The wave equation is generally regarded as a linear approximation to the equation describing the amplitude of a transversely vibrating elastic string in the plane. But, as is shown in \cite{BC96}, the assumption of transverse vibration in fact implies that the wave equation describes the vibration…
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48 results for “vibrating string”
The paper analyzes the stability of an observer error in a vibrating string system.
problem Stability analysis of observer error in a vibrating string system.
method Abstract Cauchy problem reformulation and application of LaSalle's invariance principle for infinite-dimensional systems.
result The observer error is asymptotically stable.
We develop a new geometric framework suitable for dealing with Hamiltonian field theories with dissipation. To this end we define the notions of -contact structure and -contact Hamiltonian system. This is a generalization of both the contact Hamiltonian systems in mechanics and the -symplectic Hamiltonian syst…
This research optimizes plate structures to reduce vibrations in vehicles and aircraft.
problem Minimizing structural vibrations in engineering systems for improved passenger comfort.
method Guided flow matching design optimization integrating generative flow matching and surrogate model.
result Generated plate designs with reduced vibrations compared to random search and other methods.
Improves Marsden-Weinstein reduction theory for k-polysymplectic manifolds.
problem Improving Marsden-Weinstein reduction theory for k-polysymplectic manifolds.
method Developed a theory of affine Lie group actions for k-polysymplectic momentum maps, removing technical conditions.
result Devise a k-polycosymplectic Marsden-Weinstein reduction theory.
Energy-Based In-Domain Control and Observer Design for Infinite-Dimensional Port-Hamiltonian Systemsmath.OC
In this paper, we consider infinite-dimensional port-Hamiltonian systems with in-domain actuation by means of an approach based on Stokes-Dirac structures as well as in a framework that exploits an underlying jet-bundle structure. In both frameworks, a dynamic controller based on the energy-Casimir method is derived in…
This is a survey of several approaches to the framework for working with infinitesimals and infinite numbers, originally developed by Abraham Robinson in the 1960s, and their constructive engagement with the Cantor-Dedekind postulate and the Intended Interpretation hypothesis. We highlight some applications including (…
Transformer model predicts train axle vibrations for safer maintenance.
problem Prevent mechanical failures in railway axles.
method Integrates Deep Autoregressive solution with spectral methods and observation models.
result Transformer model (ShaftFormer) improves predictive maintenance for railway axles.
This paper reviews traditional and modern methods for detecting structural damage using vibrations.
problem Early warning of structural damage to maintain civil structures.
method Vibration-based methods and ML/DL algorithms.
result ML and DL algorithms show superior performance in detecting structural damage.
A novel ensemble classifier improves vibration-based quality monitoring accuracy.
problem Developing high accuracy classification methods for general datasets.
method Dempster-Shafer theory of evidence with three remedies for conflicting evidences.
result The proposed ensemble classifier outperforms state-of-the-art fusion techniques.
This work models variability in composite blades' vibrations.
problem Variability in structural dynamics due to manufacturing differences.
method Defining a general model for frequency response functions using mixtures of Gaussian processes.
result A general model for frequency response functions of composite blades.
Safe Reinforcement Learning-Based Vibration Control: Overcoming Training Risks with LQR Guidancecs.LG
Safe RL-based vibration control using LQR guidance.
problem Training risks in RL-based vibration control.
method Hybrid control framework combining LQR and RL.
result LQR controller outperforms uncontrolled scenario.
The study focuses on the experiment of using three different smartphones to collect acceleration data from vibration for the road roughness detection. The Android operating system is used in the application. The study takes place on asphaltic pavement of the expressway system of Thailand, with 9 km distance. The run ve…
Stokes-Dirac structures are infinite-dimensional Dirac structures defined in terms of differential forms on a smooth manifold with boundary. These Dirac structures lay down a geometric framework for the formulation of Hamiltonian systems with a nonzero boundary energy flow. Simplicial triangulation of the underlaying m…
The paper proposes an ensemble of convolution-based methods for fault detection in gearboxes.
problem Fault detection in planetary gearboxes using vibration signals.
method Ensemble of three convolution kernel-based methods (ROCKET, 1D CNN with ResNet, FCN).
result Outperforms other approaches with over 98.8% accuracy.
Study examines how body segments respond to random vibrations.
problem Understanding human body responses to random vibrations.
method 35 participants were tested with random noise signals. Multiple linear regression models were created to determine influential predictors of peak translational gains.
result Multiple predictors, including motion direction and body segment, significantly influence peak translational gains.
Predicting Bearings' Degradation Stages for Predictive Maintenance in the Pharmaceutical Industrystat.ML
Paper predicts bearing degradation stages for pharmaceutical industry maintenance.
problem Predicting when to maintain specific parts of production machines.
method AutoEncoder-based k-means segmentation of high-frequency vibration data.
result Framework generates reliable predictions for bearing degradation stages.
We try to present an estimate relating the first Dirichlet and Neumann eigenvalues of a compact bordered Riemannian surface.
New metric tensor field on symmetric matrices simplifies eigenvector computation.
problem Complex eigenvector computation for 2x2 symmetric matrices.
method Introducing a metric tensor field on the space of symmetric matrices, resulting in a curved manifold.
result Parallel transport simplifies eigenvector computation for one-parameter families of matrices.
Affirm Lord Rayleigh's conjecture on curved spaces for clamped plates.
problem Lord Rayleigh's conjecture for vibrating clamped plates on curved spaces.
method Nodal-decomposition argument, Lévy-Gromov isoperimetric inequality, Gaussian hypergeometric functions, sharp spectral gap estimates.
result Positive curvature enhances genuine differences between low- and high-dimensional settings.
Sample size determination for a data set is an important statistical process for analyzing the data to an optimum level of accuracy and using minimum computational work. The applications of this process are credible in every domain which deals with large data sets and high computational work. This study uses Bayesian a…
This paper studies an intelligent ultimate technique for health-monitoring and prognostic of common rotary machine components, particularly bearings. During a run-to-failure experiment, rich unsupervised features from vibration sensory data are extracted by a trained sparse auto-encoder. Then, the correlation of the ex…
Derives path integrals for perturbative strings on various backgrounds.
problem Calculating path integrals for strings on curved backgrounds.
method Derives path integrals from string geometry theory by considering fluctuations around string backgrounds.
result Derives path integrals of all order perturbative strings on various backgrounds.
Design and Characterization of a Novel Motion Conversion Element: Curved Groove Ball Bearing without Retainerphysics.app-ph
Innovative ball bearing converts rotary to reciprocating motion.
problem Designing efficient motion conversion mechanisms.
method Closed curve envelopment theory and diameter-stroke ratio concept.
result Compact and vibration-reduced ball bearing design.
Evaluation of the MACE Force Field Architecture: from Medicinal Chemistry to Materials Sciencephysics.chem-ph
MACE architecture outperforms alternatives in various molecular and materials science tasks.
problem Improving machine learning force fields for diverse molecular and materials science applications.
method Evaluation of MACE architecture on various datasets and tasks, demonstrating data efficiency and excellent performance.
result MACE architecture generally outperforms alternatives across a wide range of systems, including amorphous carbon, universal materials modelling, and organic chemistry.
Identifies all perturbative vacua in bosonic string theory.
problem Identifying all perturbative vacua in bosonic string theory.
method Completely identified perturbative vacua through string fluctuations.
result Derivation of path-integrals up to any order from fluctuations.
String geometry theory connects strings to space-time and finds string vacua.
problem Identify and find the global minimum of the string vacuum.
method Identify perturbative vacua, derive path-integrals, and solve the global minimum using analytical and numerical methods.
result The global minimum of the effective potential is the string vacuum.
Derives path-integrals for superstrings on curved backgrounds using string geometry theory.
problem Calculating path-integrals for superstrings on curved backgrounds.
method Derives path-integrals from string geometry theory by considering fluctuations around string backgrounds.
result Derives path-integrals for perturbative superstrings on all string backgrounds.
Chiral string integrands simplify to ambitwistor string integrands in the tensionless limit.
problem Understanding the relationship between chiral and ambitwistor string integrands.
method Analyzing the tensionless limit of chiral superstring integrands.
result Chiral superstring integrands reduce to ambitwistor string integrands in the tensionless limit.
Perturbative string amplitudes are correctly derived from the string geometry theory, which is one of the candidates of a non-perturbative formulation of string theory. In order to derive non-perturbative effects rather easily, we formulate topological string geometry theory. We derive the perturbative partition functi…
A virtual string is a scheme of self-intersections of a closed curve on a surface. We study algebraic invariants of strings as well as two equivalence relations on the set of strings: homotopy and cobordism. We show that the homotopy invariants of strings form an infinite dimensional Lie group. We also discuss connecti…
A virtual string can be defined as an equivalence class of planar diagrams under certain kinds of diagrammatic moves. Virtual strings are related to virtual knots in that a simple operation on a virtual knot diagram produces a diagram for a virtual string. In this paper we consider three operations on a virtual string …
There is an interpretation of open string field theory in algebraic topology. An interpretation of closed string field theory can be deduced from this open string theory to obtain as well the interpretation of open and closed string field theory combined.
New formulas link string bordism to integers.
problem Understanding the third string bordism group.
method Geometric string structures and 3d TQFT.
result Integral formulas realize the string bordism isomorphism.
Extended Alexander groups are used to define an invariant for open virtual strings. Examples of non-commuting open strings and a ribbon-concordance obstruction are given. An example is given of a slice virtual open string that is not ribbon. Definitions are extended to open n-strings.
BOSS optimizes string inputs using string kernels and genetic algorithms.
problem Optimizing string inputs with constraints.
method Bayesian optimization over string kernels and genetic algorithms.
result Significantly improved optimization across various string constraints.
String topology coproduct and Turaev cobracket computed for surfaces.
problem Computing string topology coproduct and cobracket for surfaces.
method Algorithm to compute coproduct of cyclic words in terms of generators of the fundamental group.
result String cobracket is the negative of Turaev cobracket.
We present a finite-dimensional and smooth formulation of string structures on spin bundles. It uses trivializations of the Chern-Simons 2-gerbe associated to this bundle. Our formulation is particularly suitable to deal with string connections: it enables us to prove that every string structure admits a string connect…
Cobordism of virtual string links on strands is a combinatorial generalization of link cobordism. There exists a bijection between virtual string links up to cobordisms and elements of the group . This paper also shows that virtual string links up to unwelded equivalence are classified by those…
Paper shows string cobordism at 24 dims can be determined by elliptic genus.
problem Determining string cobordism at dimension 24.
method Using elliptic genus as an invariant.
result Shows string cobordism at 24 dims can be determined by elliptic genus.
Introduces string structures linking to loop spaces.
problem Understanding geometric string structures.
method Explains connections to loop spaces.
result String structures linked to loop spaces.
Geometric and topological structures related to M-branes II: Twisted String and String^c structureshep-th
The actions, anomalies, and quantization conditions allow the M2-brane and the M5-brane to support, in a natural way, structures beyond Spin on their worldvolumes. The main examples are twisted String structures. This also extends to twisted String^c structures, which we introduce and relate to twisted String structure…
Virtual stringsmath.GT
A virtual string is a scheme of self-intersections of a closed curve on a surface. We introduce virtual strings and study their geometric properties and homotopy invariants. We also discuss connections between virtual strings, Gauss words, and virtual knots.
Study topological G₂ and Spin(7) strings at 1-loop using double complexes.
problem Calculate topological string partition functions at 1-loop.
method Define double complexes for supersymmetric backgrounds using generalised geometry, compute partition functions as alternating products of determinants of Laplacians.
result Reproduce known results for G₂ string and predict for Spin(7) string.
In this note we revisit the subject of anomaly cancelation in string theory and M-theory on manifolds with String structure and give three observations. First, that on String manifolds there is no E8 x E8 global anomaly in heterotic string theory. Second, that the description of the anomaly in the phase of the M-theory…
End-to-end solution for recognizing handwritten numerals, avoiding traditional preprocessing steps.
problem Handwritten numeral string recognition with traditional preprocessing steps.
method YoLo-based model for automatic detection and recognition, avoiding heuristic-based preprocessing and segmentation.
result Proposed method reduces complexity and is a feasible end-to-end solution for numeral string recognition.
A virtual -string is a collection of oriented smooth generic loops on a surface . A stabilization of is a surgery that results in attaching a handle to along disks avoiding , and the inverse operation is a destabilization of . We consider virtual -strings up to virtual homotopy, i.e., seq…
We derive a recursion relation for hyperbolic string vertices and apply it to string field theory.
problem Deriving a recursion relation for hyperbolic string vertices and its implications for string field theory.
method Using systolic volumes and a modified Mirzakhani's recursion, we construct a higher-order vertex determination for hyperbolic string field theory.
result The higher order vertices in hyperbolic string field theory are determined by the cubic vertex iteratively for any background.