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The Rankine-Kirchhoff approximations for moist thermodynamics
The Rankine-Kirchhoff equation for the saturation vapor pressure has been derived independently many times, sometimes with the presumption of novelty. As a result, the equation is referred to in the literature by a bewildering number of different names and, often, by no name at all. In this work, the history of the Rankine-Kirchhoff equation is reviewed. The three approximations used to derive it (ideal gas, constant heat capacities, and zero-volume condensates) can be used to derive a whole system of accurate and analytic expressions of relevance to the atmosphere. Consequently, it is proposed that this set of approximations be elevated to a named entity, e.g., the Rankine-Kirchhoff approximations.
Isogeometric Bézier dual mortaring: The Kirchhoff–Love shell problem
Here in this paper we develop an isogeometric Bézier dual mortar method for coupling multi-patch Kirchhoff–Love shell structures. The proposed approach weakly enforces the continuity of the solution at patch interfaces through a dual mortar method and can be applied to both conforming and non-conforming discretizations. As the employed dual basis functions have local supports and satisfy the biorthogonality property, the resulting stiffness matrix is sparse. In addition, the coupling accuracy is optimal because the dual basis possesses the polynomial reproduction property. We also formulate the continuity constraints through the Rodrigues’ rotation operator which gives a unified framework for coupling patches that are intersected with G 1 continuity as well as patches that meet at a kink. Several linear and nonlinear examples demonstrated the performance and robustness of the proposed coupling techniques.
Violating Kirchhoff’s Law of Thermal Radiation in Semitransparent Structures
Kirchhoff’s law of thermal radiation imposes a constraint on photon-based energy harvesting processes since part of the incident energy flux is inevitably emitted back to the source. By breaking the reciprocity of the system, it is possible to overcome this restriction and improve the efficiency of energy harvesting. Here, we design and analyze a semitransparent emitter that fully absorbs normally incident energy from a given direction with zero backward and unity forward emissivity. The nearly ideal performance with wavelength-scale thickness is achieved due to the magneto-optical effect and the guided-mode resonance engineered in the emitter structure. We derive the general requirements for the nonreciprocal emitter using the temporal coupled mode theory and the symmetry considerations. As a result, we provide a realistic emitter design based on a photonic crystal slab consisting of a magnetic Weyl semimetal and silicon.
New Absolute Cavity Pyrgeometer equation by application of Kirchhoff's law and adding a convection term
An equation for the Absolute Cavity Pyrgeometer (ACP) is derived from application of Kirchhoff's law and the addition of a convection term to account for the thermopile being open to the environment, unlike a domed radiometer. The equation is then used to investigate four methods to characterise key instrumental parameters using laboratory and field measurements. The first uses solar irradiance to estimate the thermopile responsivity, the second uses a minimisation method that solves for the thermopile responsivity and transmission of the cavity, and the third and fourth revisit the Reda et al. (2012) linear least squares calibration technique. Data were collected between January and November 2020, when the ACP96 and two IRIS radiometers monitoring terrestrial irradiances were available. The results indicate good agreement with IRIS irradiances using the new equation. The analysis also indicates that while the thermopile responsivity, concentrator transmission and emissivity of an ACP can be determined independently, as an open instrument, the impact of the convection term is minor in steady-state conditions but significant when the base of the instrument is being subjected to rapid artificial cooling or heating. Using laboratory characterisation of the transmission and emissivity, together with use of an estimated solar calibration of the thermopile, generated mean differences of less than 1.5 Wm -2 to the two IRIS radiometers. A minimisation method using each IRIS radiometer as the reference also provided similar results, and the derived thermopile responsivity was within 0.3 µV W -1 m 2 of the solar-calibration-derived infrared responsivity estimate of 10.5 µV W -1 m 2 estimated using a nominal solar calibration and provide irradiances within ±2 % of the terrestrial irradiance measured by the reference pyrgeometers traceable to the International System of Units (SI). The calibration method using linear least squares regression introduced by Reda et al. (2012) that relies on rapid cooling of the ACP base but utilising the new equation was found to produce consistent results but was dependent on the assumed temperature of the air above the thermopile. This study demonstrates the potential of the ACP as another independent reference radiometer for terrestrial irradiance once the magnitude of the convection coefficient and any potential variations in it have been resolved.
Accurate expressions for the dew point and frost point derived from the Rankine-Kirchhoff approximations
Accurate, explicit, and analytic expressions are derived for the dew point and frost point as functions of temperature and relative humidity. These are derived theoretically in terms of physical constants using the Rankine-Kirchhoff approximations, which assume an ideal gas, fixed heat capacities, and zero specific volume of condensates. Compared to modern laboratory measurements, the expressions are accurate to within a few hundredths of a degree over the full range of Earth-relevant temperatures, from 180 to 273 K for the frost point and 230 to 330 K for the dew point.
An updated Lagrangian framework for Isogeometric Kirchhoff–Love thin-shell analysis
Not Available
Evolution of Robustness in Growing Random Networks
Networks are widely used to model the interaction between individual dynamic systems. In many instances, the total number of units and interaction coupling are not fixed in time, and instead constantly evolve. In networks, this means that the number of nodes and edges both change over time. Various properties of coupled dynamic systems, such as their robustness against noise, essentially depend on the structure of the interaction network. Therefore, it is of considerable interest to predict how these properties are affected when the network grows as well as their relationship to the growth mechanism. Here, we focus on the time evolution of a network’s Kirchhoff index. We derive closed-form expressions for its variation in various scenarios, including the addition of both edges and nodes. For the latter case, we investigate the evolution where single nodes with one or two edges connecting to existing nodes are added recursively to a network. In both cases, we derive the relations between the properties of the nodes to which the new node connects along with the global evolution of network robustness. In particular, we show how different scalings of the Kirchhoff index can be obtained as a function of the number of nodes. We illustrate and confirm this theory via numerical simulations of randomly growing networks.
Current divisions and distributed Joule heating of two-dimensional grid microstructures
This work presents current divisions and distributed Joule heating of two-dimensional (2D) grid microstructures. The current divisions on 2×2, 4×4, and n×n grid microstructures made of the same conductive beams are analyzed theoretically, and Kirchhoff's voltage law (KVL) and Kirchhoff's current law (KCL) are employed to determine the current division factors and directions under different voltage input cases. The equivalent resistances and Joule heating power are therefore derived. 2D 2×2 grid microstructures made of gold (60 nm in thickness) and those made of near-equiatomic NiTi (850 nm in thickness) for various independent voltage input cases are fabricated by electron-beam evaporation and co-sputtering, respectively. The equivalent resistances of these grid microstructures are measured by four-terminal resistance measurement at ambient conditions, which show a good agreement with the theoretical results. Further investigation on the electrical resistivities of evaporated gold layer (4.85 × 10 -8 Ω ∙ m) and co-sputtered NiTi (1.23 × 10 -5 Ω ∙ m) reveals that the influences of scale effect and fabrication process on the resistivity cannot be neglected. As such, it is found to be necessary to consider the materials' resistivity in the fabricated grid microstructures before their electro-thermal analysis.
An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS
Here, we present an adaptive space-time phase field formulation for dynamic fracture of brittle shells. Their deformation is characterized by the Kirchhoff–Love thin shell theory using a curvilinear surface description. All kinematical objects are defined on the shell’s mid-plane. The evolution equation for the phase field is determined by the minimization of an energy functional based on Griffith’s theory of brittle fracture. Membrane and bending contributions to the fracture process are modeled separately and a thickness integration is established for the latter. The coupled system consists of two nonlinear fourth-order PDEs and all quantities are defined on an evolving two-dimensional manifold. Since the weak form requires C 1 -continuity, isogeometric shape functions are used. The mesh is adaptively refined based on the phase field using Locally Refinable (LR) NURBS. Time is discretized based on a generalized-α method using adaptive time-stepping, and the discretized coupled system is solved with a monolithic Newton–Raphson scheme. Finally, the interaction between surface deformation and crack evolution is demonstrated by several numerical examples showing dynamic crack propagation and branching.
Galerkin formulations of isogeometric shell analysis: Alleviating locking with Greville quadratures and higher-order elements
Here we propose new quadrature schemes that asymptotically require only four in-plane points for Reissner–Mindlin shell elements and nine in-plane points for Kirchhoff–Love shell elements in B-spline and NURBS-based isogeometric shell analysis, independent of the polynomial degree p of the elements. The quadrature points are Greville abscissae associated with pth-order B-spline basis functions whose continuities depend on the specific Galerkin formulations, and the quadrature weights are calculated by solving a linear moment fitting problem in each parametric direction. The proposed shell element formulations are shown through numerical studies to be rank sufficient and to be free of spurious modes. The studies reveal comparable accuracy, in terms of both displacement and stress, compared with fully integrated spline-based shell elements, while at the same time reducing storage and computational cost associated with forming element stiffness and mass matrices and force vectors. The high accuracy with low computational cost makes the proposed quadratures along with higher-order spline bases, in particular polynomial orders, p = 5 and 6, good choices for alleviating membrane and shear locking in shells.
Three-dimensional continuum point cloud method for large deformation and its verification
This study presents a strong form based meshfree collocation method, which is named Continuum Point Cloud Method, to solve nonlinear field equations derived from classical mechanics for deformed bodies in three-dimensional Euclidean space. The method and its implementation are benchmarked against a nonlinear vector field using manufactured solutions. The analysis of mechanical fields firstly focuses on the study of St. Venant Kirchhoff and compressible neo-Hookean materials. Results for various initial boundary value problems are presented, including benchmark cases involving unidirectional tension and simple shear. Subsequently, the study concludes with an analysis of a displacement-controlled simulation of a compressible neo-Hookean material, specifically a bar that is pulled to 50% of its original length and rotated 90°. The pure tension case yields a 1.5% error in displacement between computed and expected values and a combined tension and torsion loading case provides further insight into material behavior under complex loading conditions. The resulting normal axial and transverse stress-strain curves are also presented. Lastly, the consistency and robustness of the proposed nonlinear numerical schemes are successfully demonstrated through various numerical experiments.
Surface Energy Modulated Self‐Assembly of Percolative Gallium Nanodroplet Films for Stretchable Electronics
Advancements in soft robotics and wearable technologies have led to an increased need for flexible and stretchable electronic systems. Liquid metals like Gallium (Ga) and its alloys offer high potential in the field of stretchable electronics and photonics due to their inherent high conductivity and malleability. However, their high surface tension and native oxide formation hinder uniform wetting and continuous film formation to get conducting films. Here, we report a fabrication strategy to realize electrically conductive Ga thin films with effective thicknesses around 100 nm on polymeric and elastomeric substrates. By enhancing the surface energy of the elastomer, we create uniform Ga nanodroplets capable of sustaining stretchability up to 200% strain. Our devices exhibit electronic conduction primarily through tunneling and display strain tunable piezoresistive characteristics, which are explained using Kirchhoff's resistive network and Simmon's analytical tunneling current model. To showcase the device's capability in fields of stretchable electronics, we demonstrate several functional prototypes, including flexible devices integrated with Light Emitting Diodes (LEDs), curvature and pressure sensors, and soft robotic grippers capable of sensing object curvature. The demonstrated devices highlight the potential of this approach for scalable integration of stretchable electronics in soft robotic and wearable platforms.
Microbial community diversity changes during voltage reversal repair in a 12-unit microbial fuel cell
Microbial fuel cell stacks (MFC-Stack) are often confronted with voltage reversals, likely due to an interplay between microbial community dynamics and insufficient electric circuit balancing. Herein, we provide new insight into voltage reversals by examining the microbiomes of twelve MFC units of a 12-liter Pilot-MFC-Stack during repair. Different biofilm repair methods (self-healing, electrostimulation, and re-acclimatization upon cross-inoculation) were used to evaluate the microbial community response. In addition, MFC-Stack simulation was performed based on Kirchhoff’s Second Law to predict values for source potentials and post-evaluate internal resistances. Analysis of the 16S rRNA amplicon sequencing data suggests that the biofilm repair methods could slowly heal damaged biofilms. Notably, severely voltage reversed MFC units had low electrogen relative abundances (18%) and positive anode potentials, while strong bioanodes and contained more than 50% electrogens and had negative anode potentials. Between-community analyses (beta diversity ordination and multinomial regression) of the voltage reversed MFC units revealed differences among biofilms in contrast to healthy/strong MFC units. Permutational multivariate analysis of variance (PERMANOVA) confirmed that reversed biofilms were, indeed, significantly (p < 0.05) different from stronger ones. Overall, these analyses demonstrated the utility of combining electrotechnical and microbial community analyses, especially beta diversity ordination and multinomial regression, to understand problematic MFC units and the potential success of a biofilm repair method. Finally, thicker biofilms were usually healthier and stronger, although thickness was no guarantee for proper structure and power function as all factors were interdependent. There was an evolutionary trend that strong anodes became stronger/healthier and others weaker. This spontaneous trend has to be considered to avoid irreversible voltage reversals and to repair electrogenic biofilms in an MFC-Stack.
CU-BENs: A structural modeling finite element library
The present work discusses capabilities within the finite element library CU-BENs. CU-BENs focuses on applying the finite element method to structural mechanics problems encountered within the context of inverse problems and partitioned fluid–structure interaction; thus element formulations are primarily of a structural type — truss, frame, and triangular discrete Kirchhoff theory shells. CU-BENs defaults to the skyline sparse storage scheme for the system matrix, but also supports other storage schemes when using external libraries such as LAPACK and UMFPACK. CU-BENs includes built-in nonlinear solution strategies, such as the Newton Raphson method and modified spherical arc length method, that are available within static analyses as well within the context of transient dynamic analyses involving a generalized-α implementation of the Newmark implicit time integration scheme.
Internal Structure of the Central Garlock Fault Zone From Ridgecrest Aftershocks Recorded by Dense Linear Seismic Arrays
Abstract We provide high‐resolution seismic imaging of the central Garlock fault using data recorded by two dense seismic arrays that cross the Ridgecrest rupture zone (B4) and the Garlock fault (A5). Analyses of fault zone head waves and P ‐wave delay times at array A5 show that the Garlock fault is a sharp bimaterial interface with P waves traveling ∼5% faster in the northern crustal block. The across‐fault velocity contrast agrees with regional tomography models and generates clear P ‐wave reflections in waveforms recorded by array B4. Kirchhoff migration of the reflected waves indicates a near‐vertical fault between 2 and 6 km depth. The P ‐wave delay times imply a ∼300‐m‐wide transition zone near the Garlock fault surface trace beneath array A5, offset to the side with faster velocities. The results provide important constraints for derivations of earthquake properties, simulations of ruptures and ground motion, and future imaging studies associated with the Garlock fault.
Broadband nonreciprocal thermal emissivity and absorptivity
A body that violates Kirchhoff’s law of thermal radiation exhibits an inequality in its spectral directional absorptivity and emissivity. Achieving such an inequality is of fundamental interest as well as a prerequisite for achieving thermodynamic limits in photonic energy conversion and radiative cooling. Thus far, inequalities in the spectral directional emissivity and absorptivity have been limited to narrow spectral resonances, or wavelengths well beyond the infrared regime4. Bridging the gap from basic demonstrations to practical applications requires control over a broad spectral range of the unequal spectral directional absorptivity and emissivity. In this work, we demonstrate broadband nonreciprocal thermal emissivity and absorptivity by measuring the thermal emissivity and absorptivity of gradient epsilon-near-zero InAs layers of subwavelength thicknesses (50 nm and 150 nm) with an external magnetic field. The effect occurs in a spectral range (12.5–16 μm) that overlaps with the infrared transparency window and is observed at moderate (1 T) magnetic fields.
Temperature-independent thermal radiation
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