We analyse a method for the construction of the potential-energy function from the moments of the ground-state density. The sum rule on which some expressions are based appear to be wrong, as well as the moments and potential-energy functions derived for some illustrative examples.
Severe thunderstorms accompanied by squalls are the most hazardous weather phenomena during pre-monsoon season in north-eastern region of India. An attempt has been made in this paper to study some parameters for forecasting thundersqualls over Calcutta (Airport) during pre-monsoon season. Parameterisation of thermodynamic components alongwith the synoptic support during thundersqualls over Calcutta has been discussed here. A forecasting aspect for propagation speed of thunderstorm cell at Calcutta in pre-monsoon season has been examined with respect to radar-echo positions, mid-level winds and convective available potential energy (CAPE). Occurrences of multiple thundersqualls over Calcutta Airport within a few hours’ interval have been discussed and examined through hodograph analysis, radar observations and synoptic situations.
A method of testing the significance of Z- Statistic is introduced in this paper to discern the role of Convective Available Potential Energy (CAPE) and Convective Inhibition Energy (CINE) in forecasting the occurrence of pre-monsoon thunderstorms over Gangetic West Bengal (GWB). The result reveals that a negative correlation exists between CAPE and CINE. It further indicates that a range for the lower values of CINE can be fixed where the frequency of occurrence of such storms will be maximum, but such range, either for lower or for higher values of CAPE, is not possible. The paper, thus, ends with a very interesting finding that a measure of CINE is the only relevant parameter whereas CAPE has no significant role in forecasting the occurrence of pre-monsoon thunderstorms over GWB, which is in contrast to the concept of severe thunderstorms of Great Plains of America.
Atmospheric disturbances caused by seismic activity are a complex phenomenon. The Lithosphere–Atmosphere–Ionosphere Coupling (LAIC) (LAIC) mechanism gives a detailed idea to understand these processes to study the possible impacts of a forthcoming earthquake. The atmospheric gravity wave (AGW) is one of the most accurate parameters for explaining such LAIC process, where seismogenic disturbances can be explained in terms of atmospheric waves caused by temperature changes. The key goal of this work is to study the perturbation in the potential energy associated with stratospheric AGW prior to many large earthquakes. We select seven large earthquakes having Richter scale magnitudes greater than seven (
) in Japan (Tohoku and Kumamoto), Mexico (Chiapas), Nepal, and the Indian Ocean region, to study the intensification of AGW using the atmospheric temperature profile as recorded from the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) satellite. We observe a significant enhancement in the potential energy of the AGW ranging from 2 to 22 days prior to different earthquakes. We examine the conditions of geomagnetic disturbances, typhoons, and thunderstorms during our study and eliminate the possible contamination due to these events.
Solids with dimpled potential-energy surfaces are ubiquitous in nature and, typically, exhibit structural (elastic or phonon) instabilities. Dimpled potentials are not harmonic; thus, the conventional quasiharmonic approximation at finite temperatures fails to describe anharmonic vibrations in such solids. At sufficiently high temperatures, their crystal structure is stabilized by entropy; in this phase, a diffraction pattern of a periodic crystal is combined with vibrational properties of a phonon glass. As temperature is lowered, the solid undergoes a symmetry-breaking transition and transforms into a lower-symmetry phase with lower lattice entropy. Here, we identify specific features in the potential-energy surface that lead to such polymorphic behavior; we establish reliable estimates for the relative energies and temperatures associated with the anharmonic vibrations and the solid–solid symmetry-breaking phase transitions. We show that computational phonon methods can be applied to address anharmonic vibrations in a polymorphic solid at fixed temperature. To illustrate the ubiquity of this class of materials, we present a range of examples (elemental metals, a shape-memory alloy, and a layered charge-density-wave system); we show that our theoretical predictions compare well with known experimental data.
We show that Gaussian process regression (GPR) allows representing multivariate functions with low-dimensional terms via kernel design. When using a kernel built with HDMR (High-dimensional model representation), one obtains a similar type of representation as the previously proposed HDMR-GPR scheme while being faster and simpler to use. We tested the approach on cases where highly accurate machine learning is required from sparse data by fitting potential energy surfaces and kinetic energy densities.