arXiv subjects

Daniel Muller

Publications and source records attributed to Daniel Muller.

16 recordsLinked to original sources

arXiv2025

Six-dimensional cosmological models with conformal extensions

We consider the background cosmological solutions in the $6D$ (six-dimensional) model with one time and five space coordinates. The theory of our interest has the action composed by the Einstein term, cosmological constant, and two conformal terms constructed from the third powers of the Weyl tensor. It is shown how the highest derivative terms in the equations of motion can be isolated that opens the way for their numerical integration. There are flat anisotropic solutions which make one of the flat isotropic subspaces to be static. Depending on the value of bare cosmological constant, either two-dimensional or three-dimensional subspace can be static. In particular, there is a physically favorable solution with three ``large'' space coordinates and two extra inner dimensions stabilized. This solution is stable for a wide range of coupling constants, but this requires a special value of the bare cosmological constant.

gr-qc↗

arXiv2025

Initial conditions for Starobinsky inflation in general quadratic gravity

We consider initial conditions leading to Starobinsky inflation in the general quadratic gravity, where the action of the theory contains one more curvature square invariant in addition to $R^2$. We have chosen corresponding coefficients in a way so that the inflationary solution keeps to be stable. Our numerical results show that despite the configuration of initial conditions in the $(H,R)$ plane, leading to Starobinsky inflation can change considerably from the $R^2$ theory, realization of inflation does not need a fine-tuning of the initial conditions.

gr-qc↗

arXiv2023

Slow Solar Wind Connection Science during Solar Orbiter's First Close Perihelion Passage

The Slow Solar Wind Connection Solar Orbiter Observing Plan (Slow Wind SOOP) was developed to utilise the extensive suite of remote sensing and in situ instruments on board the ESA/NASA Solar Orbiter mission to answer significant outstanding questions regarding the origin and formation of the slow solar wind. The Slow Wind SOOP was designed to link remote sensing and in situ measurements of slow wind originating at open-closed field boundaries. The SOOP ran just prior to Solar Orbiter's first close perihelion passage during two remote sensing windows (RSW1 and RSW2) between 2022 March 3-6 and 2022 March 17-22, while Solar Orbiter was at a heliocentric distance of 0.55-0.51 and 0.38-0.34 au from the Sun, respectively. Coordinated observation campaigns were also conducted by Hinode and IRIS. The magnetic connectivity tool was used, along with low latency in situ data, and full-disk remote sensing observations, to guide the target pointing of Solar Orbiter. Solar Orbiter targeted an active region complex during RSW1, the boundary of a coronal hole, and the periphery of a decayed active region during RSW2. Post-observation analysis using the magnetic connectivity tool along with in situ measurements from MAG and SWA/PAS, show that slow solar wind, with velocities between 210 and 600 km/s, arrived at the spacecraft originating from two out of the three of the target regions. The Slow Wind SOOP, despite presenting many challenges, was very successful, providing a blueprint for planning future observation campaigns that rely on the magnetic connectivity of Solar Orbiter.

astro-ph.SR↗

arXiv2023

Wada Boundaries on a Hyperbolic Pair of Pants

In this paper the geodesics of an open multiply connected hyperbolic manifold are presented from the dynamical system point of view. The approach is completely numerical. Similar to the closed hyperbolic case there is a zero-measure set of periodic orbits. The difference is that now, most of the geodesics escape to infinity through one of the topologically distinct channels, and initial conditions are identified to which channel the orbit escapes. The initial condition mesh reveals basins of attraction to each channel. We verified that the basin boundary points are of the Wada type by two independent methods. We have also calculated the basin entropy of the system, and verified that it depends on the opening angle of the escape channels. The manifold chosen is the pair of pants together with the leaves, so there are $3$ distinct exit channels.

nlin.CD↗

arXiv2021

The Magnetic Origin of Solar Campfires

Solar campfires are fine-scale heating events, recently observed by Extreme Ultraviolet Imager (EUI), onboard Solar Orbiter. Here we use EUI 174\AA\ images, together with EUV images from SDO/AIA, and line-of-sight magnetograms from SDO/HMI to investigate the magnetic origin of 52 randomly selected campfires in the quiet solar corona. We find that (i) the campfires are rooted at the edges of photospheric magnetic network lanes; (ii) most of the campfires reside above the neutral line between majority-polarity magnetic flux patch and a merging minority-polarity flux patch, with a flux cancelation rate of $\sim$10$^{18}$Mx hr$^{-1}$; (iii) some of the campfires occur repeatedly from the same neutral line; (iv) in the large majority of instances, campfires are preceded by a cool-plasma structure, analogous to minifilaments in coronal jets; and (v) although many campfires have `complex' structure, most campfires resemble small-scale jets, dots, or loops. Thus, `campfire' is a general term that includes different types of small-scale solar dynamic features. They contain sufficient magnetic energy ($\sim$10$^{26}$-10$^{27}$ erg) to heat the solar atmosphere locally to 0.5--2.5MK. Their lifetimes range from about a minute to over an hour, with most of the campfires having a lifetime of $<$10 minutes. The average lengths and widths of the campfires are 5400$\pm$2500km and 1600$\pm$640km, respectively. Our observations suggest that (a) the presence of magnetic flux ropes may be ubiquitous in the solar atmosphere and not limited to coronal jets and larger-scale eruptions that make CMEs, and (b) magnetic flux cancelation is the fundamental process for the formation and triggering of most campfires.

astro-ph.SR↗

arXiv2021

Static cosmological solutions in quadratic gravity

We consider conditions for existence and stability of a static cosmological solution in quadratic gravity. It appears that such a solution for a Universe filled by only one type of perfect fluid is possible in a wide range of the equation of state parameter $w$ and for both positively and negatively spatially curved Universe. We show that the static solution for the negative curvature is always unstable if we require positive energy density of the matter content. On the other hand, a static solution with positive spatial curvature can be stable under certain restrictions. Stability of this solution with respect to isotropic perturbation requires that the coupling constant with the $R^2$ therm in the Lagrangian of the theory is positive, and the equations of state parameter $w$ is located in a rather narrow interval. Nevertheless, the stability condition does not require violation of the Strong Energy Condition. Taking into account anisotropic perturbations leads to further restrictions on the values of coupling constants and the parameter $w$.

gr-qc↗

arXiv2019

Relative Net Utility and the Saint Petersburg Paradox

The famous Saint Petersburg Paradox (St. Petersburg Paradox) shows that the theory of expected value does not capture the real-world economics of decision-making problems. Over the years, many economic theories were developed to resolve the paradox and explain gaps in the economic value theory in the evaluation of economic decisions, the subjective utility of the expected outcomes, and risk aversion as observed in the game of the St. Petersburg Paradox. In this paper, we use the concept of the relative net utility to resolve the St. Petersburg Paradox. Because the net utility concept is able to explain both behavioral economics and the St. Petersburg Paradox, it is deemed to be a universal approach to handling utility. This paper shows how the information content of the notion of net utility value allows us to capture a broader context of the impact of a decision's possible achievements. It discusses the necessary conditions that the utility function has to conform to avoid the paradox. Combining these necessary conditions allows us to define the theorem of indifference in the evaluation of economic decisions and to present the role of the relative net utility and net utility polarity in a value rational decision-making process.

econ.GN↗

arXiv2018

Automated Tactical Decision Planning Model with Strategic Values Guidance for Local Action-Value-Ambiguity

In many real-world planning problems, action's impact differs with a place, time and the context in which the action is applied. The same action with the same effects in a different context or states can cause a different change. In actions with incomplete precondition list, that applicable in several states and circumstances, ambiguity regarding the impact of the action is challenging even in small domains. To estimate the real impact of actions, an evaluation of the effect list will not be enough; a relative estimation is more informative and suitable for estimation of action's real impact. Recent work on Over-subscription Planning (OSP) defined the net utility of action as the net change in the state's value caused by the action. The notion of net utility of action allows for a broader perspective on value action impact and use for a more accurate evaluation of achievements of the action, considering inter-state and intra-state dependencies. To achieve value-rational decisions in complex reality often requires strategic, high level, planning with a global perspective and values, while many local tactical decisions require real-time information to estimate the impact of actions. This paper proposes an offline action-value structure analysis to exploit the compactly represented informativeness of net utility of actions to extend the scope of planning to value uncertainty scenarios and to provide a real-time value-rational decision planning tool. The result of the offline pre-processing phase is a compact decision planning model representation for flexible, local reasoning of net utility of actions with (offline) value ambiguity. The obtained flexibility is beneficial for the online planning phase and real-time execution of actions with value ambiguity. Our empirical evaluation shows the effectiveness of this approach in domains with value ambiguity in their action-value-structure.

cs.AI↗

arXiv2018

Economics of Human-AI Ecosystem: Value Bias and Lost Utility in Multi-Dimensional Gaps

In recent years, artificial intelligence (AI) decision-making and autonomous systems became an integrated part of the economy, industry, and society. The evolving economy of the human-AI ecosystem raising concerns regarding the risks and values inherited in AI systems. This paper investigates the dynamics of creation and exchange of values and points out gaps in perception of cost-value, knowledge, space and time dimensions. It shows aspects of value bias in human perception of achievements and costs that encoded in AI systems. It also proposes rethinking hard goals definitions and cost-optimal problem-solving principles in the lens of effectiveness and efficiency in the development of trusted machines. The paper suggests a value-driven with cost awareness strategy and principles for problem-solving and planning of effective research progress to address real-world problems that involve diverse forms of achievements, investments, and survival scenarios.

cs.AI↗

arXiv2012

Geodesic Motion on Closed Spaces: Two Numerical Examples

The geodesic structure is very closely related to the trace of the Laplace operator, involved in the calculation of the expectation value of the energy momentum tensor in Universes with non trivial topology. The purpose of this work is to provide concrete numerical examples of geodesic flows. Two manifolds with genus $g=0$ are given. In one the chaotic regions, form sets of negligible or zero measure. In the second example the geodesic flow, shows the presence of measurable chaotic regions. The approach is "experimental", numerical, and there is no attempt to an analytical calculation.

gr-qc↗

arXiv2007

Casimir Effect in $E^3$ closed spaces

As it is well known the topology of space is not totally determined by Einstein's equations. It is considered a massless scalar quantum field in a static Euclidean space of dimension 3. The expectation value for the energy density in all compact orientable Euclidean 3-spaces are obtained in this work as a finite summation of Epstein type zeta functions. The Casimir energy density for these particular manifolds is independent of the type of coupling with curvature. A numerical plot of the result inside each Dirichlet region is obtained.

gr-qc↗

arXiv2006

About Starobinsky inflation

It is believed that soon after the Planck era, space time should have a semi-classical nature. According to this, the escape from General Relativity theory is unavoidable. Two geometric counter-terms are needed to regularize the divergences which come from the expected value. These counter-terms are responsible for a higher derivative metric gravitation. Starobinsky idea was that these higher derivatives could mimic a cosmological constant. In this work it is considered numerical solutions for general Bianchi I anisotropic space-times in this higher derivative theory. The approach is ``experimental'' in the sense that there is no attempt to an analytical investigation of the results. It is shown that for zero cosmological constant $Λ=0$, there are sets of initial conditions which form basins of attraction that asymptote Minkowski space. The complement of this set of initial conditions form basins which are attracted to some singular solutions. It is also shown, for a cosmological constant $Λ> 0$ that there are basins of attraction to a specific de Sitter solution. This result is consistent with Starobinsky's initial idea. The complement of this set also forms basins that are attracted to some type of singular solution. Because the singularity is characterized by curvature scalars, it must be stressed that the basin structure obtained is a topological invariant, i.e., coordinate independent.

gr-qc↗

arXiv2004

Casimir Effect in Compact Universes

The Casimir effect in compact hyperbolic Universes was numerically obtained in previous publications. In this talk, I expose these results.

gr-qc↗

arXiv2002

Casimir energy density in closed hyperbolic universes

The original Casimir effect results from the difference in the vacuum energies of the electromagnetic field, between that in a region of space with boundary conditions and that in the same region without boundary conditions. In this paper we develop the theory of a similar situation, involving a scalar field in spacetimes with compact spatial sections of negative spatial curvature.

gr-qc↗

arXiv2001

Casimir energy in a small volume multiply connected static hyperbolic pre-inflationary Universe

A few years ago, Cornish, Spergel and Starkman (CSS), suggested that a multiply connected ``small'' Universe could allow for classical chaotic mixing as a pre-inflationary homogenization process. The smaller the volume, the more important the process. Also, a smaller Universe has a greater probability of being spontaneously created. Previously DeWitt, Hart and Isham (DHI) calculated the Casimir energy for static multiply connected flat space-times. Due to the interest in small volume hyperbolic Universes (e.g. CSS), we generalize the DHI calculation by making a a numerical investigation of the Casimir energy for a conformally coupled, massive scalar field in a static Universe, whose spatial sections are the Weeks manifold, the smallest Universe of negative curvature known. In spite of being a numerical calculation, our result is in fact exact. It is shown that there is spontaneous vacuum excitation of low multipolar components.

gr-qc↗

arXiv2000

Orbits in a Neighboring Dwarf Galaxy According to MOND

We study the orbits in the MOND theory within a dwarf galaxy of mass Md at a distance of ~100kpc from a neighboring galaxy of mass Mg, such as ours. It is assumed that a second mass m<<Md is gravitationally bound to Md by a previously calculated potential for the MOND theory. This potential is obtained for a free falling mass Md in a constant external gravitational acceleration field. The numerical technique of surfaces of section is used to study the stability of the phase-space orbits in the dwarf galaxy. Equatorial orbits with sufficiently small eccentricities e<0.65 are found to be stable with respect to small chang es in the initial conditions. (The equatorial plane is perpendicular to the direction of the external gravitational acceleration, which is along the line joining Md and Mg.) For decreasing values of the conserved component of the angular momentum, in the direction of the external gravitational acceleration, equatorial stability is lost.

astro-ph↗