Value Of Critical Mass Research Articles

Advancing nuclear science education through IRL Integration: A case experiment on criticality mass determination at the Kartini research reactor

Research reactors serve critical roles across multiple domains—from physics to medicine—while distinctly not being used for electrical power generation. The Kartini Research Reactor located in Indonesia exemplifies the integration of research reactors in education and scientific research, particularly highlighting its educational applications through the Internet Reactor Laboratory (IRL). Established in 1978 and operational since 1979, the Training Research and Isotope Production by General Atomic (TRIGA) Mark II reactor is instrumental in advancing nuclear science with facilities like the Lazy Suzan/Rotate Rack and Beam Port. The IRL significantly enhances its educational process, enabling remote access to reactor physics experiments, thus facilitating global university participation in nuclear engineering education. This capability allows for the real-time visualization of reactor operations and detailed presentation of operational data and experiment results, enriching the learning experience. This paper demonstrates the Kartini Reactor's educational utility through a case study investigating reactor criticality and determining the critical fuel mass under safe operational parameters. Employing telecommunication hardware and software, the study achieved reactor criticality by inserting 5 fuel elements, totaling 2524.57 g. The critical mass determination was further refined by plotting the inverse of counts against the total mass of U-235. This approach utilized both polynomial and linear trend lines to analyze the data. While the polynomial analysis provided upper and lower thresholds for critical mass, the linear regression offered a precise critical mass value of 2428.62 g, showcasing a deviation of only 4% from the experimental findings.

Research Classification using the Malaysian Research and Development Classification System (MRDCS)

Classifying research projects or research publication into research areas is crucial in many statistical analyses including for example in bibliometric analysis. Research publication classification usually takes place at the level of journals, where subject categories based on available databases like the Web of Science or SciVal are some of the popular classification systems. However, journal-level classification systems have limitation especially when classifying multidisciplinary journals. To overcome this limitation, it is suggested that a classification system that can classify research be constructed based on the areas of research proposals and their related publications. Successful grant applications/research projects and their publications were clustered into research areas based on the Malaysian Research and Development Classification System (MRDCS) (6th Edition). A total of 1738 research projects managed by Universiti Malaya’s Research Cluster from year 2015 to 2017 were mapped. The strengths and the limitations of the proposed classification system are also discussed. Results indicate that out of the 20 research categories, Medical and Health Sciences, Social Sciences, Economics, Business and Management, Humanities, and Engineering and Technology emerge as the top five research categories with the highest critical mass value based on the number of projects. Classification mapping also found Engineering and Technology, Medical and Health Sciences, Material Sciences, Social Sciences, and Applied Sciences and Technologies to be the top five research categories that produced the highest number of outputs in terms of publications.

NLS ground states on the half-line with point interactions

We investigate the existence and the uniqueness of NLS ground states of fixed mass on the half-line in the presence of a point interaction at the origin. The nonlinearity is of power type, and the regime is either L^{2}-subcritical or L^{2}-critical, while the point interaction is either attractive or repulsive. In the L^{2}-subcritical case, we prove that ground states exist for every mass value if the interaction is attractive, while ground states exist only for sufficiently large masses if the interaction is repulsive. In the latter case, if the power is less or equal to four, ground states coincide with the only bound state. If instead, the power is greater than four, then there are values of the mass for which two bound states exist, and neither of the two is a ground state, and values of the mass for which two bound states exist, and one of them is a ground state. In the L^{2}-critical case, we prove that ground states exist for masses strictly below a critical mass value in the attractive case, while ground states never exist in the repulsive case.

Periodic orbits in the neighborhood of the triangular equilibrium points in the photogravitational restricted three body problem – Part 1

Objective: To find the periodic orbits using Fourier series expansions around the libration points L4 and L5 in the frame work of planar restricted threebody by considering the more massive primary a source of radiation.Methods/Statistical analysis: Period of the periodic orbits around the libration point L4 is found using the variational equations and function of the two finite masses. The period is independent on the size the orbit. When terms of higher order are retained in the analysis the period depends on the size of the orbit. Findings: The value of the critical mass is found in the photogravitational restricted three–body problem and is shown that the critical mass value corresponding to the small mass increases with the size of the orbit. It is shown that the classes of periodic orbits with infinitesimal limiting orbits L4 exist for values of the small mass greater than the critical mass value m0: A comparison between these orbits with and without radiation pressure is made. Applications: Periodic orbits can be used to explore small solar system bodies, including asteroids and comets. Perturbation due to solar radiation pressure has to be understood and should be taken care of during human exploration mission. Keywords: Photogravitational restricted problem; triangular liberation point; periodic orbits; solar radiation pressure; Fourier series expansions

Polyethylene loss of ductility during oxidation: Effect of initial molar mass distribution

This paper reports a study of thermal oxidation induced embrittlement in several polyethylene grades differing mainly by the broadness of the molar mass distribution (ranging for lower than 3 to more than 30). Thermal oxidation was monitored at macromolecular scale (Gel Permeation Chromatography, Differential Scanning Calorimetry) and macroscopic scale (tensile tests). As expected, the samples undergo predominant chain scission and plastic deformation is suppressed below a critical molar mass value (M’C). Even though this latter was previously reported to be independent of the initial weight average molar mass, it is shown here that it depends on initial polydispersity index. Samples were also shown to undergo chemicrystallization, i.e. that segments released by chain scissions migrate into the crystalline phase with a yield increasing with initial polydispersity index. Finally, the main novelty of this work is to evidence that the previously proposed end-of-life criteria at macromolecular level linked to loss of ductility (critical molar mass, crystallization yield) depend on the initial polydispersity index.

Critical mass of public goods and its coevolution with cooperation

In this study, the enhancing parameter represented the value of the public goods to the public in public goods game, and was rescaled to a Fermi–Dirac distribution function of critical mass. Public goods were divided into two categories, consumable and reusable public goods, and their coevolution with cooperative behavior was studied. We observed that for both types of public goods, cooperation was promoted as the enhancing parameter increased when the value of critical mass was not very large. An optimal value of critical mass which led to the best cooperation was identified. We also found that cooperations emerged earlier for reusable public goods, and defections became extinct earlier for the consumable public goods. Moreover, we observed that a moderate depreciation rate for public goods resulted in an optimal cooperation, and this range became wider as the enhancing parameter increased. The noise influence on cooperation was studied, and it was shown that cooperation density varied non-monotonically as noise amplitude increased for reusable public goods, whereas decreased monotonically for consumable public goods. Furthermore, existence of the optimal critical mass was also identified in other three regular networks. Finally, simulation results were utilized to analyze the provision of public goods in detail.

On the stability of triangular points in the relativistic R3BP with oblate primaries and bigger radiating

We consider a version of the relativistic R3BP which includes the effects of oblateness of the primaries and radiation of the bigger primary as well on the stability of triangular points. We observe that the positions of the triangular points and their stability are affected by the relativistic effect apart from the radiation and oblateness of the primaries. It is further seen for these points that the range of stability region increases or decreases according as the part of the critical mass value, depending upon relativistic terms, radiation and oblateness coefficients, is positive or negative. A numerical exploration shows that in the Sun–Saturn, Sun–Uranus, Sun–Neptune systems, the oblateness has no influence on their positions and range of stability region; whereas it has a little influence on the Sun–Mars, Sun–Jupiter systems. On the other hand, we found that radiation pressure has an observable effect on the solar system.

Combined effect of oblateness, radiation and a circular cluster of material points on the stability of triangular liberation points in the R3BP

This paper studies the motion of an infinitesimal mass in the framework of the restricted three-body problem (R3BP) under the assumption that the primaries of the system are radiating-oblate spheroids, enclosed by a circular cluster of material points. It examines the effects of radiation and oblateness up to J4 of the primaries and the potential created by the circular cluster, on the linear stability of the liberation locations of the infinitesimal mass. The liberation points are found to be stable for 0<μ<μc and unstable for \(\mu_{c}\le\mu\le\frac{1}{2}\), where μc is the critical mass value depending on terms which involve parameters that characterize the oblateness, radiation forces and the circular cluster of material points. The oblateness up to J4 of the primaries and the gravitational potential from the circular cluster of material points have stabilizing propensities, while the radiation of the primaries and the oblateness up to J2 of the primaries have destabilizing tendencies. The combined effect of these perturbations on the stability of the triangular liberation points is that, it has stabilizing propensity.

The influence of triaxiality and oblateness on the triangular points of double pulsars in the ER3BP

We consider the motion of a test particle around a triaxial primary and an oblate companion orbiting each other in elliptic orbits about their common barycenter in the neighborhood of triangular libration points. The positions and stability of these points are influenced by the triaxiality and oblateness of the primary and secondary, and by the semi-major axis and eccentricity of the orbits. The triangular points are stable for 0<μ<μc; where μ is the mass ratio (μ≤1/2) and μc is the critical mass value influenced by the eccentricity, oblateness, semi major axis and triaxiality factors. The size of the region of stability increases with decreasing values of triaxiality and oblateness. An application of the results obtain to double neutron star binaries results show that the positions and stability of the triangular points of PSR J1518+4904, PSR B1534+12, PSR B1914+16 and PSR B2127+11c are affected by the parameters in the systems’ dynamics.

Reduction the secular solution to periodic solution in the generalized restricted three-body problem

The aim of the present work is to reduce the secular solution around the triangular equilibrium points to periodic solution in the frame work of the generalized restricted thee-body problem. This model is generalized in sense that both the primaries are oblate and radiating as well as the gravitational potential from a belt. We show that the linearized equation of motion of the infinitesimal body around the triangular equilibrium points has a secular solution when the value of mass ratio equals the critical mass value. Moreover, we reduce this solution to periodic solution, as well as some numerical and graphical investigations for the effects of the perturbed forces are introduced. This model can be used to examine the existence of a dust particle near the triangular points of an oblate and radiating binary stars system surrounded by a belt.

Application of binary pulsars to axisymmetric bodies in the Elliptic R3BP

Binary systems hosting astrophysical compact objects such as white dwarfs and/or neutron stars provide excellent test beds for studying the impact of the oblateness of the main bodies in the restricted three-body problem (R3BP). The case is investigated when the primary bodies are non-luminous, non-spherical (oblate) bodies and the third body of infinitesimal mass is also an oblate spheroid. The existence of extra solar planets orbiting these systems constitutes a three-body problem which makes them excellent models for this axisymmetric ER3BP. The positions of the equilibrium points are affected by the oblateness parameters of the three-bodies; this is shown for double neutron star binaries. The triangular points are stable for 0<μ<μc; where μ is the mass ratio (μ≤1/2) and μc is the critical mass value influenced by the eccentricity, semi major axis and oblateness factors. The size of the region of stability increases with decreasing values of the oblateness. The oblateness of the system’s bodies does not affect the nature of the stability of the collinear points since they remain unstable. Due to the almost equal masses of the primaries, our study shows that even the triangular points of these systems are unstable.

The effect of oblateness in the perturbed restricted three-body problem

In this paper the restricted three-body problem is generalized in the sense that the effects of oblateness of the three participating bodies as well as the small perturbations in the Coriolis and centrifugal forces are considered. The existence of equilibrium points, their linear stability and the periodic orbits around these points are studied under these effects. It is found that the positions of the collinear points and y-coordinate of the triangular points are not affected by the small perturbations in the Coriolis force. While x-coordinate of the triangular points is neither affected by the small perturbations in the Coriolis force nor the oblateness of the third body. Furthermore, the critical mass value and the elements of periodic orbits around the equilibrium points such as the semi-major and the semi-minor axes, the angular frequencies and corresponding periods may change by all the parameters of oblateness as well as the small perturbations in the Coriolis and centrifugal forces. This model could be applicable to send satellite or place telescope in stable regions in space.

Stability of the Triangular Points Under Combined Effects of Radiation and Oblateness in the Restricted Three-Body Problem

This paper deals with the existence of triangular points and their linear stability when the primaries are oblate spheroid and sources of radiation considering the effect of oblateness up to 10−6 of main terms in the restricted three-body problem; we see that the locations of the triangular points are affected by the oblateness of the primaries and solar radiation pressure. It is further seen that these points are stable for 0 ≤ μ ≤μ c ; and unstable for μ c ≤ μ ≤1/2; where μ c is the critical mass value depending on terms which involve parameters that characterize the oblateness and radiation repulsive forces such that $$ \mu_{c} \in (0,1/2) $$ ; in addition to this an algorithm has been constructed to calculate the critical mass value.

On the Spectrum of Lattice Massive SU(2) Yang–Mills

On the basis of extended simulations we provide some results concerning the spectrum of Massive SU(2) Yang-Mills on the lattice. We study the "time" correlator of local gauge invariant operators integrated over the remaining three dimensions. The energy gaps are measured in the isospin I=0,1 and internal spin J=0,1 channels. No correlation is found in the I=1,J=0 channel. In the I=1, J=1 channel and far from the critical mass value $m_c$ the energy gap roughly follows the bare value $m$ (vector mesons). In approaching the critical value $m_c$ at $\beta$ fixed, there is a bifurcation of the energy gap: one branch follows the value $m$, while the new is much larger and it shows a more and more dominant weight. This phenomenon might be the sign of two important features: the long range correlation near the fixed point at $\beta \to \infty$ implied by the low energy gap and the screening (or confining) mechanisms across the $m=m_c$ associated to the larger gap. The I=0, J=0,1 gaps are of the same order of magnitude, typically larger than the I=1, J=1 gap (for $m>>m_c$). For $m\sim m_c$ both I=0 gaps have a dramatic drop with minima near the value $m$. This behavior might correspond to the formation of I=0 bound states both in the J=0 and J=1 channels.

Black hole evaporation within a momentum-dependent metric

We investigate the black hole thermodynamics in a ``deformed'' relativity framework where the energy-momentum dispersion law is Lorentz-violating and the Schwarzchild-like metric is momentum-dependent with a Planckian cutoff. We obtain net deviations of the basic thermodynamical quantities from the Hawking-Bekenstein predictions: actually, the black hole evaporation is expected to quit at a nonzero critical mass value (of the order of the Planck mass), leaving a zero temperature remnant, and avoiding a spacetime singularity. Quite surprisingly, the present semiclassical corrections to black hole temperature, entropy, and heat capacity turn out to be identical to the ones obtained within some quantum approaches.

Combined effects of perturbations, radiation and oblateness on the periodic orbits in the restricted three-body problem

This paper investigates the periodic orbits around the triangular equilibrium points for 0<μ<μc, where μc is the critical mass value, under the combined influence of small perturbations in the Coriolis and the centrifugal forces respectively, together with the effects of oblateness and radiation pressures of the primaries. It is found that the perturbing forces affect the period, orientation and the eccentricities of the long and short periodic orbits.

Numerical requirements for simulations of self-gravitating and non-self-gravitating discs

We define three requirements for accurate simulations that attempt to model circumstellar discs and the formation of collapsed objects (e.g. planets) within them. First, we define a resolution requirement based on the wavelength for neutral stability of self-gravitating waves in the disc, where a Jeans analysis does not apply. For particle-based or grid-based simulations, this criterion takes the form, respectively, of a minimum number of particles per critical (‘Toomre’) mass or maximum value of a ‘Toomre number’, T=δx/λT, where the wavelength, λT, is the wavelength for neutral stability for waves in discs. The requirements are analogues of the conditions for cloud collapse simulations as discussed in Bate & Burkert and Truelove et al., where the required minimum resolution was shown to be twice the number of neighbours per Jeans mass or four–five times the local Jeans wavelength, λJ, for particle or grid simulations, respectively. We apply our criterion to particle simulations of disc evolution and find that in order to prevent numerically induced fragmentation of the disc, the Toomre mass must be resolved by a minimum of six times the average number of neighbour particles used. We investigate the origin of the apparent discrepancy between the number of particles required by the cloud and disc fragmentation criteria and find that it is due largely to ambiguities in the definition of the Jeans mass, as used by different authors. We reconcile the various definitions, and when an identical definition of the Jeans mass is used, the condition that J≲ 1/4 in the Truelove condition is equivalent to requiring about 10–12 times the average number of neighbour particles per Jeans mass in a smoothed particle hydrodynamics (SPH) simulation, reducing the difference between simulations of discs and clouds to about two. While the numbers of particles per critical mass are similar for both the Jeans and Toomre formalisms, the Toomre requirement is more restrictive than the Jeans requirement when the local value of the Toomre stability parameter Q falls below about one half. Second, we require that particle-based simulations with self-gravity use a variable gravitational softening, in order to avoid inducing fragmentation by an inappropriate choice of softening length. We show that using a fixed gravitational softening length for all particles can lead either to artificial suppression or enhancement of structure (including fragmentation) in a given disc, or both in different locations of the same disc, depending on the value chosen for the softening length. Unphysical behaviour can occur whether or not the system is properly resolved by the new Toomre criterion. Third, we require that three-dimensional SPH simulations resolve the vertical structure with at least ∼4 particle smoothing lengths per scaleheight at the disc mid-plane, a value which implies a substantially larger number per vertical column because the disc itself extends over many scaleheights. We suggest that a similar criterion applies to grid-based simulations. We demonstrate that failure to meet this criterion leads to underestimates in the mid-plane density of up to 30–50 per cent at resolutions common in the literature. As a direct consequence, gas pressures will be dramatically underestimated and simulations of self-gravitating systems may artificially and erroneously inflate the likelihood of fragmentation. We outline an additional condition on the vertical resolution in simulations that include radiative transfer in order to ensure a correct description of the cooling, specifically that the temperature structure near the disc photosphere must be well resolved. As an example, we demonstrate that for an isentropic vertical structure, the criterion translates into resolution comparable to H/20 near the disc photosphere, to avoid serious errors in transfer rates of thermal energy in and out of the disc. Finally, we discuss results in the literature that purport to form collapsed objects and conclude that many are likely to have violated one or more of our criteria, and have therefore made incorrect conclusions regarding the likelihood for fragmentation and planet formation.

A Detailed Reassessment of the Criticality Property of Pure241 Am

We present results of new calculations of criticality of pure 241Am using several basic evaluated neutron-nuclear cross section databases. The re-assessment of the criticality property of 241Am presented in this paper is relevant to studies of criticality safety, nuclear waste incineration and non-proliferation. Our calculations start from the basic evaluated nuclear data files and use the NJOY-MCNP code system. This paper invalidates the earlier conclusion and belief in a section of the national and international literature that the minor actinide241 Am is better than 235U or 239Pu as a nuclear fuel. Further our calculated critical mass is larger by 28% than the 197kg reported in 1997 by Nojiri and Fukasaku who used the SCALE-4.3 system using the same ENDF/B-IV data, showing that there is large discrepancy due to the use of different computational codes and/or QA in nuclear data processing. Our calculated value of critical mass using JENDL-3.2 is 75kg. This result is essentially in agreement with Nojiri and Fukasaku who used the same JENDL-3.2 data and the then available version of the NJOY-MCNP systems.

THE QUASI-CLASSICAL MODEL OF THE SPHERICAL CONFIGURATION IN GENERAL RELATIVITY

We consider the quasi-classical model of the spin-free configuration on the basis of the self-gravitating spherical dust shell in general relativity. For determination of the energy spectrum of the stationary states on the basis of quasi-classical quantization rules it is required to carry out some regularization of the system. It is realized by an embedding of the initial system in the extended system with rotation. Then, the stationary states of the spherical shells are S-states of the system with the intrinsic momentum. The quasi-classical treatment of a stability of the configuration is associated with the Langer modification of a square of the quantum mechanical intrinsic momentum. It gives value of critical bare mass of the shell determining threshold of stability. For the shell with the bare mass smaller or equal to the Planck's mass, the energy spectra of bound states are found. We obtain the expression for tunneling probability of the shell and construct the quasi-classical model of the pair creation and annihilation of the shells.

Surface phenomena in general relativistic stellar models: critical mass and stability

The influence of surface phenomena on general relativistic stellar models is investigated, with particular emphasis on the critical mass value and the adiabatic stability. It will be shown, in a particular model, that for a given radius, the maximum value of the total mass (compatible with a static, singularity-free configuration) is a decreasing function of the surface tension coefficient. It will also be shown that the inclusion of surface phenomena enhances the adiabatic instability of the model in the high density regime.