Rigid Rotation Research Articles

Modifications of SPH towards three-dimensional simulations of an icy moon with internal ocean

There are some traces of the existence of internal ocean in some icy moons, such as the vapor plumes of Europa and Enceladus. This implies a region of liquid water beneath the surface ice shell. Since liquid water would be essential for the origin of life, it is important to understand the development of these internal oceans, particularly their temperature distribution and evolution. The balance between tidal heating and radiative cooling is believed to sustain liquid water beneath an icy moon’s surface. We aim to simulate the tidal heating of an internal ocean in an icy moon using 3-dimensional numerical fluid calculations with the Smoothed Particle Hydrodynamics (SPH) method. We incorporated viscosity and thermal conduction terms into the governing equations of SPH. However, we encountered two issues while calculating rigid body rotation using SPH with a viscous term: (1) conventional viscosity formulations generated unphysical forces that hindered rotation, and (2) there was artificial internal energy partitioning within the layered structure, which was due to the standard SPH formulations. To address the first issue, we modified the viscosity formulation. For the second, we adopted Density Independent SPH (DISPH) developed in previous studies to improve behavior at discontinuous surfaces. Additionally, we implemented radiative cooling using an algorithm to define fluid surfaces via the particle method. We also introduced an equation of state accounting for phase transitions. With these modifications, we have refined the SPH method to encompass all necessary physical processes for simulating the evolution of icy moons with internal oceans.

Theoretical characteristics of a three-point Roberts linkage.

The Roberts linkage is recognized for enabling long-period pendulum motion in a compact format. Utilizing this characteristic, we are developing a three-point Roberts linkage for vibration isolation systems, with an eye toward its potential contribution to the development of next-generation interferometric gravitational wave antennas. In this article, we derived the equations to determine the essential parameters when using this linkage as a vibration isolation system, namely, the equivalent pendulum length and the relationship between translational motion of the center of mass and rigid body rotation, from size parameters. In addition, we analyzed the behavior in response to various errors.

In-situ synchrotron high energy X-ray diffraction study on the deformation mechanisms of D019-α2 phase during high-temperature compression in a TiAl alloy

The α2 phase with an ordered hexagonal structure has a strong mechanical anisotropy. The limited plasticity interacting with crystallographic texture formation undoubtedly complicate the deformation mechanisms of the α2 phase. Taking advantage of in-situ synchrotron high energy X-ray diffraction (HEXRD), this study unveils the origin of the α2 texture and its correlation with plastic deformation. Upon loading at 800 °C, the dislocation glide in the γ phase initiates at a stress of 370 MPa and that in the α2 phase at a stress of 670 MPa. Nevertheless, the texture evolution of the α2 phase sets in in parallel with that of the γ phase, and these textures are preliminarily established at a stress of 650 MPa. A main <11 2‾ 0> fiber texture with the c axis of the α2 unit cell aligned vertically to the compression axis has been unexpectedly evolved. This texture forms primarily via rigid body rotation and is correlated with glide and twin activation in the neighboring γ phase. The preferential orientation primarily favors double prismatic glide in α2 and in addition triggers the tensile twin activation. The grain rotation caused by the tensile twin slightly affects the α2 transverse texture evolution. The results unveil a complex interaction between the α2 phase deformability, texture evolution and the combined elastic-plastic deformation of the phases γ and α2 in TiAl alloys.

Understanding secondary order parameters in perovskites with tilted octahedra

In the family of perovskite materials, the tilts of BX 6 octahedra are the most common type of structural distortion. Conventionally, the formation of low-symmetry perovskite phases with tilted octahedra is analyzed by considering only primary order parameters. However, octahedral tilting also gives rise to secondary order parameters which contribute to additional atomic displacements, ordering and lattice distortions. Our study highlights the significant impact of secondary order parameters on the structural formation and emergent physical properties of perovskites. Through group-theoretical and crystallographic analyses, we have identified all secondary order parameters within Glazer-type tilt systems and clarified their physical manifestations. We explore the fundamental symmetry relationships among various structural degrees of freedom in perovskites, including tilt-induced ferroelasticity, correlations between displacements and ordering of atoms occupying different positions, and the potential for rigid unit rotations and unconventional octahedral tilts. Particular emphasis is placed on the emergence of secondary order parameters and their coupling with primary order parameters, as well as their symmetry-based hierarchy, illustrated through a modified Bärnighausen tree. We applied our theoretical insights to elucidate phase transitions in well known perovskites such as CaTiO3 and RMnO3 (where R = La and lanthanide ions), thereby demonstrating the significant influence of secondary order parameters on crystal structure formation. Our results serve as a symmetry-based guide for the design, identification and structural characterization of perovskites with tilted octahedra, and for understanding tilt-induced physical properties.

Anisotropy of object nonrigidity: High-level perceptual consequences of cortical anisotropy.

We present a surprising anisotropy in perceived object nonrigidity, a complex, higher-level perceptual phenomenon, and explain it unexpectedly by the distribution of low-level neural properties in primary visual cortex. We examined the visual interpretation of two rigidly connected rotating circular rings. At speeds where observers predominantly perceived rigid rotation of the rings rotating horizontally, observers perceived only nonrigid wobbling when the image was rotated by 90°. Additionally, vertically rotating rings appeared narrower and longer compared to their physically identical horizontally rotating counterparts. We show that these perceived shape changes can be decoded from V1 outputs by incorporating documented anisotropies in orientation selectivity. We then show that even when the shapes are matched, the increased nonrigidity persists in vertical rotations, suggesting that motion mechanisms also play a role. By incorporating cortical anisotropies into optic flow computations, we show that the kinematic gradients (Divergence, Curl, Deformation) for vertical rotations align more with physical nonrigidity, while those for horizontal rotations align closer to rigidity, indicating that cortical anisotropies contribute to the orientation dependence of the perception of nonrigidity. Our results reveal how high-level percepts are shaped by low-level anisotropies, which raises questions about their evolutionary significance, particularly regarding shape constancy and motion perception.

Implementation of the Zienkiewicz–Pande Model into a Four‐Dimensional Lattice Spring Model for Plasticity and Fracture

ABSTRACTPlasticity and fracture problems have always been hot topics in numerical methods. In this work, a universal implementation procedure for the elasto‐plastic constitutive model is developed in the four‐dimensional lattice spring model (4D‐LSM), in which the Jaumann stress rate is incorporated to exclude the influence of the rigid rotation in the particle stress, expanding the ability of 4D‐LSM to deal with large elastic deformation problems by its own to large plastic deformation problems. As an example, the Zienkiewicz–Pande (ZP) constitutive model is implemented. Several numerical examples are carried out to check the performance of the implemented model. Through a comparison with analytical solutions, available experimental data, and other numerical results, the stability of the developed plastic framework and the correctness of the stress calculation scheme are verified. Meanwhile, numerical results show that the developed code is capable of solving elasto‐plastic large deformation problems. With the advantage of 4D‐LSM in handling fracture problems, the ability of the embedded model to solve plastic fracture problems is verified with a simple maximum deformation failure criterion.

Mechanism analysis of burn-up failure for needle roller bearing at high-speed gear in manual transmission

Adequate lubrication conditions of needle roller bearings are crucial for the normal operation of transmission. Addressing the burn-up and adhesion failures of needle roller bearings during transmission bench trials, two rigid body rotation physical models were developed to analyze and model the lubrication effect on the inner and outer surfaces of needle roller bearing. Through theoretical analysis and lubrication simulation, it was found that under the critical condition of d/D=0.553, the centrifugal force F on the outer ring surface of the needle bearing was related to the density of lubricant, rotational speed, as well as the angle and size of oil hole, rather than the position of the oil holes; Moreover, the centrifugal force F on the needle roller bearing at input shaft was related to the speed of transmission gear and was also associated with the clearance size between needle roller and cage. Theoretical analysis, simulation, and experimental results have demonstrated that the lubrication performance of needle roller bearings during operation at lower rotary speed gears was inferior to that at higher speed gears, and the lubrication was also less effective when the cage clearance was narrower. Employing angled oil inlets (holes), appropriately enlarging the diameter of oil inlets (holes), and increasing the clearance width between needle roller and cage will contribute to the improvement of lubrication effect.

CFD-DEM investigation of centrifugal slurry pump with polydisperse particle feeds

Polydisperse particle feed into centrifugal slurry complicates hydraulic performance and wall erosion but is poorly understood. This paper presents a numerical study of a centrifugal slurry pump, focusing on the effect of particle size distribution (PSD) using the combined computational fluid dynamics and discrete element method (CFD-DEM). It incorporates rigid impeller rotation and wall erosion. On this basis, the hydraulic and erosion model validity is verified by clear water performance and jet erosion test, respectively. Additionally, this CFD-DEM model is compared with the dense discrete phase model (DDPM), demonstrating more precise erosion prediction as its fully resolved particle-particle interactions. Generally, total pump erosion severity intensifies when the PSD is broadened. Compartment-wise, it indicates the necessity of tailoring flow structure to enlarge drag force, therefore, mitigate particle aggregation in the impeller. This in-house CFD-DEM model is promising for addressing particle-fluid flow problems in centrifugal pumps or coupling with data driven method.

Kyanite microstructural and microchemical characteristics reveal differences in growth, deformation and chemical modification: A case study from the Paleoproterozoic suture zone of South Harris, NW Scotland

Based on petrological association, cathodoluminescence (CL), trace element signatures and orientation relationships, two generations of kyanite are distinguished in a high temperature, high pressure garnet-biotite-aluminosilicate bearing migmatite of South Harris, NW Scotland. The migmatite shows a garnet and biotite rich domain (Grt-Bt domain) which is cut at a low angle by a dominantly coarse-grained plagioclase-quartz leucosome. In addition, a fine-grained plagioclase-quartz-kyanite domain (Plag-Qtz-Ky domain) is present intercalated with the Grt-Bt domain and subparallel to the plagioclase-quartz domain. Type 1 kyanite is coarse grained and associated with Bt clusters and garnet within the Grt-Bt domain. It grew relatively early, syn- to post-garnet growth, in a suprasolidus environment resulting in crystallographically determined oscillatory CL and trace element zoning. Grains record evidence of progressive deformation in the crystal plastic regime, where deformation is accommodated by dislocation glide, climb and deformation twinning. The dominant activated slip system is (100)<001> with minor component of <100>, while deformation twins show a ∼ 180° rotation around ∼<001> axis and a twin plane near (001). Grains appear to be impervious to deformation induced diffusion with all zoning remaining sharp despite crystal plastic deformation. Grains in direct contact with the Plag-Qtz-Ky domain show late modification of the CL and trace element signature suggesting melt-mediated interface-coupled dissolution-precipitation reaction. This modification resulted in crosscutting lobate high trace element regions and irregular rims with low Cr and V content. These rims show similar CL and trace element characteristics as Type 2 kyanite which are exclusively seen within the Plag-Qtz-Ky domain suggesting that Type 2 grains are cogenetic with Type 1 rims. Type 2 grains are finer grained than Type 1 grains and show near uniform CL and trace element distributions with rare oscillatory zoned and relatively higher Cr & V bright cores. Type 2 show either no or very localized internal deformation features. However, they exhibit a clear shape preferred orientation which coincides with a crystallographic preferred orientation where the longest shape axis is parallel to <001>. We propose that Type 2 kyanite grains underwent melt-present deformation by rigid body rotation in an externally derived melt with different trace element chemistry than the host rock. This melt thus interacted chemically by melt-mediated interface-coupled dissolution-precipitation reactions with the surrounding rocks forming the Type 1 rims.Our study shows detailed analysis of kyanite is an important tool for giving constraints on the deformation, P–T and melting history of high-grade metamorphic rocks and migmatites.

Dynamic Analysis of Rigid–Flexible Structures with Piezoelectric Actuation and Control

In this paper, the dynamic equation of a rigid body coupled with two flexible beams was established, considering the rotational motion of the rigid body and the elastic deflection of the flexible beams. The coupling effect between the rigid body rotation and flexible beam vibration was studied in detail. The dynamic response of the flexible beam with piezoelectric effect was established based on Hamilton’s principle. Under the premise of ignoring the nonlinear vibration coupling term of flexible beams, only the first two modes of transverse displacement and one directional rotation motion were studied in case studies. It was found that the coupling term caused by rigid body rotation can slightly alter the natural frequency and amplitude of flexible beams, mainly reflected in the first-order mode. With increasing the external excitation on the rigid body, the induced transverse displacement at the tip of the flexible beam increased significantly. Meanwhile, when the flexible beam was under external excitation, the vibration could also induce rigid body rotation. With the inverse piezoelectric effect, one may actively actuate the flexible beam vibration and rigid body rotation or control the undesired motion of the system. The control effect can be adjusted by varying the applied voltage excitation on the piezoelectric patches as well as patch positions. The conclusions drawn from this study can be applied to active precise control of space facilities such as satellites. Based on the dynamic modeling of rigid–flexible multi-body systems, this paper completed the study of the coupling effects of rigid body rotation and flexible body vibration, and proposed an application idea for completing small-angle maneuvers of rigid–flexible multi-body systems through piezoelectric control.

Constitutive behavior of asymmetric multi-material honeycombs with bi-level variably-thickened composite architecture

Bi-level tailoring of cellular metamaterials involving a dual design space of unit cell and elementary beam level architectures has recently gained traction for the ability to achieve extreme elastic constitutive properties along with modulating multi-functional mechanical behavior in an unprecedented way. This article proposes an efficient analytical approach for the accurate evaluation of all constitutive elastic constants of asymmetric multi-material variably-thickened hexagonal lattices by considering the combined effect of bending, stretching, and shearing deformations of cell walls along with their rigid rotation. A tri-member unit cell is conceptualized, wherein all nine constitutive constants are obtained through the mechanics under one cell wall direction and subsequent repetitive coordinate transformations. We enhance the design space of lattice metamaterials substantially here by introducing multiple exploitable dimensions such as asymmetric geometry, multi-material unit cells and variably-thickened cell walls, wherein the conventional monomaterial auxetic and non-auxetic hexagonal configurations can be analyzed as special cases along with other symmetric and asymmetric lattices such as a range of rectangular and rhombic geometries. The generic analytical approach along with extensive numerical results presented in this paper opens up new avenues for efficient optimized design of the next-generation multi-functional lattices and cellular metamaterials with highly tailored effective elastic properties.

Left ventricular deformation in the presence of left ventricular 'rigid body rotation' in healthy adults-three-dimensional speckle-tracking echocardiographic insights from the MAGYAR-Healthy Study.

During the heart cycle, the left ventricle (LV) not only shows a contraction-relaxation pattern, but LV has a rotational mechanics, as well. It is a known fact that certain pathologies may be associated with an absence of LV twist, when LV basal and apical regions rotate in the same clockwise (cw) or counterclockwise (ccw) direction called LV 'rigid body rotation' (LV-RBR), but it can also occur in healthy subjects. The present cohort study aimed to examine LV strains in healthy subjects with LV-RBR versus with normally directed LV rotational mechanics by three-dimensional speckle-tracking echocardiography (3DSTE). The study consisted of 181 healthy individuals, from which 171 cases had normally directed LV rotational mechanics (mean age: 32.5±12.3 years, 79 males) and 10 healthy subject showed LV-RBR (mean age: 35.4±11.3 years, 3 males). Complete two-dimensional (2D) Doppler echocardiography and 3DSTE were performed in all healthy individuals. None of routine 2D Doppler echocardiographic parameters showed differences between the groups examined. There were no subjects with ≥ grade 1 regurgitation on any valves or with significant stenosis on any valves. 3DSTE-derived LV volumes, global and mean segmental strains did not differ between the groups examined. Apical anterior and lateral segments showed reduced segmental LV circumferential strain (CS) (-18.9%±8.5% vs. -26.7%±10.7%, P=0.02; -27.3%±12.6% vs. -34.8%±13.2%, P=0.08, respectively) and LV area strain (AS) (-26.8%±9.8% vs -36.8%±12.0%, P=0.01; -35.7%±13.2% vs. -45.0%±14.6%) in healthy subjects having LV-RBR as compared to cases with normally directed LV rotational mechanics. These abnormalities were present only in subjects having cwLV-RBR. Although global LV deformation is normal in the presence of LV-RBR in healthy adults, reduction of apical anterior and lateral LV-CS (and LV-AS) are present in cases with cwLV-RBR only suggesting segmental deformation abnormalities.

A partially debonded rigid elliptical inclusion with a liquid slit inclusion occupying the debonded portion

We derive a closed-form solution to the plane strain problem of a partially debonded rigid elliptical inclusion in which the debonded portion is filled with a liquid slit inclusion when the infinite isotropic elastic matrix is subjected to uniform remote in-plane stresses. The original boundary value problem is reduced to a Riemann–Hilbert problem with discontinuous coefficients, and its analytical solution is derived. By imposing the incompressibility condition of the liquid slit inclusion and balance of moment on a circular disk of infinite radius, we obtain a set of two coupled linear algebraic equations for the two unknowns characterizing the internal uniform hydrostatic tension within the liquid slit inclusion and the rigid body rotation of the rigid elliptical inclusion. As a result, these two unknowns can be uniquely determined revealing the elastic field in the matrix.

Utilizing Euler poles for the evaluation of plate rigidity in numerical mantle convection models

SUMMARY Evidence that the Earth’s surface is divided into a tessellation of piece-wise rigidly translating plates is the primary observation supporting the solid-state creep-enabled convection paradigm, utilized to investigate evolution of the Earth’s mantle. Accordingly, identifying the system properties that allow for obtaining dynamically generated plates remains a primary objective in numerical global mantle convection simulations. The first challenge for analysing fluid dynamic model output for the generation of rigid plates is to identify candidate plate boundaries. Here, we utilize a previously introduced numerical tool for plate boundary detection which uses a user specified threshold (tolerance) to automatically detect candidate plate boundaries. The numerical tool is applied with different sensitivities, to investigate the nature of the surface velocity fields generated in three calculations described in earlier work. The cases examined differ by the values that they specify for the model yield stress, a parameter that can allow the formation of tightly focussed bands of surface deformation. The three calculations we examine include zones comprising possible plate boundaries that are characterized by convergence, divergence and strike-slip behaviour. Importance of the potential plate boundaries is assessed by examining the rigidity of the inferred model generated plates. The rigidity is measured by comparing the model velocities to the rigid rotation velocities implied by the statistically determined Euler poles for each candidate plate. We quantify a lack in rigidity by calculating a deformity field based on disagreement of actual surface velocity with rotation about the Euler pole. For intermediate yield stress and boundary detection threshold value, we find that the majority of the model surface can translate almost rigidly about distinct plate Euler poles. Regions that conform poorly to large-scale region rigid translation are also obtained but we find that generally these regions can be decomposed into subsets of smaller plates with a lower tolerance value. Alternatively, these regions may represent diffuse boundary zones. To clarify the degree to which the mantle convection model behaviour shows analogues with Earth’s current-day surface motion, we apply the plate boundary detection and Euler pole calculation methods to previously published terrestrial strain-rate data. Strong parallels are found in the response of the terrestrial data and mantle convection calculations to the threshold value, such that appropriate choice of that parameter results in very good agreement between observations and convection model character. We conclude that plates generated by fluid dynamic convection models can exhibit motion that is markedly rigid, and define statistics (plateness) and fields (deformity) by which the generation of self-consistently determined plate rigidity can be quantified, as well as describing how plate recognition might be optimized. We also note that in agreement with the Earth’s current state, we obtain a dozen dominant plates in the case exhibiting the most plate-like (rigid) surface, suggesting that this approximate number of plates is perhaps intrinsic to the geometry, surface area and physical properties of Earth’s mantle.

A New Coding System for the Identification of Left Ventricular Rotation Patterns and Their Relevance to Myocardial Function

Rotational mechanics is a fundamental determinant of left ventricular ejection fraction (LVEF). The coding system currently employed in clinical practice does not distinguish between rotational patterns. We propose an alternative coding system that makes possible to identify the rotational pattern of the LV and relate it to myocardial function. Echocardiographic images were used to generate speckle tracking-derived transmural global longitudinal strain (tGLS) and rotational parameters. The existence of twist (basal and apical rotations in opposite directions) is expressed as a rotational gradient with a positive value that is the sum of the basal and apical rotation angles. Conversely, when there is rigid rotation (basal and apical rotations in the same direction) the resulting gradient is assigned a negative value that is the subtraction between the two rotation angles. The rotational patterns were evaluated in 87 healthy subjects and 248 patients with LV hypertrophy (LVH) and contrasted with their myocardial function. Our approach allowed us to distinguish between the different rotational patterns. Twist pattern was present in healthy controls and 104 patients with LVH and normal myocardial function (tGLS ≥ 17%, both). Among 144 patients with LVH and myocardial dysfunction (tGLS < 17%), twist was detected in 83.3% and rigid rotation in 16.7%. LVEF was < 50% in 34.7%, and all patients with rigid rotation had a LVEF < 50%. The gradient rotational values showed a close relationship with LVEF (r = 0.73; p < 0.001). The proposed coding system allows us to identify the rotational patterns of the LV and to relate their values with LVEF.

Does the quasi-static polarizability have principal axes?

Beyond strict statics, the dipole polarizability tensor is a complex symmetric matrix. Such matrices may not be diagonalizable by an orthogonal similarity transformation (a rigid rotation of the reference frame). In this paper, we provide examples of polarizability tensors that have no real principal axes and discuss the conditions under which this counter-intuitive phenomenon can occur.

Left Ventricular Twist and the "Rigid Body Rotation" Pattern in Patients Treated with Anthracyclines or Anti-HER2.

Background: During the physiological cardiac cycle, the helix orientation of the muscle fibres induces the rotation of the apex relative to the base of the left ventricular (LV). In heart failure, LV torsion is impaired, and rotation at basal and apical levels occurs in the same direction, a phenomenon called rigid body rotation (RBR). We aimed to evaluate whether the RBR pattern and GLS together could improve the diagnosis of cardiotoxicity in patients treated with anthracyclines and/or anti-HER2. Methods: With an observational, retrospective study involving 175 patients (mean age 55 ± 12 years, 94% females), we evaluated the development of cancer therapeutic-related cardiac dysfunction (CTRCD) defined according to ESC guidelines. We characterised LV dysfunction by echocardiographic standard and speckle-tracking (GLS and RBR pattern) measurements. Patients with a previous diagnosis of structural heart disease or atrial fibrillation were excluded. Results: At the time of enrolment, the chemotherapy regimen included trastuzumab (96%), pertuzumab (21%), and anthracyclines (13%). Twenty-two patients (12.5%) developed cardiotoxicity, and thirteen patients developed an RBR within 6 months of follow-up. In all cases, the RBR pattern was associated with cardiotoxicity (p < 0.001), reporting an optimal specificity but poor sensitivity at three and six months. However, the addition of the RBR pattern to the global longitudinal strain (GLS) ≥ -16% increased the odds ratio (OR) from 25.6 to 32.6 at three months and from 32.5 to 49.6 at six months rather than GLS alone. Conclusions: The RBR pattern improves the diagnostic accuracy of GLS for the detection of cardiotoxicity secondary to anthracyclines and anti-HER2-based treatments.

Investigation of flow-induced sound source generation in a centrifugal pump

Abstract This study investigates the mechanism of sound source generation in a centrifugal pump under different flow conditions. The calculated results are in good agreement with experimental data by employing the delayed detached eddy simulation and flow-acoustic coupling method to compute the flow-induced noise. Based on the vortex sound theory and vorticity binary decomposition, the sound source (STA) is divided into a shear-induced source (STS) and a rigid rotation-induced source (STR). The results show that the sound source induced by shear is the main factor. The fluctuation amplitude of STS can be nine times larger than STR at monitor point near the tongue under the design flow rate condition. There is a mutual cancellation effect between the STS and STR. The fluctuation amplitude of STA at the blade passing frequency is 86% of STS at monitor point near the tongue under high flow rate conditions, indicating that sometimes rigid rotation can suppress noise generation.

In-cylinder flow evolution in the horizontal plane of a motoring compression ignition engine

This study used the two-dimensional particle image velocimetry technique to quantify the in-cylinder horizontal plane velocity field evolution in a swirl-supported light-duty single-cylinder diesel engine. The data were acquired at a constant engine speed of 1600 revolutions per minute. For each case, the distance of the laser sheet from the fire deck was varied (z = 5, 10, and 20 mm) to investigate the axial variations in the flow field during the flow evolution in the compression stroke. A vortex identification algorithm was used to detect the swirl center and its deviation from the rigid body rotation. A Bessel fit was obtained using the experimental data. The result revealed that the in-cylinder flow was not axisymmetric. The swirl center approached the geometrical center as the piston approached the top dead center. The flow evolved at the farthest plane from the fire deck. The axial diffusion of angular momentum resulted in the formation of the swirl flow structure in the plane closer to the fire deck. Angular momentum analysis of a simplified geometry has been presented to explain the swirl amplification. The estimated results were compared with the experimental results to show the momentum stratification in the engine cylinder later in the compression stroke.

Thermodynamic functions of germane isotopologues AGeH4 (A = 70, 72, 73, 74, 76) calculated from high-resolution IR spectra

Standard thermodynamic functions of germane isotopologues 70GeH4, 72GeH4, 73GeH4, 74GeH4, and 76GeH4 are calculated in “harmonic oscillator – rigid rotator” and “anharmonic oscillator – oscillating non-rigid rotator” approximations and by the direct summation of the experimental energy values. To found the values of thermodynamic functions in the 200–700 K temperature range, approximation coefficients are determined by regression analysis. The isotope effect influence on the values of the standard isobaric heat capacity, entropy, enthalpy of heating, and the reduced isobaric-isothermal potential of germane is established. Limiting requirements for the accuracy of determining the spectral parameters for detecting the influence of the isotope effect on the thermodynamic functions and interatomic distances in the germane molecule are formulated.