Additive Constant Research Articles

Two fundamental constants of gravity unifying dark matter and dark energy

The common nature of the dark sector—dark energy and dark matter—as shown in Gurzadyan (arXiv:1712.10014, 2017) follows readily from the consideration of the generalized Newtonian potential as a weak-field version of General Relativity. The generalized potential satisfying Newton’s theorem on the equivalence of sphere’s gravity and that of a point mass located in its center contains an additional constant, which along with the gravitational constant is able to explain quantitatively both dark energy (the cosmological constant) and dark matter. So, gravity is defined not by one but two fundamental constants. We show that the second constant is dimension-independent and matter-uncoupled and hence is even more universal than the gravitational constant, thus affecting the strategy of observational studies of dark energy and of the search of dark matter.

Convergence of finite element approximation for electrical impedance tomography with the complete electrode model

This paper discusses the convergence of the finite element approximation for the forward problem of electrical impedance tomography with the complete electrode model. When the domain is polygonal and conforming finite element method is employed with linear triangle or tetrahedron elements, we prove that the estimated voltages on the electrodes converge to the true ones up to an additive constant, as the sizes of elements in the underlying mesh all tend to zero.

Experimental and theoretical analysis of the DMASP cantilever vibration behavior based on the MCS theory in moist environment

A micro cantilever (MC) and a probe are two main components of the atomic force microscope (AFM). The dimensions of these components are in micro scales while their oscillation amplitude is on a nanometer scale. The present study intended to not only increase the accuracy of the simulation with regard to geometric discontinuities based on the Timoshenko beam model using the modified couple stress (MCS) theory but also increase the accuracy of the prediction of a system behavior by considering the hysteresis effect into the system vibration equations based on Bouc–Wen model. Since, the classical theory disregarded the molecular structure of matter and neglected the microstructure size dependency, which raise its physical breakdowns in micro and nanoscale applications. Therefore, some micro continuum theories are developed to account for the microstructure effects by introducing additional material constants to the conventional ones. Due to the lack of the experimental results for this kind of MCs, this paper is focused on the both experimental and simulation results by utilizing the DMASP MC. The roughness of the surfaces affects the MC vibration behavior in the air medium. Therefore, surface roughness affecting van der Waals force has been considered in the air medium. Furthermore, the simulation results are compared with experimental results in the air medium with different moisture content during the surface topography. Due to the results, the best surface topography is achieved in the third vibration mode. Since the piezoelectric MC can tolerate the limited voltage, for this AFM MC type, the best surface topography is achieved in the third mode. Hence, this paper highly recommends using the third vibration mode during the surface topography. Finally, based on the EFAST method the most effective parameters on the AFM MC performance are the piezoelectric layer length, thickness and the probe length.

Critical plane–based multiaxial fatigue life prediction of turbine disk alloys by refining normal stress sensitivity

For engineering components subjected to complex multiaxial loadings, critical plane approaches like Fatemi–Socie criterion have been commonly utilized for life prediction of these components. Within the Fatemi–Socie criterion, the normal stress sensitivity parameter k is usually fitted from additional experimental data, which introduces inconvenience for practice especially under limited testing data conditions. In this regard, a simple critical plane–based damage parameter is put forward with no additional material constants, which attempts to provide a robust method for multiaxial fatigue analysis of turbine disk alloys. Using experimental datasets of TC4 and GH4169 alloys under different loadings, the proposed model provides better correlations with fatigue life of the two alloys than the models of Smith–Watson–Topper and Wang–Brown.

Ultimate Data Hiding in Quantum Mechanics and Beyond

The phenomenon of data hiding, i.e. the existence of pairs of states of a bipartite system that are perfectly distinguishable via general entangled measurements yet almost indistinguishable under LOCC, is a distinctive signature of nonclassicality. The relevant figure of merit is the maximal ratio (called data hiding ratio) between the distinguishability norms associated with the two sets of measurements we are comparing, typically all measurements vs LOCC protocols. For a bipartite $n\times n$ quantum system, it is known that the data hiding ratio scales as $n$, i.e. the square root of the real dimension of the local state space of density matrices. We show that for bipartite $n_A\times n_B$ systems the maximum data hiding ratio against LOCC protocols is $\Theta\left(\min\{n_A,n_B\}\right)$. This scaling is better than the previously obtained upper bounds $O\left(\sqrt{n_A n_B}\right)$ and $\min\{n_A^2, n_B^2\}$, and moreover our intuitive argument yields constants close to optimal. In this paper, we investigate data hiding in the more general context of general probabilistic theories (GPTs), an axiomatic framework for physical theories encompassing only the most basic requirements about the predictive power of the theory. The main result of the paper is the determination of the maximal data hiding ratio obtainable in an arbitrary GPT, which is shown to scale linearly in the minimum of the local dimensions. We exhibit an explicit model achieving this bound up to additive constants, finding that the quantum mechanical data hiding ratio is only of the order of the square root of the maximal one. Our proof rests crucially on an unexpected link between data hiding and the theory of projective and injective tensor products of Banach spaces. Finally, we develop a body of techniques to compute data hiding ratios for a variety of restricted classes of GPTs that support further symmetries.

Density-functional energy gaps of solids demystified

The fundamental energy gap of a solid is a ground-state second energy difference. Can one find the fundamental gap from the gap in the band structure of Kohn–Sham density functional theory? An argument of Williams and von Barth (WB), 1983, suggests that one can. In fact, self-consistent band-structure calculations within the local density approximation or the generalized gradient approximation (GGA) yield the fundamental gap within the same approximation for the energy. Such a calculation with the exact density functional would yield a band gap that also underestimates the fundamental gap, because the exact Kohn–Sham potential in a solid jumps up by an additive constant when one electron is added, and the WB argument does not take this effect into account. The WB argument has been extended recently to generalized Kohn–Sham theory, the simplest way to implement meta-GGAs and hybrid functionals self-consistently, with an exchange–correlation potential that is a non-multiplication operator. Since this operator is continuous, the band gap is again the fundamental gap within the same approximation, but, because the approximations are more realistic, so is the band gap. What approximations might be even more realistic?

Interface-Dependent Efficiency Tradeoff in Si-Based Carrier-Selective Solar Cells

Carrier-selective (CS) silicon solar cells are of recent research interest, and a variety of different materials have been investigated in this regard. However, the efficiency tradeoff with CS material/interface properties is not yet fully explored. In this context, through detailed analytical and numerical modeling, here we provide several interesting insights on the same. First, we show that perfect band alignment is a desirable feature only if the interface is devoid of any trap states. Otherwise, a band offset of around 0.2–0.4 eV provides sufficient band bending to reduce the effect of interface recombination, thus improving the performance. Surprisingly, the interface passivation quality for the minority carrier extraction layer is found to be far less demanding than that for the majority carrier extraction layer. In addition, doping density and dielectric constant of CS layers have a similar effect as band offset on solar cell performance. Our results have obvious implications toward the selection of appropriate materials as CS layers, and hence, are of broad interest to the community.

Linear and quadratic ranges in representation stability

We prove two general results concerning spectral sequences of FI-modules. These results can be used to significantly improve stable ranges in a large portion of the stability theorems for FI-modules currently in the literature. We work this out in detail for the cohomology of configuration spaces where we prove a linear stable range and the homology of congruence subgroups of general linear groups where we prove a quadratic stable range. Previously, the best stable ranges known in these examples were exponential. Up to an additive constant, our work on congruence subgroups verifies a conjecture of Djament.

Degenerate Hessian structures on radiant manifolds

We present a rigorous mathematical treatment of Ruppeiner geometry, by considering degenerate Hessian metrics defined on radiant manifolds. A manifold [Formula: see text] is said to be radiant if it is endowed with a symmetric, flat connection and a global vector field [Formula: see text] whose covariant derivative is the identity mapping. A degenerate Hessian metric on [Formula: see text] is a degenerate metric tensor that can locally be written as the covariant Hessian of a function, called potential. A function on [Formula: see text] is said to be extensive if its Lie derivative with respect to [Formula: see text] is the function itself. We show that the Hessian metrics appearing in equilibrium thermodynamics are necessarily degenerate, owing to the fact that their potentials are extensive (up to an additive constant). Manifolds having degenerate Hessian metrics always contain embedded Hessian submanifolds, which generalize the manifolds defined by constant volume in which Ruppeiner geometry is usually studied. By means of examples, we illustrate that linking scalar curvature to microscopic interactions within a thermodynamic system is inaccurate under this approach. In contrast, thermodynamic critical points seem to arise as geometric singularities.

Invariants for Rari- and Multi-Constant Theories with Generalization to Anisotropy in Biological Tissues

The rari-constant theory of linear elasticity is based on the assumption that elasticity in solids is caused by only pair potentials with coaxial forces acting between atoms. The strain energy of each pair potential depends on the square of the strain between the atoms in the pair. This strain can be determined by taking the inner product of the strain tensor with a structural tensor that is the tensor product of a unit vector with itself. It is shown that the 15 independent constants in the rari-constant theory can be generated by a complete set of 15 structural tensors. It is also shown that the 6 additional independent constants in the multi-constant theory can be generated by taking the inner product of 6 of these structural tensors with the square of the strain tensor. A generalization of these results for nonlinear elasticity is discussed with reference to recent work which compares the structural and generalized structural tensor approaches to modeling fibrous tissues.

Experiencia mexicana en el diseño de seguros ganaderos paramétricos satelitales de tipo catastrófico: bases conceptuales y teóricas

El desarrollo de instrumentos de gestión de riesgos climáticos permite instrumentar acciones de adaptación ante el cambio climático, además de hacer ef iciente el uso de recursos f inancieros para mitigar los impactos. En México, el empleo de estos instrumentos no se ha documentado, por lo que en este trabajo se desarrolla un marco conceptual-teórico para la instrumentación de seguros ganaderos paramétricos satelitales, con la f inalidad de exponer sus ventajas y delimitar sus alcances. Para tal f in, se aplicaron los conceptos de unidad de riesgo, umbral de pago y elementos asociados al seguro, para establecer el riesgo climático que se asocia a las actividades agropecuarias, principalmente por sequías. Bajo el requerimiento crítico de una relación lineal entre el índice espectral y la biomasa vegetal, sin constante aditiva, se usó el índice espectral NDVIcp, optimizado por diversos efectos, lo que dio lugar al desarrollo de un esquema de seguro técnicamente sólido, sin el requisito de contar con información histórica de producción agropecuaria y que, además, refleja f ielmente la realidad en campo. Todo lo anterior, permitió sentar las bases para el diseño de un seguro ganadero paramétrico satelital de tipo catastróf ico sólido, transparente y conceptualmente accesible a los usuarios del mismo.

Evaluation and comparison of critical plane criteria for multiaxial fatigue analysis of ductile and brittle materials

This paper conducts a comparative evaluation on typical critical plane criteria, including Fatemi-Socie, Wang-Brown, modified Smith-Watson-Topper (MSWT) and proposed modified generalized strain energy (MGSE) criteria for multiaxial fatigue analysis of ductile/brittle materials. Experimental datasets of four materials under uniaxial tension, torsion and proportional/non-proportional multiaxial loadings are introduced for model comparison. This study results indicate that criteria with additional material constants yield robust life predictions for different materials. Moreover, the criteria with shear and uniaxial fatigue properties are respectively suitable for ductile and brittle materials, particularly the MGSE superior to others for ductile/brittle materials while MSWT only for brittle materials.

Exact solutions for elastic response in micro- and nano-beams considering strain gradient elasticity

This paper presents the exact solutions derived for the static bending response of simply supported isotropic micro- and nano-beams. The governing differential equations of equilibrium and the associated boundary conditions for the beam are derived by applying the variational principle over the internal energy functional involving strain and strain gradient terms. The Mindlin’s Form II model for higher order metrics of energy involving strain gradient terms and three additional material length constants has been used for the current formulation. Constitutive relations for stress and the higher order stress in an isotropic solid, which are the conjugates of strain and strain gradient, respectively, are provided in this paper. The exact solutions for the displacement vector are obtained by solving the governing differential equations. The significance of the gradients and the corresponding conjugates are studied using numerical examples of micro- and nano-beams. These results are compared with those obtained from the classical model of elasticity for structures which does not involve strain gradients. Due to the consideration of strain gradients, the structures exhibit a significant increase in stiffness as the beam dimensions are reduced. The profiles for stress developed across the thickness are presented to study the change in the behavior of the structures at a micro- and nano-level. The importance of considering strain gradients for the design of low-dimensional structures in sensitive applications is noted. The exact solutions developed in this paper can be used as benchmark solutions for validating further research on the behavior of low-dimensional bodies using computational models and experiments. The present study calls for the development of new failure theory of isotropic materials possessing strain gradients.

Convergence and Efficiency of Adaptive Importance Sampling Techniques with Partial Biasing

We propose a new Monte Carlo method to efficiently sample a multimodal distribution (known up to a normalization constant). We consider a generalization of the discrete-time Self Healing Umbrella Sampling method, which can also be seen as a generalization of well-tempered metadynamics. The dynamics is based on an adaptive importance technique. The importance function relies on the weights (namely the relative probabilities) of disjoint sets which form a partition of the space. These weights are unknown but are learnt on the fly yielding an adaptive algorithm. In the context of computational statistical physics, the logarithm of these weights is, up to an additive constant, the free-energy, and the discrete valued function defining the partition is called the collective variable. The algorithm falls into the general class of Wang–Landau type methods, and is a generalization of the original Self Healing Umbrella Sampling method in two ways: (i) the updating strategy leads to a larger penalization strength of already visited sets in order to escape more quickly from metastable states, and (ii) the target distribution is biased using only a fraction of the free-energy, in order to increase the effective sample size and reduce the variance of importance sampling estimators. We prove the convergence of the algorithm and analyze numerically its efficiency on a toy example.

Rate Constants for the Reactions of OH Radical with the ( E)/( Z) Isomers of CF3CF═CHCl and CHF2CF═CHCl.

The rate constants for the reactions of OH radical with ( E)- and ( Z)-isomers of CF3CF═CHCl and CHF2CF═CHCl have been measured over the temperature range of 250-430 K. Kinetic measurements have been performed using flash and laser photolysis methods combined with laser-induced fluorescence. Arrhenius rate constants have been determined as k(( E)-CF3CF═CHCl) = (1.09 ± 0.03) × 10-12 · exp[(50 ± 10)K/ T], k(( Z)-CF3CF═CHCl) = (8.02 ± 0.19) × 10-13 · exp[-(100 ± 10)K/ T], k(( E)-CHF2CF═CHCl) = (1.50 ± 0.03) × 10-12 · exp[(160 ± 10)K/ T], and k(( Z)-CHF2CF═CHCl) = (1.36 ± 0.03) × 10-12 · exp[(360 ± 10)K/ T] cm3 molecule-1 s-1. Infrared absorption spectra have also been measured at room temperature. The atmospheric lifetimes of ( E)-CF3CF═CHCl, ( Z)-CF3CF═CHCl, ( E)-CHF2CF═CHCl, and ( Z)-CHF2CF═CHCl have been estimated as 8.9, 20, 4.6, and 2.6 days, respectively, and their global warming potentials and ozone depletion potentials were determined as 0.23, 0.88, 0.060, and 0.016 and 0.00010, 0.00023, 0.000057, and 0.000030, respectively. Additionally, the rate constants for OH radical addition and IR spectra of these compounds were determined computationally. Consistent with experiment, our calculations indicate that the reactivity toward OH radical addition is reduced as ( Z)-CHF2CF═CHCl > ( E)-CHF2CF═CHCl > ( E)-CF3CF═CHCl > ( Z)-CF3CF═CHCl, where the ( E)/( Z) reactivity is reversed for CF3CF═CHCl and CHF2CF═CHCl. The calculations reproduced the observed temperature dependencies of the rate constants for the OH radical reactions, which is slightly positive for ( Z)-CF3CF═CHCl but negative for the other compounds.

EPR spectroscopy determination of the rate constants for addition of [O4S]•– radical anion to double bonds

The rate constants for addition of the radical anion [O4S]•– at C=C and C=O double bonds of N,N-dimethylacrylamine have been evaluated by the electron paramagnetic resonance technique.

Teaching systems thinking to general education students

Under the proposition that all college students are able to learn to think in more systemic ways, and understand the value of systems modeling for assisting their thinking, I designed a course for freshmen with no more than basic algebra. In this course the students were exposed to basic systems concepts with a focus on system dynamics modeling (using Donella Meadows’ Thinking in Systems) of a permaculture-based food production system. They were given a basic problem: How much land area would be needed to collect enough solar energy in food plant photosynthesis per year to feed a community of fifty vegetarians? They were told that the farm would be in the Seattle WA, USA area so they could find the average monthly insolation values. Several additional rate constants and conversion factors were provided so they could build a spreadsheet-based model to generate the number of calories needed.This paper provides anecdotal evidence that systems theory naïve students were able to successfully build a model (in teams) but also were able to apply systems thinking to aspects of their own lives as demonstrated in essays (individuals). Many students reported “seeing the world differently” as a result of the course, particularly seeing how different aspects of the world are connected through various relations. As a result of these successes the course was upgraded to be a little more advanced for upper division students.2Problem-Project-based Learning - PPBL, a pedagogy for active learning.

Energy-based anomaly detection for mixed data

Anomalies are those deviating significantly from the norm. Thus, anomaly detection amounts to finding data points located far away from their neighbors, i.e., those lying in low-density regions. Classic anomaly detection methods are largely designed for single data type such as continuous or discrete. However, real-world data is increasingly heterogeneous, where a data point can have both discrete and continuous attributes. Mixed data poses multiple challenges including (a) capturing the inter-type correlation structures and (b) measuring deviation from the norm under multiple types. These challenges are exaggerated under (c) high-dimensional regimes. In this paper, we propose a new scalable unsupervised anomaly detection method for mixed data based on Mixed-variate Restricted Boltzmann Machine (Mv.RBM). The Mv.RBM is a principled probabilistic method that estimates density of mixed data. We propose to use free energy derived from Mv.RBM as anomaly score as it is identical to data negative log-density up to an additive constant. We then extend this method to detect anomalies across multiple levels of data abstraction, an effective approach to deal with high-dimensional settings. The extension is dubbed \(\mathtt {MIXMAD}\), which stands for MIXed data Multilevel Anomaly Detection. In \(\mathtt {MIXMAD}\), we sequentially construct an ensemble of mixed-data Deep Belief Nets (DBNs) with varying depths. Each DBN is an energy-based detector at a predefined abstraction level. Predictions across the ensemble are finally combined via a simple rank aggregation method. The proposed methods are evaluated on a comprehensive suit of synthetic and real high-dimensional datasets. The results demonstrate that for anomaly detection, (a) a proper handling of mixed types is necessary, (b) free energy is a powerful anomaly scoring method, (c) multilevel abstraction of data is important for high-dimensional data, and (d) empirically Mv.RBM and \(\mathtt {MIXMAD}\) are superior to popular unsupervised detection methods for both homogeneous and mixed data.

Quantifying Competitiveness in Paging with Locality of Reference

The classical paging problem is to maintain a two-level memory system so that a sequence of requests to memory pages can be served with a small number of faults. Standard competitive analysis gives overly pessimistic results as it ignores the fact that real-world input sequences exhibit locality of reference. Initiated by a paper of Borodin et al. (J Comput Syst Sci 50:244–258, 1995) there has been considerable research interest in paging with locality of reference. In this paper we study the paging problem using an intuitive and simple locality model that records inter-request distances in the input. A characteristic vector mathcal{C} defines a class of request sequences with certain properties on these distances. The concept was introduced by Panagiotou and Souza (In: Proceedings of 38th annual ACM symposium on theory of computing (STOC), 2006). As a main contribution we develop new and improved bounds on the performance of important paging algorithms. A strength and novelty of the results is that they express algorithm performance in terms of locality parameters. In a first step we develop a new lower bound on the number of page faults incurred by an optimal offline algorithm opt. The bound is tight up to a small additive constant. Technically, the result relies on a new approach of relating the number of page faults to the number of memory hits and amortizing suitably. Based on these expressions for opt’s cost, we obtain nearly tight upper and lower bounds on lru’s competitiveness, given any characteristic vector mathcal{C}. Furthermore, we compare lru to fifo and fwf. For the first time we show bounds that quantify the difference between lru’s performance and that of the other two strategies. The results imply that lru is strictly superior on inputs with a high degree of locality of reference. There exist general input families for which lru achieves constant competitive ratios whereas the guarantees of fifo and fwf tend to k, the size of the fast memory. Finally, we report on an experimental study that demonstrates that our theoretical bounds are very close to the experimentally observed ones. Hence our contributions bring competitive paging again closer to practice.

Correcciones atmosféricas relativas de imágenes de satélite: patrones invariantes y modelos atmosféricos

To use information obtained with satellite technology reliably, it is necessary to eliminate or reduce the disruptive effects associated with the spectral information captured by sensors on space platforms. In this paper we analyze the inversion of radiative models of the atmosphere, which consists in determining the additive and multiplicative constants in each spectral band to make the necessary atmospheric corrections. The methodology proposes the use of invariant patterns of soil lines and dense vegetation for the inversion of radiative models. The results showed that, without knowledge of the atmospheric model or the type of aerosol, soil line data were relatively insufficient (low correlation) to obtain the additive and multiplicative constants of the atmospheric inversions, with problems of multiple solutions in the inversion process. Under similar conditions, the same was found for additive constants with the dense vegetation line, but for the multiplicative constants the results were favorable (R2 > 0.9). In contrast, with the knowledge of the atmospheric model and the aerosol model, estimates of additive and multiplicative constants were highly satisfactory (R2 > 0.99) in both cases. For soil line inversions, only one constraint of the two available was used. In conclusion, the use of invariant soil-line patterns allows us to establish two basic relationships to invert the radiative simulations of the atmosphere, prior to functional compaction, and field measurements can be made so that the proposed atmospheric correction process in this work can be considered in absolute and not relative terms.