General Solution Research Articles

Relational Programming with Foundational Models

Foundation models have vast potential to enable diverse AI applications. The powerful yet incomplete nature of these models has spurred a wide range of mechanisms to augment them with capabilities such as in-context learning, information retrieval, and code interpreting. We propose Vieira, a declarative framework that unifies these mechanisms in a general solution for programming with foundation models. Vieira follows a probabilistic relational paradigm and treats foundation models as stateless functions with relational inputs and outputs. It supports neuro-symbolic applications by enabling the seamless combination of such models with logic programs, as well as complex, multi-modal applications by streamlining the composition of diverse sub-models. We implement Vieira by extending the Scallop compiler with a foreign interface that supports foundation models as plugins. We implement plugins for 12 foundation models including GPT, CLIP, and SAM. We evaluate Vieira on 9 challenging tasks that span language, vision, and structured and vector databases. Our evaluation shows that programs in Vieira are concise, can incorporate modern foundation models, and have comparable or better accuracy than competitive baselines.

Dynamic stiffness formulations for exact modal and dynamic response analysis of three-dimensional acoustic cavities in cylindrical coordinates

Exact dynamic stiffness (DS) models for three-dimensional (3D) cavities in cylindrical coordinates under any classical acoustic boundary conditions (BCs) are proposed in this paper. The paper first derives the exact general solutions that satisfy the governing differential equations. Then, these general solutions are used to develop the DS matrices for 3D cavities in cylindrical coordinates by substituting them into the acoustic pressure and normal velocity BCs. Subsequently, the Wittrick–Williams algorithm, along with the analytical expressions of the j0 count for various shaped cavities, is applied to compute natural frequencies. Finally, reliable and efficient techniques for dynamic response solution are employed. The DSM provides benchmark solutions for various 3D cavities. The convergence, universality, and efficiency of the proposed method in modal and response analysis are illustrated by comparing the results obtained using the DSM and FEM. The calculation time when using the DSM is only 0.1% of that when using the commercial finite element method, while maintaining the same accuracy. This research not only provides an effective technique for analyzing the cylindrical acoustic pressure field in engineering, but also establishes a foundation for the analysis of structural–acoustic coupling in tubular structures.

Blockchain-based efficient verifiable outsourced attribute-based encryption in cloud

Attribute-based encryption (ABE) has been widely applied in cloud services for access control. However, a large number of pairing operations required for decryption affect the wide use of ABE on lightweight devices. A general solution is to outsource the heavy computation to the cloud service provider (CSP), leaving the lighter computation to the data user. Nevertheless, it is impractical to assume that the CSP will provide free services. A recent ABE scheme with payable outsourced decryption ABEPOD (TIFS’20) provides a solution for the above payment issue. The CSP is generally untrusted, however, ABEPOD does not offer a verification mechanism for the data user to verify the correctness of the message. Moreover, the use of dual key pairs in ABEPOD incurs a significant computational overhead for data users during the key generation phase. We address the above issues by presenting a new blockchain-based verifiable outsourced attribute-based encryption system that enables data users to verify the correctness of plaintexts. We implement batch verification using homomorphic technical to optimize the verification process. We use the technique of dichotomous search to accurately locate problematic plaintexts. Additionally, we optimize three key-generation algorithms to transfer the computational cost from the data user to the key generation center. We offer the formal security models and the instantiation system with security analysis. As compared to ABEPOD, we further optimize the key-generation algorithms such that the computational overhead of transformation-key and verification-key generation for data users is reduced from O(Ω) to O(1) and reduced by half respectively, where Ω is the number of attributes.

Role of Explicit Solvation in Computational Modeling of Chemical Reactions: Mechanism of Cu(I) Transfer Between Thiolate-Based Chelators in Water.

Solvation plays important roles in controlling the thermodynamic and kinetic aspects of chemical reactions. The conventional approaches to treat solvation via electronic structure methods are likely to become inadequate, when the reacting solutes have strong electrostatic and hydrogen bonding interactions with the solvent and undergo significant structural changes during the course of the reaction. In this article, we present evidence of such solvent and structural effects in the computational study of the Cu(I) transfer reaction between thiolate-based chelators dithiobutylamine (DTBA) and dithiotheritol (DTT) in water, inspired from biological copper trafficking phenomena. We propose a general solution to the problem by combining classical molecular dynamics (MD) simulations of the bulk system and static quantum chemistry calculations. The fluctuating solvation shell was estimated from MD, and energetics was assessed by averaging QM energies of a series of molecular clusters constructed from the MD snapshots. Applying this approach, we propose a reaction pathway with estimates of relative intermediate stabilities and barriers, which suggest the overall reaction to be reversible in nature and likely to go through both two and three coordinated intermediates, confirming previous studies of similar protein analogues. An interesting fact that emerged from our study was the strong indication that the rate-determining step is the deprotonation of initial thiol bound Cu(I) complex, without involving any Cu(I)-S bonds. The proposed method will lead to a better treatment of solvations, and these mechanistic insights will aid our understanding of biological copper(I) trafficking.

Analytical determination of the dynamic response of layered saturated frozen foundation to moving loads under plane strain conditions

Based on the theory of solid porous media with pores, a calculation model of two-dimensional layered saturated frozen soil foundation is established. The study focuses on the dynamic response of layered saturated frozen soil medium placed on an impermeable rigid bedrock when subjected to a uniform surface moving strip load in motion. Firstly, the governing equation of saturated frozen soil is established. Then, the Helmholtz vector decomposition theorem, coordinate transformation, and Fourier integral transformation are used to decouple the governing equation of saturated frozen soil, and the general solution of the potential function is obtained, and the general solution of the stress and displacement of each layer of saturated frozen soil is derived. Using the transfer and reflection matrix (TRM) method, the semi-analytical solution of layered saturated frozen soil medium in the frequency domain is derived. Finally, the dynamic response of each phase of the saturated frozen soil in the time domain is obtained by the fast Fourier transform. After verifying the accuracy of the solution by comparing the model degradation with the existing literature, the effects of soil shear modulus, load moving speed, temperature, porosity, contact parameter, and frequency on the dynamic response of homogeneous foundation, soft interlayer foundation, and hard interlayer foundation are analyzed in detail. The results show that the stratification of the foundation is of great significance for accurately evaluating the dynamic response of saturated frozen soil.

Existence and uniqueness of the motion of a particle subject to a unilateral constraint and friction

We prove that there exists a unique solution to the initial value problem describing the motion of a particle subject to a unilateral constraint and Coulomb friction, if the external force acting on the particle is an analytic function of time and of the particle’s position and velocity. Previous work claimed that this problem has a local series solution that corresponds to an analytic function, after any impacts have been resolved. However, a counterexample to that claim was recently discovered, involving a particle starting to slide, in which the series solution is divergent, and thus does not correspond to an analytic function. This paper corrects previous arguments by considering a general formal series solution for a particle that is starting to slide.

Stress intensity factors and full-field stresses for a hypocycloid-type crack within a thermo-elastic material

This study focuses on the failure analysis of a hypocycloid-type crack within a thermo-elastic material. Employing the conformal mapping method, analytical continuation theorem, and principle of superposition, the explicit general solution for stress intensity factors (SIFs) associated with an arbitrary-edged hypocycloid-type crack is determined analytically under the influence of remote homogeneous heat flux and mechanical load. The superposition method combines stress functions and SIFs for two distinct loading conditions. The outcomes of the normalized SIFs are affected by the magnitude and orientation of the heat flux and mechanical load. A full-field stress distribution is provided to account for variations in SIFs. Certain combinations of loads lead to maximum SIF values, rendering the system highly vulnerable to damage, while two specific scenarios inhibit crack propagation, thereby reducing the risk of structural failure.

Newtonian laws of motion and conservation principles

Newton’s laws of motion and Newtonian conservation principles such as those for energy and momentum involve the assumption that the vanishing of a certain total time derivative, on integration, yields a fixed constant value as an immediate consequence. While this may ultimately be the case for additional reasons, it is possible to have a properly vanishing total time derivative and yet the individual partial derivates are non-zero. Here, for a particular problem and based only on the requirement that the total time derivative of the quantity vanishes, we investigate the particular mechanism leading to a conventional conservation principle. For the energy and angular momentum totals for planar steady orbiting motion, the partial differential conditions may be formally solved to obtain the general solutions. We determine the general structure for variable energy and angular momentum for which the total time derivatives vanish, and from which it is apparent that the standard expression for constant energy and angular momentum is recovered.

Three-Dimensional General Solutions of Orthorhombic Quasicrystals With Constraints

Abstract This study employs the Lur'e operator method to derive generalized solutions for orthorhombic quasicrystals, incorporating anisotropy factors as constraints. The solutions derived contain the Lekhnitskii–Hu–Nowacki and Elliott–Lodge solutions as special cases. The corresponding fundamental solutions or Green's functions within the infinite space are also derived, offering a comprehensive characterization of quasicrystal anisotropy. It is noteworthy that Green's functions in orthorhombic quasicrystals can be simplified to those in hexagonal quasicrystals or conventional orthorhombic crystals, with possible broad engineering applications.

A coupling framework between OpenFAST and WEC-Sim. Part I: Validation and dynamic response analysis of IEA-15-MW-UMaine FOWT

This study proposes a coupling strategy between OpenFAST and WEC-Sim (OWS) to provide a general solution for the design of offshore floating wind turbines (FOWTs). The fully-coupled calculation is implemented by transferring the tower-base loads from OpenFAST to WEC-Sim, which in turn transfers the platform displacements, velocities and accelerations back to the former. The cross-platform data interface is achieved via S-function in Simulink, and a parallel route in OWS ensures a comparable calculation speed compared with OpenFAST. The model validation is conducted based on the IEA-15-MW reference wind turbine (RWT) and UMaine-VolturnUS-S semisubmersible platform with the reference site located at the northern North Sea. Through code-to-code comparisons against OpenFAST, the newly developed OWS model is tested in various environmental conditions to ensure its correctness and reliability. Furthermore, the dynamic responses of the FOWT are comprehensively investigated using spectral analysis. The time lag of the platform displacements with respect to the incident wave is quantitatively evaluated based on correlation analysis. Generally, there is little time lag between the heave displacement and the wave, but the time lag in the pitch direction (6–9 s) is approximately twice that (3–4 s) in the surge direction.

On the development and analysis of coupled surface–subsurface models of catchments. Part 2. A three-dimensional benchmark model and its properties

The objective of this three-part work is to formulate and rigorously analyse a number of reduced mathematical models that are nevertheless capable of describing the hydrology at the scale of a river basin (i.e. catchment). Coupled surface and subsurface flows are considered. In this second part, we construct a benchmark catchment scenario and investigate the effects of parameters within their typical ranges. Previous research on coupled surface–subsurface models have focused on numerical simulations of site-specific catchments. Here, our focus is broad, emphasising the study of general solutions to the mathematical models, and their dependencies on dimensionless parameters. This study provides a foundation based on the examination of a geometrically simple three-dimensional benchmark scenario. We develop a non-dimensional coupled surface–subsurface model and extract the key dimensionless parameters. Asymptotic methods demonstrate under what conditions the model can be reduced to a two-dimensional form, where the principal groundwater and overland flows occur in the hillslope direction. Numerical solutions provide guidance on the validity of such reductions, and demonstrate the parametric dependencies corresponding to a strong rainfall event.

An Analytical Mechanics Model for the Rotary Sliding Triboelectric Nanogenerator.

In recent years, global attention towards new energy has surged due to increasing energy demand and environmental concerns. Researchers have intensified their focus on new energy, leading to advancements in technologies like triboelectrification, which harnesses energy from the environment. The invention of the triboelectric nanogenerator (TENG) has led to new possibilities, with the rotary sliding TENG standing out for its superior performance. However, understanding its mechanical behavior remains a challenge, potentially leading to structural issues. This paper introduces a novel analytical mechanics model to analyze the mechanical performance of the stator of the rotary sliding TENG, offering a new analytical solution. The solution also presents an innovative approach to solving axisymmetric problems in elasticity theory since it challenges a traditional assumption that the stress function depends solely on the radial coordinate, proposing a new stress function to derive a more general solution, supplementing the classical approach in the theory of elasticity. Through the obtained solutions, the mechanical characteristics of the rotary sliding TENG during operation are analyzed. A clearer relationship between mechanical characteristics and electrical output is expected to provide a theoretical basis for the design of the rotary sliding TENG.

Construction and forward kinematics of a novel reconfigurable parallel mechanism

In this paper, a kind of hybrid kinematics chain with variable constraints is constructed by using a 6R spatial bifurcated chain and 4-DOF serial limbs, by using them, a 3-DOF Reconfigurable Parallel Mechanisms (RPM) was constructed, which has four motion modes: 3T, 2T1R, 2R1T, and 3R motion modes. Using screw theory, the change of wrench system in the hybrid kinematics chain caused by the reconfiguration of the 6R bifurcated chain is analyzed, which affects the wrench system of the moving platform (MP), and thus causes the reconfiguration of the parallel mechanism (PM). The triangular pyramid fixed to the MP was found as auxiliary geometry and used to intuitively describe the constraint relationship between joint axes in limbs. The latter was used to establish a unified forward kinematics model of the RPM in four motion modes. The general forward kinematics solution procedure for this type of RPM is given. The overall Jacobian matrix was obtained by screw theory for singularity analysis. The condition number of the Jacobian matrix measures the degree to which the mechanism is close to the singular configuration. Based on the Monte Carlo simulation, point cloud images representing the workspace of RPM were obtained.

Revisiting the observability and identifiability properties of a popular HIV model

This paper revisits the observability and identifiability properties of a popular ODE model commonly adopted to characterize the HIV dynamics in HIV-infected patients with antiretroviral treatment. These properties are determined by using the general analytical solution of the unknown input observability problem, introduced very recently in Martinelli (2022). This solution provides the systematic procedures able to determine the state observability and the parameter identifiability of any ODE model, in particular, even in the presence of time varying parameters. Four variants of the HIV model are investigated. They differ because some of their parameters are considered constant or time varying. Fundamental new properties, which also highlight an error in the scientific literature, are automatically determined and discussed. Additionally, for each variant, the paper provides a quantitative answer to the following practical question: What is the minimal external information (external to the available measurements of the system outputs) required to make observable the state and identifiable all the model parameters? The answer to this fundamental question is obtained by exploiting the concept of continuous symmetry, recently introduced in Martinelli (2019). This concept allows us to determine a first preliminary general result which is then applied to the HIV model. Finally, for each variant, the paper concludes by providing a redefinition of the state and of the parameters in order to obtain a full description of the system only in terms of a state which is observable and a set of parameters which are identifiable (both constant and time varying).

The equation characterizations of generalized inverses in a ring with involution

In this paper, we study the relation between the generalized inverse properties of an element in a ring with involution and related equations. Mainly, by exploring the existence of the solution in a given set and the expressions of the general solution to these constructed related equation, we obtain a lot of new characterizations of EP elements, partial isometries, SEP elements, Hermitian elements and normal elements.

An ANS/ATFs‐based unsymmetric solid‐shell finite element algorithm for high‐quality finite deformation analysis of hyper‐elastic shell

AbstractAn effective updated Lagrangian (UL) algorithm is designed for extending the recent distortion‐tolerant unsymmetric 8‐node, 24‐DOF hexahedral solid‐shell element, US‐ATFHS8, to finite deformation analysis of hyper‐elastic shell structures. The distinguishing feature of this unsymmetric element is that two different interpolation schemes are employed for virtual displacement and real stress calculations, respectively. The assumed natural strain (ANS) method with shell assumptions, referring to the current configuration, is introduced to modify the strain tensors derived from the assumed virtual displacement fields in terms of isoparametric coordinates, thereby mitigating shear locking and trapezoidal locking. On the other hand, the analytical trial functions (ATFs) derived from the general solutions of homogenous governing equations for linear elasticity are updated in each increment step to obtain the incremental deformation gradient, which is then utilized for calculating the real stresses for curing the numerical difficulties in large deformation problems. Numerical examples show that the proposed algorithm enables the hyper‐elastic solid‐shell element US‐ATFHS8 to exhibit excellent performance in both regular and distorted meshes and yield considerable results even when other models cannot work.

UTILIZATION OF THOMAS MODEL TO PREDICT THEBREAKTHROUGH CURVES FOR ADSORPTION AND IONEXCHANGE

Fixed bed sorption processes such as adsorption and ion exchange do not operate at steady state. The design equations are differential that usually require numerical methods to solve. Thomas gives a general analytical solution for these equations. It is based on second-order reaction kinetics and the assumption of Langmuir isotherm. Computer program for the solution of Thomas model was designed using MATLAB 7.0. Four sets of experimental data are tested to show the capability of Thomas model to predict the breakthrough curves for adsorption and ion exchange processes. These data represent the sorption of o-cresol from water by activated carbon, acetic acid from air by activated carbon, phenol from water by natural zeolite, and trichloroethylene from air by zeolite- 5A.The results show that there are a good agreement between the experimental data and the model.

Analytical solution for one‐dimensional thaw consolidation model with double moving boundaries

AbstractA one‐dimensional thaw consolidation model considering the density change from pore ice to pore water is established, and the model describes a special type of moving boundary problem with double moving boundaries. An analytical solution for the model under a time‐varying external load is developed using certain form of superposition principle and the similarity type of general solution. Some known solutions in literature can be recovered as special cases of the analytical solution once the density change from pore ice to pore water is neglected. If the thawing front was to cease at certain time, consolidation of thawed soil in a fixed region is then encountered, and an analytical solution for the post‐thawing consolidation problem is developed using the Green's function method. Computational examples of the analytical solutions are presented. First, comparison between our model and classical model of Morgenstern and Nixon (MN model) is conducted, showing the error caused by neglecting the density change from pore ice to pore water. The MN model overestimates the excessive pore water pressure at locations near the soil surface, while underestimates it at locations near the thawing front; the error caused by neglecting the density change becomes more pronounced with increasing ice content of frozen soil. Second, comparison between the thaw consolidation process under an instant load and that under a corresponding exponential load is made. The difference in thaw consolidation behavior between the two situations mainly displays during the early stage, when there is obvious discrepancy between the two external loads; the degree of consolidation and thaw consolidation settlement are more sensitive to the discrepancy in external load than the excessive pore water pressure is.

Electromagnetic analysis of a wound rotor synchronous machine using an improved subdomain technique considering finite permeability of the core

This study proposed an improved analytical method for electromagnetic field analysis of a wound rotor synchronous machine (WRSM) considering the permeability of soft magnetic materials. A simplified analytical model considering the magnetic permeability of each region is presented. The governing equations of each region are derived from Maxwell’s equations and the electromagnetic field theory, and a general solution is derived by using mathematical techniques. The analytical solutions of all domains are derived by calculating the boundary conditions. To validate the proposed analytical method, the radial and circumferential magnetic flux densities are compared with finite element analysis (FEA) results. In addition, electromagnetic performance parameters such as flux linkage, back-electromotive force, and torque are determined using electromagnetic theories. In particular, the magnetic saturation of the soft magnetic material is due to field and armature current, and the superiority of the proposed method is demonstrated by comparing the improved analytical method considering the global saturation of each region with the nonlinear FEA result considering local saturation. The proposed analytical method can be widely used in the initial and optimal design of WRSM because it can consider saturation of the core due to changes in field and armature current.

General 2-D Analytical Framework for No-Load Analysis of Interior Permanent Magnet Machines

Solving two-dimensional (2-D) Maxwell’s equations in interior permanent magnet (IPM) motors is fairly complex due to the asymmetrical geometry of rotor magnets in the cylindrical coordinate system. This paper presents a general imaging solution to enable the 2-D open-circuit modeling of the family of IPM machines. Interior magnets are replaced/modeled with (i) virtual magnets on the surface of the rotor body (mapping interior magnets to the surface of the rotor body), and (ii) virtual volume current on the surface of the rotor body. The specifications of the virtual magnet (i.e., the remnant flux density) and the virtual volume current (i.e., current density level) are determined via magnetic circuit model. Next, the 2-D flux distribution of the transformed machines are calculated by solving 2-D Maxwell’s equations and considering relevant boundary conditions. Meanwhile, the effect of stator slots on flux profile is accounted by injecting proper amount of surface magnetizing current on the stator bore. Analytical results are supported via finite element method (FEM) and a series of experimental measurements.