scholarly journals Polynomial Loops: Beyond Termination

10.29007/nxv1 ◽  
2020 ◽  
Author(s):  
Marcel Hark ◽  
Florian Frohn ◽  
Jürgen Giesl
Keyword(s):  
The Body ◽  
Halting Problem ◽  
Non Linear ◽  
Single Assignment ◽  
Termination Problem

In the last years, several works were concerned with identifying classes of programswhere termination is decidable. We consider triangular weakly non-linear loops(twn-loops) over a ring Z ≤ S ≤ R_A , where R_A is the set of all real algebraicnumbers. Essentially, the body of such a loop is a single assignment(x_1, ..., x_d) ← (c_1 · x_1 + pol_1, ..., c_d · x_d + pol_d)where each x_i is a variable, c_i ∈ S, and each pol_i is a (possibly non-linear)polynomial over S and the variables x_{i+1}, ..., x_d. Recently, we showed thattermination of such loops is decidable for S = R_A and non-termination issemi-decidable for S = Z and S = Q.In this paper, we show that the halting problem is decidable for twn-loops over anyring Z ≤ S ≤ R_A. In contrast to the termination problem, where termination on allinputs is considered, the halting problem is concerned with termination on a giveninput. This allows us to compute witnesses for non-termination.Moreover, we present the first computability results on the runtime complexity ofsuch loops. More precisely, we show that for twn-loops over Z one can alwayscompute a polynomial f such that the length of all terminating runs is boundedby f( || (x_1, ..., x_d) || ), where || · || denotes the 1-norm. As a corollary, weobtain that the runtime of a terminating triangular linear loop over Z isat most linear.

scholarly journals Speculating Ancestor(ie)s: The Cavernous Memory of White Innocence and Fluid Embodiments of Afrofuturist Memory-Work

Humanities ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 138
Author(s):  
Javier Ernesto Perez
Keyword(s):  
Racial Violence ◽  
The Body ◽  
Embodied Knowledge ◽  
Narrative Strategies ◽  
Critical Dialogue ◽  
Star Wars ◽  
The Past ◽  
Memory Work ◽  
Non Linear ◽  
White Innocence

Enduring legacies of racial violence signal the need to reconcile with the past. This paper comparatively explores various speculative works that either reinforce a paradigm of White innocence that serves to deny such legacies or center critical dialogue between the past and present. It draws on a range of theoretical works, including Seshadri-Crooks’s (2000) Lacanian analysis of race, Taylor’s (2003) notion of the body as repertoire for embodied knowledge, Wright’s (2015) concept of Black epiphenomenal time, and Hartman’s (2008b) method of ‘critical fabulation.’ Through an analysis of the narrative tropes of caves and mirrors in the Star Wars Skywalker saga (1977–1983; 2015–2019), this paper firstly unpacks the bounded individualism that permits protagonists Luke and Rey Skywalker to refute their evil Sith lord ancestry and prevail as heroes. It then turns to the works Black Panther (2018) and Watchmen (2019) to comparatively examine Afrofuturist narrative strategies of collectivity, embodiment, and non-linear temporality that destabilize bounded notions of self and time to reckon with the complexities of the past. It concludes that speculative approaches to ancestral (dis)connections are indicative of epistemological frameworks that can either circumvent or forefront ongoing demands to grapple with the past.

Non-Linear Characteristics in the Dynamic Responses of Seated Subjects Exposed to Vertical Whole-Body Vibration

2002 ◽  
Vol 124 (5) ◽  
pp. 527-532 ◽  
Author(s):  
Yasunao Matsumoto ◽  
Michael J. Griffin
Keyword(s):  
Frequency Response ◽  
The Body ◽  
Dynamic Responses ◽  
Whole Body ◽  
Apparent Mass ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Resonance Frequencies ◽  
Non Linear ◽  
Vibration Magnitude

The effect of the magnitude of vertical vibration on the dynamic response of the seated human body has been investigated. Eight male subjects were exposed to random vibration in the 0.5 to 20 Hz frequency range at five magnitudes: 0.125, 0.25, 0.5, 1.0 and 2.0 ms−2 r.m.s. The dynamic responses of the body were measured at eight locations: at the first, fifth, and tenth thoracic vertebrae (T1, T5, T10), at the first, third, and fifth lumbar vertebrae (L1, L3, L5) and at the pelvis (the posterior-superior iliac spine). At each location, the motions on the body surface were measured in the three orthogonal axes within the sagittal plane (i.e., the vertical, fore-and-aft, and pitch axes). The force at the seat surface was also measured. Frequency response functions (i.e., transmissibilities and apparent mass) were used to represent the responses of the body. Non-linear characteristics were observed in the apparent mass and in the transmissibilities to most measurement locations. Resonance frequencies in the frequency response functions decreased with increases in the vibration magnitude (e.g. for the vertical transmissibility to L3, a reduction from 6.25 to 4.75 Hz when the vibration magnitude increased from 0.125 to 2.0 ms−2 r.m.s.). The transmission of vibration within the spine also showed some evidence of a non-linear characteristic. It can be concluded from this study that the dynamic responses of seated subjects are clearly non-linear with respect to vibration magnitude, whereas previous studies have reported inconsistent conclusions. More understanding of the dependence on vibration magnitude of both the dynamic responses of the soft tissues of the body and the muscle activity (voluntary and involuntary) is required to identify the causes of the non-linear characteristics observed in this study.

Application of a Boundary Element Method for Wave-Body Interaction Problems Considering the Non-Linear Water Surface

2017 ◽  
Author(s):  
Daniel Ferreira González ◽  
Jonas Bechthold ◽  
Moustafa Abdel-Maksoud
Keyword(s):  
Water Surface ◽  
Three Dimensional ◽  
Free Water ◽  
Numerical Approach ◽  
Panel Method ◽  
The Body ◽  
Time Step ◽  
Non Linear ◽  
Wigley Hull ◽  
Tank Test

In this paper an existing time domain panel method, which was originally developed for propeller flow simulations, is extended by implementing the mixed Eulerian-Lagrangian approach for the computation of the non-linear free water surface. The three-dimensional panel method uses a constant source and doublet density distribution on each panel and a Dirichlet boundary condition to solve the velocity potential in every time step. Additionally, a formulation for the acceleration potential is included in order to determine the hydrodynamic forces accurately. The paper gives an overview on the governing equations and introduces the numerical approach. Validation results of the developed method are presented for the wave resistance of a submerged spheroid and a wigley hull. Additionally, the wave diffraction due to a surface piercing cylinder in regular waves is validated regarding the forces and the water surface elevation around the body. Here, the computations are compared with other numerical methods as well as tank test results. Apart from this, the paper deals with an application example showing simulations of an artificial service vessel catamaran in waves. The forces on the hull with and without forward speed are presented. The paper concludes with a discussion of the presented results and a brief outlook on further work.

Finite Element Simulation of Physical Phenomena in Real Conditions of a Single Grain Cutting Process

2016 ◽  
Vol 862 ◽  
pp. 288-297
Author(s):  
Monika Forysiewicz ◽  
Leon Kukielka ◽  
Katarzyna Gotowala
Keyword(s):  
Plastic Strain ◽  
Initial Conditions ◽  
The Body ◽  
Numerical Calculations ◽  
Cutting Process ◽  
Deformation Tensor ◽  
Plasticity Condition ◽  
Mixed Hardening ◽  
Abrasive Grain ◽  
Non Linear

The cutting process was presented as a real object as well as its physical and mathematical modelling. For the description of the non-linear phenomena, at the typical increment ratio, the updated Lagrange's description was used. Adequate deformation and stress increments measurements were used, e.g. Green-Lagrange's deformation tensor increment and the increment of the Piola-Kirchhoff's second symmetrical tensor. Nonlinearity of the material was described by means of the increment model taking into consideration the deformation and deformation rate records. The workpiece is treated as a body in which there may be elastic deformation (in the range of reversible deformation) and visco and plastic (in terms of irreversible deformation), with nonlinear hardening. For the construction of the material model Huber-Mises-Hencky's non-linear plasticity condition was used, associated principle of flow as well as mixed hardening (isotopic-kinematic). The condition of the material after pre-machining processes was also taken into account by means of implementation of initial conditions of: displacement, strain and stress. Yield stress of the body was described by a Cowper-Symonds' model allows for linear-isotropic, kinematic or mixed plastic strain hardening and the effect of the intensity of plastic strain velocity. The applications in ANSYS program and results of numerical calculations were presented. A method of generating a three-dimensional abrasive grain with a geometry close to actual were describes. The influence of the process parameters on the states of strains and stresses and on the quality of the product was presented. Numerical calculations of cutting process with single abrasive grain were made and investigated the deformation and stress occurring in the workpiece. The experimental test stand of single abrasive grain cutting process, the test plan and the verifications of results of numerical simulations were describes. The results were statistically developed and that’s give the models in the regression function form.

scholarly journals Customized Human Skin Simulants

2018 ◽  
Author(s):  
Arnab Chanda
Keyword(s):  
Human Skin ◽  
Constitutive Models ◽  
Mechanical Tests ◽  
The Body ◽  
Porcine Skin ◽  
Personal Protection Equipment ◽  
Wearable Technologies ◽  
Stiffness Properties ◽  
Non Linear ◽  
Close Range

A simulant which precisely mimics the linear and non-linear mechanical properties of “the human skin” would be indispensable for assessment of load responses (and discomfort) produced by wearable technologies in the aerospace industry, be it an electronic sensor or a full body suit. In the current work, for the first time, a methodology has been developed to fabricate customized human skin simulants for any person and part of the body. The material comprises of four parts of silicone, which when mixed in different ratios, produces skin simulants with different stiffness properties. Extensive mechanical tests have been performed on different variants of the human skin simulants, and their stress versus strain responses have been matched with actual human skin test data from the literature. Also, the fracture properties of the simulants have been found to be in close range of the actual human skin. Additionally, non-linear hyperelastic constitutive models were used to fully characterize the mechanical behavior of the skin simulant variants. Mechanical tests on freshly excised porcine skin were conducted to validate our test results. To date, such accurate skin simulants has not been developed anywhere to the best of our knowledge. The material is cheap ($15/lb), has no biosafety or handling issues (unlike cadavers, cowhides or porcine skin), and castable to any shape or size. Besides testing, the skin simulants could also be used to develop liners for the wearable technologies, which are just like the skin of the person wearing it, thus reducing discomfort due to material mismatch and friction. Additionally, the skin simulants find applications in the area of manufacturing of prosthetics (liners) and orthotics, military grade armors and personal protection equipment (PPE), and testing of non-lethal and less-lethal ballistics.

Non-linear Optimization Scheme Applied to EIT Medical Images Based on the Gauss-Newton Method With Iterative Conductivity Update and Total Variation Regularization

2021 ◽  
Author(s):  
Bruno Miguel Gil Rosa ◽  
Guang-Zhong Yang
Keyword(s):  
Inverse Problem ◽  
Total Variation ◽  
Linear Optimization ◽  
Linear Method ◽  
The Body ◽  
Total Variation Regularization ◽  
Back Projection ◽  
Distribution Map ◽  
Optimization Scheme ◽  
Non Linear

Abstract Medical imaging modalities are vast and include the well-established techniques of Computerized Tomography (CT), Magnetic Resonance Imaging (MRI) or Ultrasounds. Though the underlying physics differs amongst modalities, a similar Inverse Mapping is shared: the recovery of the internal physical property under analysis from measurements obtained at the exterior of the body. In the lesser common technique of Electrical Impedance Tomography (EIT), measurement of the voltage levels around a body part are used to retrieve the internal distribution map for conductivity. The complexity of the Inverse Problem in EIT surpasses that found for the Forward Problem (or Mapping), both in terms of mathematical formulation and computational overload. The ill-posed nature of the Inverse Problem further contributes to that intricacy, and solutions to tackle it will be presented in this paper by means of a non-linear optimization scheme involving the iterative Gauss-Newton (GN) method with Total Variation (TV) regularization, applied to two-dimensional (2D) body domains only. The proposed scheme is also compared to other traditional reconstruction algorithms like 2D back-projection and the sensitivity approximation to the Jacobian matrix of the system of equations governing EIT. Results from conductivity map reconstructions in anatomical phantoms have shown an improvement in signal-to-noise ratio (SNR) and distribution map error (DME) of 36% and 11% for the proposed non-linear method relative to the back-projection and single-step GN method with sensitivity approximation.

INFRARED DRYING OF RHUBARBS CUBES

2015 ◽  
Author(s):  
Aivars ABOLTINS ◽  
Janis PALABINSKIS
Keyword(s):  
Sample Thickness ◽  
The Body ◽  
Thickness Effect ◽  
Water Evaporation ◽  
Drying Time ◽  
Drying Characteristics ◽  
Infrared Drying ◽  
Non Linear Equation ◽  
Non Linear ◽  
Heating Up

In order to obtain dehydrated products of high quality, infrared drying in rhubarb cubes was researched at different sample thicknesses with IR film drying possibilities with small heating up to 40 oC. The drying characteristics of rhubarb cubes were studied using non-linear multiple regression analysis. Using experimental data, the two arguments non-linear equation was obtained to evaluate the drying time and sample thickness effect on rhubarb moisture. The determination coefficient of this correlation was R2 = 0.98. The results indicated that after 20 hours drying rhubarb samples with thickness 0.5 cm are dried up to 2 %, samples with 1 cm and 2 cm thickness dried up to 17 % and 25 % correspondingly. 1 cm thick rhubarb samples temperature rose from 24 oC to 33 oC during the experiment. With decreasing moisture of the product more infrared energy is used to warm the body and less for water evaporation.

Non-linear simulations of wave-induced motions of a floating body by means of the mixed Eulerian-Lagrangian method

2000 ◽  
Vol 214 (6) ◽  
pp. 841-855 ◽  
Author(s):  
M Kashiwagi
Keyword(s):  
Velocity Potential ◽  
Hydrodynamic Force ◽  
Computation Time ◽  
The Body ◽  
Floating Body ◽  
Parametric Oscillation ◽  
Non Linear ◽  
Temporal Derivative ◽  
Wave Induced ◽  
The Waves

A non-linear calculation method based on the mixed Eulerian-Lagrangian (MEL) method is presented for wave-induced motions of a two-dimensional floating body. Attention is focused on an effective calculation of the hydrodynamic force associated with the temporal derivative of the velocity potential in the Bernoulli pressure equation. Unlike other existing methods, the acceleration field can be computed simultaneously with the velocity field, which contributes greatly to a reduction in the computation time. Computations are performed for a wall-sided model and a flared model, and numerical results of the waves at upwave and downwave positions and the body motions (sway, heave and roll) are compared with corresponding experiments. The overall agreement is very good, confirming the validity of the present method. The parametric oscillation in roll, observed for the flared model, is also discussed.

A Study of Systemology and Astronomic Atomic Structures

2017 ◽  
Vol 13 (1) ◽  
pp. 4507-4521
Author(s):  
Jessie Davis Ward
Keyword(s):  
The Body ◽  
Atomic Structures ◽  
Linear Behavior ◽  
Non Linear ◽  
Universal Expansion ◽  
The Brain ◽  
The Universe

This Paper utalizes Universal Expansion to derive the System Laws, rules that govern non-linear behavior. Examples of Systems are Sudoku, the Body, the Brain, and the Universe.

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