A simple model for interpreting temperature variability and its higher-order changes

Atmospheric temperature distributions are often identified with their variance, while the higher-order moments receive less attention. This can be especially misleading for extremes, which are associated with the tails of the Probability Density Functions (PDFs), and thus depend strongly on the higher-order moments. For example, skewness is related to the asymmetry between positive and negative anomalies, while kurtosis is indicative of the ”extremity” of the tails. Here we show that for near-surface atmospheric temperature, an approximate linear relationship exists between kurtosis and skewness squared. We present a simple model describing this relationship, where the total PDF is written as the sum of three Gaussians, representing small deviations from the climatological mean together with the larger amplitude cold and warm temperature anomalies associated with synoptic systems. This model recovers the PDF structure in different regions of the world, as well as its projected response to climate change, giving a simple physical interpretation of the higher-order temperature variability changes. The kurtosis changes are found to be largely predicted by the skewness changes. Building a deeper understanding of what controls the higher-order moments of the temperature variability is crucial for understanding extreme temperature events and how they respond to climate change.

Predicting relationships between solar jet variables

Studies of spicules and similar solar jets reveal a strong correlation between some of the kinematic variables, particularly between the initial velocity V, and the subsequent deceleration, a. It has been proposed that there is a linear relationship between these two variables and that this offers proof for a shock wave mechanism acting on the spicules, although the linear equations found are all different. It is shown here that the relationship is better described by a non-linear form: V is proportional to the square root of a. This relationship between V and a also provides a simple physical interpretation for the results. The different linear equations are found to be simply tangents to this (a, V) curve. Another method used to investigate the (a, V) connection is to determine the correlation coefficients between the kinematic variables from their scatter plots. It is also shown how these correlations also can be predicted from the mean value of the acceleration and height and their standard deviations for the sample under consideration. The implications of these results and the possibility that spicule behaviour is partly due to magnetic fields are discussed.

Lateral Torsional Buckling of Steel Beams Elastically Restrained at the Support Nodes

The study shows the results of theoretical investigations into lateral torsional buckling of bisymmetric I-beams elastically restrained against warping and against rotation in the plane of lateral torsional buckling (i.e., against lateral rotation) at the support nodes. The analysis accounted for the whole variation range of node stiffnesses, from complete warping freedom to full restraint, and from complete lateral rotation freedom to full restraint. It was assumed the beams are simply supported against bending about the major axis of the section. To determine the critical moment, the energy method was used. Both the twist angle function and the lateral deflection function of the beam were described using power polynomials with simple physical interpretation. Computer programmes were developed to make numerical and symbolic “computations”. General approximation formulas for the critical moment for lateral torsional buckling were derived. The formulas covered the basic and most frequently found loading diagrams. Detailed computations were performed for different values of the index of fixity against warping and against rotation in the plane of lateral torsional buckling. The critical moments determined using the programmes devised and approximation formulas were compared with the values obtained with LTBeam software (FEM). A very good congruence of results was found.

CONSTRUCTIVE THEORY OF IMAGE FORMATION FOR OBJECTS IN PARTIALLY COHERENT LIGHT

The constructive (approximate) theory of image formation for one-dimensional binary objects by a partially coherent projective diffraction-limited system at any ratio of the angular sizes of a light source and an aperture diaphragm is developed. For such objects the solution of a two-dimensional task can be consolidated to one-dimensional: to calculation of integral in the form of convolution of an object with the generalized pulse response with the subsequent nonlinear transformation. It is shown that the profile of the images created in partially coherent light is defined by the threshold system performance providing reliable finding of edge position of binary objects. Approximation of this characteristic is proposed. The theory allows simple physical interpretation of the phenomena in partially coherent projective systems.

Hallmarking quantum states: unified framework for coherence and correlations

Quantum coherence and distributed correlations among subparties are often considered as separate, although operationally linked to each other, properties of a quantum state. Here, we propose a measure able to quantify the contributions derived by both the tensor structure of the multipartite Hilbert space and the presence of coherence inside each of the subparties. Our results hold for any number of partitions of the Hilbert space. Within this unified framework, global coherence of the state is identified as the ingredient responsible for the presence of distributed quantum correlations, while local coherence also contributes to the quantumness of the state. A new quantifier, the "hookup", is introduced within such a framework. We also provide a simple physical interpretation, in terms of coherence, of the difference between total correlations and the sum of classical and quantum correlations obtained using relative-entropy-based quantifiers.

Demystifying the constancy of the Ermakov–Lewis invariant for a time-dependent oscillator

It is well known that the time-dependent harmonic oscillator (TDHO) possesses a conserved quantity, usually called Ermakov–Lewis invariant. I provide a simple physical interpretation of this invariant as well as a whole family of related invariants. This interpretation does not seem to have been noticed in the literature before. The procedure also allows one to tackle some key conceptual issues which arise in the study of quantum fields in the external, time-dependent backgrounds like in the case of particle production in an expanding universe and Schwinger effect.

Model-Based Analysis of Friction-Induced Subsynchronous Whirl for a Rotor Contacting With Clearance Bearings Under Axial Load

For rotors supported by active magnetic bearings (AMBs), clearance bearings are commonly used to provide backup support under loss of AMB functionality. Test data from real machines shows that vibration during touchdown on backup bearings may involve steady forward whirling of the rotor with a subsynchronous frequency. This excitation is believed to be due to friction forces transmitted between the rotor and a bearing end-face under axial load. This paper proposes a new analytical approach to model and predict such friction-driven forward whirl behaviors. A set of constraint equations are derived that relate a circular whirl motion of arbitrary orbital speed to the frequency response functions for the rotor-housing structure. This model is coupled with an evaluation of Coulomb friction associated with slip between the rotor and the supporting end-face of a thrust bearing. The resulting equations can be used to compute a set of possible whirl motions via a root-finding procedure. A case study is undertaken for a 140 kW energy storage flywheel. Model-based predictions are compared with measured data from spin-down tests and show a good level of agreement. The study confirms the role of friction-related forces in driving forward-whirl response behaviors. It also highlights the key role of housing and machine support characteristics in response behavior. This influence is shown to be complex and not open to simple physical interpretation. Therefore, the proposed analytical method is seen as a useful tool to investigate this influence while avoiding the need for time consuming numerical simulations.

Lateral-Torsional Buckling of Beams Elastically Restrained Against Warping at Supports

The study presents the results of theoretical investigations into lateral torsional buckling (LTB) of bi-symmetric I-beams, elastically restrained against warping at supports. Beam loading schemes commonly used in practice are taken into account. The whole range of stiffness of the support joints, from free warping to warping fully restrained, is considered. To determine the critical moment, the energy method is used. The function of the beam twist angle is described with power polynomials that have simple physical interpretation. Computer programs written in symbolic language for numerical analysis are developed. General approximation formulas are devised. Detailed calculations are performed for beams with end-plate joints. Critical moments determined with programs and approximation formulas are compared with the results obtained by other researchers and with those produced by FEM. Very good accuracy of results is obtained.

Gravity in six elegant steps

The kinematical description of gravity, based on the principle of equivalence, is extraordinarily beautiful. In striking contrast, the field equation [Formula: see text] is conceptually ugly, lacking in simple physical interpretation or even in common ground to describe the left- and right-hand sides. This paper shows how one can develop all of gravity in an elegant manner by recognizing that the gravitational dynamics describes the heating and cooling of spacetime.

Model-Based Analysis of Friction-Induced Sub-Synchronous Whirl for a Rotor Contacting With Clearance Bearings Under Axial Load

For rotors supported by active magnetic bearings (AMBs), clearance bearings are commonly used to provide backup support under loss of AMB functionality. Test data from real machines shows that rotor vibration during touchdown on backup bearings may involve steady forward whirling at a sub-synchronous frequency. This excitation is believed to be due to friction forces transmitted between the rotor and a bearing end-face under axial load. This paper proposes a new analytical approach to model and predict such friction-driven forward whirl behaviors. A set of constraint equations are derived that relate a circular whirl motion of arbitrary orbital speed to the frequency response functions of the rotor-housing structure. This model is coupled with an evaluation of Coulomb friction associated with slip between the rotor and the supporting end-face of a thrust bearing. The resulting equations can be used to compute a set of possible whirl motions via a root-finding procedure. A case study is undertaken for a 140 kW energy storage flywheel. Model-based predictions are compared with measured data from spin-down tests and show a good level of agreement. The study confirms the role of friction-related forces in driving forward-whirl response behaviors. It also highlights the key role of housing and machine support characteristics in response behavior. This influence is shown to be complex and not open to simple physical interpretation. Therefore, the proposed analytical method is seen as a useful tool to investigate this influence while avoiding the need for time consuming numerical simulations.