi-Static Flooding Analysis Method of a Damaged Ship Considering Oil Spill and Cargo Load

When a ship is damaged at sea, it is important to predict its behavior as well as whether it is to sink or not. If the ship comes to an equilibrium, the equilibrium position and time should be estimated; otherwise, the time to sink should be estimated. Furthermore, flooding analysis should be carried out not only during the design stage of the ship for preventive reasons, but also after an accident for a better investigation of its causes. In addition, flooding analysis methods that can provide predictions in case of an accident are of particular importance, as there is no time for the required calculations in an emergency. For this purpose, a quasi-static flooding analysis method for the damaged ship in the time domain is proposed in this study. There are a number of studies in which the equilibrium position and time were estimated by flooding analysis. However, most of them have not considered the air pressure effect in fully flooded compartments, and the method of determining the fluid volume in these compartments was not accurate. In the present study, the virtual vent and accumulator method are used to calculate the reference pressure in the fully flooded compartments, and the compartment shape is considered by using polyhedral integration. Also, spilled oil and solid cargo items from the damaged ship are taken into account for realistic flooding analysis. Finally, the damage stability criteria were checked not only in the final state, but also during the entire time of the flooding, as the intermediate states can be more hazardous than the final state. To validate the feasibility of the proposed method, it was applied to a naval ship, which is considerably more stringent for damage stability. As a result, we checked the availability of this study.

Impact of substitution on reactions and stability of one-electron oxidised phenyl sulfonates in aqueous solution

Functional groups can be used to modify the equilibrium position and tune the reactivity of one electron oxidised aromatic compounds.

Efficient thrust enhancement by modified pitching motion

Thrust and/or efficiency of a pitching foil (mimicking a tail of swimming fish) can be enhanced by tweaking the pitching waveform. The literature, however, show that non-sinusoidal pitching waveforms can enhance either thrust or efficiency but not both simultaneously. With the knowledge and inspiration from nature, we devised and implemented a novel asymmetrical sinusoidal pitching motion that is a combination of two sinusoidal motions having periods T1 and T2 for the forward and retract strokes, respectively. The motion is represented by period ratio $\mathrm{\mathbb{T}} = {T_1}/T$ , where T = (T1 + T2)/2, with $\mathrm{\mathbb{T}} > 1.00$ giving the forward strokes (from equilibrium to extreme position) slower than the retract strokes (from extreme to equilibrium position) and vice versa. The novel pitching motion enhances both thrust and efficiency for $\mathrm{\mathbb{T}} > 1.00$ . The enhancement results from the resonance between the shear-layer roll up and the increased speed of the foil. Four swimming regimes, namely normal swimming, undesirable, floating and ideal are discussed, based on instantaneous thrust and power. The results from the novel pitching motion display similarities with those from fish locomotion (e.g. fast start, steady swimming and braking). The $\mathrm{\mathbb{T}} > 1.00$ motion in the faster stroke has the same characteristics and results as the fast start of prey to escape from a predator while $\mathrm{\mathbb{T}} < 1.00$ imitates braking locomotion. While $\mathrm{\mathbb{T}} < 1.00$ enhances the wake deflection at high amplitude-based Strouhal numbers (StA = fA/U∞, where f and A are the frequency and peak-to-peak amplitude of the pitching, respectively, and U∞ is the freestream velocity), $\mathrm{\mathbb{T}} > 1.00$ improves the wake symmetry, suppressing the wake deflection. The wake characteristics including wake width, jet velocity and vortex structures are presented and connected with $S{t_d}( = fd/{U_\infty })$ , ${A^{\ast}}( = A/d)$ and $\mathrm{\mathbb{T}}$ , where d is the maximum thickness of the foil.

An Improved Structural Analysis Method for Isolator with Quasi-Zero-Stiffness Characteristic

A typical quasi-zero-stiffness (QZS) vibration isolator consisting of a vertical spring and two oblique springs has been widely researched on its static and dynamic characteristics. A general criterion for determining structural parameters of QZS isolator is to achieve low nondimensional stiffness around the equilibrium position. However, lower nondimensional stiffness of linear isolator means lower isolation frequency, which may be invalid on QZS isolator. Because there is an implicit relationship between geometric parameter and stiffness ratio of QZS isolator, this study presents an improved optimization criterion for determining the optimal structural parameters of the typical QZS isolator. The optimization criterion is that the QZS isolator has the maximum displacement range around the equilibrium position without exceeding given natural frequency, rather than given nondimensional stiffness. The results show that isolator with these optimal parameters can achieve lower stiffness around the equilibrium position and better vibration isolation performance. Furthermore, an extended QZS isolator consisting of vertical spring with fixed stiffness and prestressed oblique springs is discussed to further improve stiffness characteristic. Better stiffness performance can be obtained when the prestressed oblique springs have softening stiffness and the exponent of the nonlinear stiffness is 2. Considering the existence of friction in practical application, the influence of friction on both static and dynamic characteristics is investigated. The analysis reveals that friction has little influence on its stiffness characteristic around the static equilibrium position and friction damping produced by friction affects the response amplitude and resonant frequency in dynamics.

THE TRANSIENT EFFECTS OF FLOOD WATER ON A WARSHIP IN CALM WATER IMMEDIATELY FOLLOWING DAMAGE

The safety of a ship which is damaged below the waterline will depend on the way water floods into the internal compartments. The water will cause the ship to take on an angle of heel and trim which will further affect the flooding into the compartments. The ship’s equilibrium position in calm water can be predicted using hydrostatic theory, however at present it is difficult to predict the transient behaviour between the initial upright position of the ship and its final equilibrium. In some cases, the transient motion may cause a capsize prior to a possible equilibrium position being reached. This paper describes an investigation of this phenomenon using a model of a warship with simplified, typical internal geometry. With the model initially stationary, a rapid damage event was generated, and the global motions measured, along with the water levels in some of the internal compartments, as functions of time. Immediately after the damage occurred the model rolled to starboard (towards the damage). It then rolled to port (away from the damage) before eventually returning to starboard and settling at its equilibrium value. In all the tests conducted the equilibrium heel angle was less than that reached during the initial roll to starboard. This implies that the roll damping, and the way in which the water floods into the model immediately following the damage, could both have a very important influence on the likelihood of survival.

Low magnetic-field induced high temperature dynamic magnetoelectric coupling performances in Z-type Sr3Co2Fe24O41

Magnetic-field induced dynamic magnetoelectric coupling effects and polarization performance of Z-type Sr3Co2Fe24O41 (SCFO) ceramic has been investigated. Results found that SCFO’s transverse tapered magnetic structure can induce electric polarization, and its electric polarization direction will not change under external magnetic effects. First-order dynamic magnetoelectric coupling coefficient (α) and second-order dynamic magnetoelectric coupling coefficient (β) of SCFO exhibited strong response main in magnetic structural phase transition region. The magnetoelectric structural phase transition position appeared in low magnetic field, and the magnetic moment vector and its corresponding electric polarization vector of SCFO exhibited the most unstable state near its equilibrium position, which is beneficial for inducing strong dynamic magnetoelectric coupling response. When the applied magnetic fields to SCFO increased, the magnetic moment stability near the equilibrium position increased, and the dynamic magnetoelectric coupling response decreased. Results showed that the dynamic magnetoelectric coupling response of SCFO can bear T1 = 370 K high temperature. The dynamic magnetoelectric coupling response induced by low magnetic fields in SCFO contributes to its actual application in next generation magnetoelectric information storage devices.

On the interrelation of equilibrium positions and work of friction forces on brake squeal

Brake noise, in particular brake squeal, is a permanent topic both in industry and academia since decades. Nonlinearities play a decisive role for this phenomenon. One nonlinear effect widely ignored so far is that the brake can engage multiple equilibrium positions with severe consequences on the noise behavior. In fact in an automotive disk brake, the essential elements carrier, caliper and pad are elastically coupled with each other and their behavior is nonlinear that multiple equilibrium positions are possible. The engaged equilibrium position depends, for example, on the initial conditions, external disturbances, and the transient application of the brake pressure, and in consequence configurations with or without self-exciting characteristics of the friction forces result. Obviously, a self-exciting characteristic of the friction force is a necessary precondition for the occurrence of squeal. The authors recently published some corresponding results (Koch et al. FU Mech Eng, 2021. https://doi.org/10.22190/FUME210106020K) demonstrating that for same operating parameters with respect to brake pressure (i.e., brake torque), rotational speed and temperature the engaged equilibrium position has decisive influence whether squeal occurs or not. While in Koch et al. (2021) it has just been detected whether there is squeal or not, the excitation characteristic of the friction forces becomes, beside the engaged equilibrium position, the additional focus in the present paper. Therefore, a work criterion already successfully applied in earlier publications for squeal tendency is considered. For the experimental application of the work criterion, accelerometers have to be mounted. The accelerometers’ location to be applied can be determined in the chosen setup by the camera system anyway necessary for the measurement of the engaged equilibrium position. With this refined setup, it is possible to specify the states squeal, close to squeal and far from squeal. The test series again demonstrate the decisive influence of the engaged equilibrium position (for constant operation parameters) on the occurrence of the respective state. These findings can have consequences for simulations (consideration of multiple equilibrium positions in models and respective linearization with consequences on system’s eigenvalues), but also for the design (avoidance of equilibrium positions suspicious for squeal) and experimental setups (determination of special positions) of brakes.

STATIC CHARACTERISTICS OF OFFSET 8-LOBE JOURNAL BEARINGS

The 8-lobe journal bearings have found application in the bearing systems of spindles of grinding machines. The design of bearings and the large number of lobes and oil grooves assures good cooling conditions of bearing. These bearings can be manufactured as the bearings with cylindrical, non-continuous operating surfaces separated by six lubricating grooves, bearings with the pericycloidal shape of the bearing bore, and as offset journal bearing. This paper presents the results of the computation of static characteristics of an offset 8-lobe journal bearing operating under the conditions of an aligned axis of journal and bush, adiabatic oil film, and at the static equilibrium position of journal. Different values of bearing length to diameter ratio, relative clearance, and lobe relative clearance were assumed. Reynolds' energy and viscosity equations were solved by means of an iterative procedure. Adiabatic oil film, laminar flow in the bearing gap, and aligned orientation of journal in the bearing were considered.

Chemical Equilibrium

Chemical Equilibrium reviews the principles of equilibrium in systems of gases and liquids, starting with the concepts of reversible and irreversible reactions and dynamic equilibrium. The equilibrium constant (K) and reaction quotient (Q) are described, and comparison of K and Q is used to determine the direction in which a reaction must proceed to reach equilibrium. Calculations involving K in terms of concentration and pressure are presented. The relationship between the magnitude of K, the equilibrium position and the concentrations of reactants and products is discussed for both homogeneous and heterogeneous equilibria. The chapter ends with a qualitative treatment of equilibrium based on Le Chatelier’s principle, as well as how changes in reaction conditions can disturb a chemical equilibrium and how the chemical reaction responds to those changes.