Artificial Singularity Research Articles

Structural Stability of the Transonic Shock Problem in a Divergent Three-Dimensional Axisymmetric Perturbed Nozzle

In this paper, we prove the structural stability of the transonic shocks for three-dimensional axisymmetric Euler system with swirl velocity under the perturbations for the incoming supersonic flow, the nozzle boundary, and the exit pressure. Compared with the known results on the stability of transonic shocks, one of the major difficulties for the axisymmetric flows with swirls is that corner singularities near the intersection point of the shock surface and nozzle boundary and the artificial singularity near the axis appear simultaneously. One of the key points in the analysis for this paper is the introduction of an invertible modified Lagrangian transformation which can straighten the streamlines in the whole nozzle and help to represent the solutions of transport equations explicitly. Furthermore, the simple but useful modified Lagrangian transformation makes the treatment for the singularities near the axis easy and clean. Such a technique may be helpful in studies of other problems for axisymmetric flows.

Artificial Intelligence and Singularity at Future Horizon

The term technical singularity or in simply singularity itself very ambiguous because several write-ups, postulates, theories and hypothesizes but the concern of all these again reach to same singularity of conclusion is singularity occurred in near future with including my conclusion on the basis of law of technological acceleration return.

Comments on the dispersion relation method to vector–vector interaction

Abstract We study in detail the method proposed recently to study the vector–vector interaction using the $N/D$ method and dispersion relations, which concludes that, while, for $J=0$, one finds bound states, in the case of $J=2$, where the interaction is also attractive and much stronger, no bound state is found. In that work, approximations are done for $N$ and $D$ and a subtracted dispersion relation for $D$ is used, with subtractions made up to a polynomial of second degree in $s-s_\mathrm{th}$, matching the expression to $1-VG$ at threshold. We study this in detail for the $\rho\rho$ interaction and to see the convergence of the method we make an extra subtraction matching $1-VG$ at threshold up to $(s-s_\mathrm{th})^3$. We show that the method cannot be used to extrapolate the results down to 1270 MeV where the $f_2(1270)$ resonance appears, due to the artificial singularity stemming from the “on-shell” factorization of the $\rho$ exchange potential. In addition, we explore the same method but folding this interaction with the mass distribution of the $\rho$, and we show that the singularity disappears and the method allows one to extrapolate to low energies, where both the $(s-s_\mathrm{th})^2$ and $(s-s_\mathrm{th})^3$ expansions lead to a zero of $\mathrm{Re}\,D(s)$, at about the same energy where a realistic approach produces a bound state. Even then, the method generates a large $\mathrm{Im}\,D(s)$ that we discuss is unphysical.

The role of power decay, exponential decay and Mittag-Leffler function’s waiting time distribution: Application of cancer spread

The use of fractional differential operators (Riemann–Liouvillend Caputo) to model real world problems leads to a waiting time distribution governs by the power law. This operators obeys the so-called index law of the classical mechanic and also possess an artificial singularity around the initial or starting point of the process. There are failures or limitations attached to the power-law fractional differential operator: its capacity of obeying the index-law leads waiting time distribution with no crossover behavior which is a limitation for describing real world with statistical resetting and also spread or diffusion of some material in different scales, or some kind of anomalous spread like that of cancer. The second big problem is the singularity induced by the power law decay function, this singularity leads bad memory at the zero starting point. At this point, the prediction suggested by the model are not reliable as they can sometime misleading due to influence of the artificial singularity. The introduction of non-singular kernel is welcome in the field of fractional calculus as they brought news weapons in this field to accurately model real world problems, in particular diffusion or spread in different states. We welcome them in fractional calculus for two reasons: They do not lead to inclusion of artificial singularity into the mathematical models, in this case the history of the dynamical process. The second reason is their ability of describing the two different waiting times distribution, which is an ideal waiting time distribution as such is observed in many biological phenomena such as the spread of cancer. This crossover behavior of this new fractional differential operators is due to their capacity of not obeying the index law imposed in fractional calculus. The numerical simulations presented in this paper are in perfect agreement with the conclusion of the study done in Atangana (2018) where it was proved that, the index law is irrelevant in fractional calculus as the most important fact is the effect of the fractional differential operator to the associate evolution equation. We conclude in this paper that fractional differential operators not obeying index law are suitable mathematical tools to model real world problems.

Conceptions of Artificial Intelligence and Singularity

In the current discussions about “artificial intelligence” (AI) and “singularity”, both labels are used with several very different senses, and the confusion among these senses is the root of many disagreements. Similarly, although “artificial general intelligence” (AGI) has become a widely used term in the related discussions, many people are not really familiar with this research, including its aim and status. We analyze these notions, and introduce the results of our own AGI research. Our main conclusions are that: (1) it is possible to build a computer system that follows the same laws of thought and shows similar properties as the human mind, but, since such an AGI will have neither a human body nor human experience, it will not behave exactly like a human, nor will it be “smarter than a human” on all tasks; and (2) since the development of an AGI requires a reasonably good understanding of the general mechanism of intelligence, the system’s behaviors will still be understandable and predictable in principle. Therefore, the success of AGI will not necessarily lead to a singularity beyond which the future becomes completely incomprehensible and uncontrollable.

From Divine Transcendence to the Artificial One. Challenges of the New Technologies

The invasion of the new technologies in our lives and the current dependence upon them makes us believe that in a not too distant future we will be made of more technology than biological matter. If until recently computers had hardly been discovered, today we are witnessing a real technological revolution in all the fields: biology, medicine etc. The evolution of the new technologies has raised various questions related to the future of mankind and the current human species, which determines us to make speculations regarding a future event that may occur. For this reason, in this paper I shall analyze the concept of artificial intelligence and singularity and I shall also outline the relationship between the ontological argument and the possible worlds. The idea of possible world can serve as a way of describing a metaphor (heretofore) in the philosophy of science, as singularity can exist in a possible world only if one creates the conditions of a new concept regarding fiction. We believe that technological singularity will change the values of the current society and the individual will have to face a world that depersonalizes the individual, as transhumanism draws the theoretical frameworks of a ‹‹brave new world››. In this paper, we have also analyzed the logical explanation of God's existence and the explanation of singularity through artificial intelligence. Therefore, we shall bring up for discussion the idea of virtual universe in the context of downloaded consciousness, which can be operated through artificial intelligence. Our conclusions refer to the fact that eternal life could exist artificially, but it cannot be demonstrated in terms of the ontological argument.

A geometric approach for quadrotor trajectory tracking control

This paper investigates the trajectory tracking problem for quadrotor with attitude finite-time convergence via geometric approach. First, a global geometric dynamic description is presented on the special Euclidean group (SE(3)), and the trajectory tracking control is decomposed into two cascaded tracking control loops: the position tracking control loop and the attitude tracking control loop. Then, based on the fact that the attitude tracking loop is a fast loop, a finite-time controller based on the exponential coordinate is proposed to speed up the response rate of the attitude control loop, so that the artificial singularity and redundancy can be avoided. In addition, a backstepping controller is designed for the position tracking loop to construct the thrust magnitude control input for the position dynamics and the reference rotation matrix for the attitude tracking loop. Finally, the numerical simulation results are presented to demonstrate the effectiveness of this trajectory tracking strategy.

A Casimir-Dark Energy Nano Reactor Design—Phase One

A phase one design of a new free energy nano reactor is presented. The design is based on a basically topological interpretation of the Casimir effect as a natural intrinsic property of the geometrical topological structure of the quantum-Cantorian micro spacetime. In particular we view dark energy, Hawking negative energy, Unruh temperature and zero point vacuum energy as being different sides of the same multi-dimensional coin. This new interpretation compliments the earlier conventional interpretation as vacuum fluctuation or as a Schwinger source and links the Casimir energy to the so-called missing dark energy density of the cosmos. We start with a general outline of the theoretical principle and basic design concepts of a proposed Casimir dark energy nano reactor. In a nutshell the theory and consequently the actual design depend crucially upon the equivalence between the dark energy density of the cosmos and the faint local Casimir effect produced by two sides boundary condition quantum waves. This Casimir effect is then colossally amplified as a one internal quantum wave representing a Hartle-Hawking state vector of the universe pushing from the inside against the boundary of the universe with nothing balancing it from the non-existent outside. This strange situation becomes completely natural and logical when we remember that the boundary of the universe is a one sided M&#246bius like manifold. In view of the present theory, this is essentially what leads to the observed accelerated expansion of the cosmos. As in any reactor, the basic principle in the present design is to produce a gradient so that the excess energy on one side flows to the other side. Thus in principle we will restructure the local topology of space using material nanoscience technology to create an artificial local high dimensionality with a Dvoretzky theorem like 96 percent volume measure concentration. Without going into the intricate nonlinear dynamics and technological detail, it is fair to say that this would lead us to pure, clean, free energy obtained directly from the topology of spacetime via an artificial singularity. Needless to say, the entire design is based completely on the theory of quantum wave dark energy proposed by the present author for the first time in 2011 in a conference held in the Bibliotheca Alexandrina, Egypt and a little later in Shanghai, Republic of China. The quintessence of the present theory is easily explained as the Φ3 intrinsic Casimir topological energy where Φ= (√5-1)/2 is produced from the zero set Φ of the quantum particle when we extract the empty set quantum wave Φ2 from it and find Φ-Φ2=Φ3 by restructuring space via conducting but uncharged plates similar to that of the classical Casimir experiments. Our proposed preliminary design of this Casimir-spacetime artificial singularity reactor follows in a natural way from the above.

Extracting information behind the veil of the horizon

In AdS/CFT duality, it is often argued that information behind the event horizon is encoded even in boundary correlators. However, its implication is not fully understood. We study a simple model which can be analyzed explicitly. The model is a two-dimensional scalar field propagating on the s-wave sector of the BTZ black hole formed by the gravitational collapse of a null dust. Inside the event horizon, we placed an artificial timelike singularity where one-parameter family of boundary conditions is permitted. We compute two-point correlators with two operators inserted on the boundary to see if the parameter can be extracted from the correlators. In a typical case, we give an explicit form of the boundary correlators of an initial vacuum state and show that the parameter can be read off from them. This does not immediately imply that the asymptotic observer can extract the information of the singularity since one cannot control the initial state in general. Thus, we also study whether the parameter can be read off from the correlators for a class of initial states.

S wave Kπ scattering and effects of κ in [formula omitted

Kπ S wave scattering is studied using a chiral unitary approach (ChUT) taking into account coupled channels. With the amplitudes derived from the lowest order chiral Lagrangian as the kernel of a set of coupled channel Bathe–Salpeter equations, the I = 1 / 2 S wave Kπ scattering phase shifts below 1.2 GeV can be fitted by one parameter, a subtraction constant, and a scalar resonance corresponding to the controversial κ ( K 0 ∗ ( 800 ) ) can be generated dynamically. A good description of the I = 3 / 2 S wave Kπ scattering phase shifts below 1.2 GeV can also be obtained. An artificial singularity in the cut-off method of the 2-meson loop integral of the ChUT is found. The formalism is applied to deal with the S wave Kπ final state interaction (FSI) in the decay J / ψ → K ¯ ∗ 0 ( 892 ) K + π − , and a qualitatively good fit to the data is achieved. The role of κ in the decay is discussed.

Identification and resolution of structural and algorithmic singularity in redundancy control of serial manipulations

AbstractA major difficulty that has haunted most researchers in the process of optimal redundancy resolution of robotic manipulators is the instability observed in even very simple numerical simulations. This numerical instability is not related to the structurally singular configurations of the manipulators, and in the literature has been referred to as “algorithmic singularity,” “artificial singularity,” or “unavoidable singularity.” In this work, conditions on both structural and algorithmic singularities are studied based on the Singular Value Decomposition of the Jacobian matrix, and, hence, a singularity‐free control algorithm for redundant manipulators is developed and resolved as the Lagrange problem of optimal control. It is shown that many well‐known methods for optimal redundant manipulation in the literature, including the Extended Jacobian Technique, most of constraint function‐based methods, and most of the previously reported methods on global optimization techniques, are all special cases of the formulation provided here. Further, the necessary conditions of the global optimality for this general formulation are derived in explicit form and the source of “algorithmic singularity” is rigorously identified and resolved. © 2995 John Wiley & Sons, Inc.

Artificial Singularity in the MultichannelND−1Equations of the New Strip Approximation

Artificial Singularity in the Multichannel<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mn /></mml:mrow></mml:msup></mml:mrow></mml:math>Equations of the New Strip Approximation

Artificial Singularity in the MultichannelND−1Equations of the New Strip Approximation

It is shown that the Wiener-Hopf technique introduced by Chew in the single-channel case to remove the artificial singularity near the strip boundary can be applied straightforwardly to the multichannel case. The singular $N{D}^{\ensuremath{-}1}$ equations are reduced to a system of Fredholm equations which can be solved directly by numerical methods. No new Wiener-Hopf operators arise.

Artificial Singularity in theNDEquations of the New Strip Approximation

The singularity introduced artificially into the equations of the new strip approximation, in order to bridge the gap between low and high energies, is investigated in detail. By explicit construction, it is shown that a necessary and sufficient condition for a (unique) solution of the $\frac{N}{D}$ equations to exist is that the unitarity constraint on the cross section just above the strip boundary should be obeyed. The only singularities of the solution in the right-half angular momentum plane ($\mathrm{Re}J\ensuremath{\ge}0$) are Regge poles.