Invariant Flux Research Articles

Estimation of best geometric and operational parameters of a nanophotonics-enabled solar membrane desalination system: A numerical investigation

Nanophotonics-enabled solar membrane desalination (NESMD) system is a sustainable method to address water scarcity by desalinating seawater using solar energy. A layer of nanoparticles absorbs heat, creating localized heating within feed channel, which generates a vapor pressure difference between feed and permeate channels. Distillate water is collected in permeate channel. Numerical modelling of NESMD system, integrating optical and thermal modules in COMSOL Multiphysics, efficiently enumerates distillate flux at specified locations under varying ambient conditions. Reliability of the simulation model is confirmed through validation against in-house experimental results. A set of most effective dimensions and component specifications for NESMD system are computed that maximize distillate flux. Setup width exhibits invariant distillate flux within a range of 2–30 cm, while a feed thickness of 2 mm yields maximum distillate flux, with no change observed for permeate thickness within a range of 2–10 mm. An optimal setup length is determined within 80–200 cm range under varying operating conditions. Membrane porosity of 0.85 is selected to balance both vapor diffusivity and mechanical strength. The optimum membrane thickness lies within 180–225 µm range. An NESMD system with these best suited specifications is demonstrated to produce freshwater at the rate of 4.63 l/m2 per day.

The tadpole conjecture in the interior of moduli space

We revisit moduli stabilization on Calabi-Yau manifolds with a discrete symmetry. Invariant fluxes allow for a truncation to a symmetric locus in complex structure moduli space and hence drastically reduce the moduli stabilization problem in its dimensionality. This makes them an ideal testing ground for the tadpole conjecture. For a large class of fourfolds, we show that an invariant flux with non-zero on-shell superpotential on the symmetric locus necessarily stabilizes at least 60% of the complex structure moduli. In case this invariant flux induces a relatively small tadpole, it is thus possible to bypass the bound predicted by the tadpole conjecture at these special loci. As an example, we discuss a Calabi-Yau hypersurface with h3,1 = 3878 and show that we can stabilize at least 4932 real moduli with a flux that induces M2-charge Nflux = 3.

Evaluating the Adiabatic Invariants in Magnetized Plasmas Using a Classical Ehrenfest Theorem.

In this article, we address the reliance on probability density functions to obtain macroscopic properties in systems with multiple degrees of freedom as plasmas, and the limitations of expensive techniques for solving Equations such as Vlasov's. We introduce the Ehrenfest procedure as an alternative tool that promises to address these challenges more efficiently. Based on the conjugate variable theorem and the well-known fluctuation-dissipation theorem, this procedure offers a less expensive way of deriving time evolution Equations for macroscopic properties in systems far from equilibrium. We investigate the application of the Ehrenfest procedure for the study of adiabatic invariants in magnetized plasmas. We consider charged particles trapped in a dipole magnetic field and apply the procedure to the study of adiabatic invariants in magnetized plasmas and derive Equations for the magnetic moment, longitudinal invariant, and magnetic flux. We validate our theoretical predictions using a test particle simulation, showing good agreement between theory and numerical results for these observables. Although we observed small differences due to time scales and simulation limitations, our research supports the utility of the Ehrenfest procedure for understanding and modeling the behavior of particles in magnetized plasmas. We conclude that this procedure provides a powerful tool for the study of dynamical systems and statistical mechanics out of equilibrium, and opens perspectives for applications in other systems with probabilistic continuity.

Periodic Clifford symmetry algebras on flux lattices

Real Clifford algebras play a fundamental role in the eight real Altland-Zirnbauer symmetry classes and the classification tables of topological phases. Here, we present another elegant realization of real Clifford algebras in the $d$-dimensional spinless rectangular lattices with $\pi$ flux per plaquette. Due to the $T$-invariant flux configuration, real Clifford algebras are realized as projective symmetry algebras of lattice symmetries. Remarkably, $d$ mod $8$ exactly corresponds to the eight Morita equivalence classes of real Clifford algebras with eightfold Bott periodicity, resembling the eight real Altland-Zirnbauer classes. The representation theory of Clifford algebras determines the degree of degeneracy of band structures, both at generic $k$ points and at high-symmetry points of the Brillouin zone. Particularly, we demonstrate that the large degeneracy at high-symmetry points offers a rich resource for forming novel topological states by various dimerization patterns, including a $3$D higher-order semimetal state with double-charged bulk nodal loops and hinge modes, a $4$D nodal surface semimetal with $3$D surface solid-ball zero modes, and $4$D M\"{o}bius topological insulators with a eightfold surface nodal point or a fourfold surface nodal ring. Our theory can be experimentally realized in artificial crystals by their engineerable $\mathbb{Z}_2$ gauge fields and capability to simulate higher dimensional systems.

Hubbard model on the kagome lattice with time-reversal invariant flux and spin-orbit coupling

We study the Hubbard model with time-reversal invariant flux and spin-orbit coupling and position-dependent onsite energies on the kagome lattice, using numerical and analytical methods. In particular, we perform calculations using real space dynamical mean-field theory (R-DMFT). To study the topological properties of the system, we use the topological Hamiltonian approach. We obtain a rich phase diagram: for weak and intermediate interactions, depending on the model parameters, the system is in the band insulator, topological insulator, or metallic phase, while for strong interactions the system is in the Mott insulator phase. We also investigate the magnetic phases that occur in this system. For this purpose, in addition to R-DMFT, we also use two analytical methods: perturbation theory for large interactions and onsite energies, and stochastic mean-field theory.

Analytical model and material equivalent methods for steady state heat partition coefficient between two contact discs in multi-disc clutch

The heat partition coefficient between two finite thickness contact discs during long-time sliding is studied with a coupled finite element method. Results show that the heat partition coefficient varies from its initial value to another steady state value rapidly instead of being a constant all the time. An analytical solution of the temperature field under invariant heat flux input is deduced, which tells that there exists a unique critical thickness ratio between the contact discs that keeps the heat partition coefficient a constant. An equivalent method for single-material contact bodies is proposed that is capable of calculating the steady state heat partition coefficient for any thickness ratio. It reveals that the steady state heat partition coefficient only has relationship with the mass density and the heat capacity of the materials and the thickness ratio. Based on this method, a two-step material equivalent method is further proposed for the contact discs that have friction linings on them. The solution shows that the steady state heat partition coefficient in this situation is also only determined by the material properties and the layer thicknesses. A test bench of multi-disc clutch is set up and a series of sliding experiments are conducted to validate the proposed equivalent methods and solutions of steady state heat partition coefficient. The measured experimental temperature variations show that the temperature level of the separator disc in the clutch is overestimated with the constant heat partition coefficient of semi-infinite model, while it is close to those calculated results with steady state heat partition coefficient. Therefore, the temperature fields of the contact discs during long-time sliding with constant speed can be figured out efficiently using the steady state heat partition coefficient with only small error, and these equivalent methods benefit the multi-disc clutch design and temperature estimation in practical applications.

Lorentz invariant relative velocity and relativistic binary collisions

This paper reviews the concept of Lorentz invariant relative velocity that is often misunderstood or unknown in high energy physics literature. The properties of the relative velocity allow to formulate the invariant flux and cross-section without recurring to nonphysical velocities or any assumption about the reference frame. Applications such as the luminosity of a collider, the use as kinematic variable, and the statistical theory of collisions in a relativistic classical gas are reviewed. It is emphasized how the hyperbolic properties of the velocity space explain the peculiarities of relativistic scattering.

A Riemann solver for a system of hyperbolic conservation laws at a general road junction

The kinematic wave model of traffic flow on a road network is a system of hyperbolic conservation laws, for which the Riemann solver is of physical, analytical, and numerical importance. In this paper, we present a new Riemann solver at a general network junction in the demand-supply space. In the Riemann solutions, traffic states on a link include the initial, stationary, and interior states, and a discrete Cell Transmission Model flux function in interior states is used as an entropy condition, which is consistent with fair merging and first-in-first-out diverging rules. After deriving the feasibility conditions for both stationary and interior states, we obtain a set of algebraic equations, and prove that the Riemann solver is well-defined, in the sense that the stationary states, the out-fluxes of upstream links, the in-fluxes of downstream links, and kinematic waves on all links can be uniquely solved. In addition, we show that the resulting global flux function in initial states is the same as the local one in interior states. Hence we presents a new definition of invariant junction models, in which the global and local flux functions are the same. We also present a simplified framework for solving the Riemann problem with invariant junction flux functions.

New Solutions for Non-Abelian Cosmic Strings.

We study the properties of classical vortex solutions in a non-Abelian gauge theory. A system of two adjoint Higgs fields breaks the SU(2) gauge symmetry to Z_{2}, producing 't Hooft-Polyakov monopoles trapped on cosmic strings, termed beads; there are two charges of monopole and two degenerate string solutions. The strings break an accidental discrete Z_{2} symmetry of the theory, explaining the degeneracy of the ground state. Further symmetries of the model, not previously appreciated, emerge when the masses of the two adjoint Higgs fields are degenerate. The breaking of the enlarged discrete symmetry gives rise to additional string solutions and splits the monopoles into four types of "semipole": kink solutions that interpolate between the string solutions, classified by a complex gauge-invariant magnetic flux and a Z_{4} charge. At special values of the Higgs self-couplings, the accidental symmetry broken by the string is continuous, giving rise to supercurrents on the strings. The SU(2) theory can be embedded in a wide class of grand unified theories (GUTs), including SO(10). We argue that semipoles and supercurrents are generic on GUT strings.

Chiral exact relations for helicities in Hall magnetohydrodynamic turbulence.

Besides total energy, three-dimensional incompressible Hall magnetohydrodynamics (MHD) possesses two inviscid invariants, which are the magnetic helicity and the generalized helicity. Exact relations are derived for homogeneous (nonisotropic) stationary Hall MHD turbulence (and also for its inertialess electron MHD limit) with nonzero helicities and in the asymptotic limit of large Reynolds numbers. The universal laws are written only in terms of mixed second-order structure functions, i.e., the scalar product of two different increments. It provides, therefore, a direct measurement of the dissipation rates for the corresponding invariant flux. This study shows that the generalized helicity cascade is strongly linked to the left polarized fluctuations, while the magnetic helicity cascade is linked to the right polarized fluctuations.

Defects, strain relaxation, and compositional grading in high indium content InGaN epilayers grown by molecular beam epitaxy

We investigate the structural properties of a series of high alloy content InGaN epilayers grown by plasma-assisted molecular beam epitaxy, employing the deposition temperature as variable under invariant element fluxes. Using transmission electron microscopy methods, distinct strain relaxation modes were observed, depending on the indium content attained through temperature adjustment. At lower indium contents, strain relaxation by V-pit formation dominated, with concurrent formation of an indium-rich interfacial zone. With increasing indium content, this mechanism was gradually substituted by the introduction of a self-formed strained interfacial InGaN layer of lower indium content, as well as multiple intrinsic basal stacking faults and threading dislocations in the rest of the film. We show that this interfacial layer is not chemically abrupt and that major plastic strain relaxation through defect introduction commences upon reaching a critical indium concentration as a result of compositional pulling. Upon further increase of the indium content, this relaxation mode was again gradually succeeded by the increase in the density of misfit dislocations at the InGaN/GaN interface, leading eventually to the suppression of the strained InGaN layer and basal stacking faults.

Excavations at the gravitationally collapsed site: Recent findings

Hawking effect was digged out of the gravitationally collapsed site forty years back when it was realised that quantum effects at the horizon could propagate outward to infinity giving rise to a thermal flux at late-times. However, the situation regarding non-asymptotic observers was never completely clear. Also, recently a debate has sprung in the community as to what would infallingobservers perceive while crossing the horizon. We set out to settle this question and more at least semi-classically in the articles [7] and [8] with a fresh approach. We introduce a new set of coordinates that are regular everywhere, consider the adiabatic expansion of detector response and its link to the trajectory-dependent ‘effective’ temperature/s and also local invariant observables, energy density and flux, built from renormalized stress energy tensor. This paper is a concise summary of the new procedure and the results obtained thereof.

CarbonTracker-CH<sub>4</sub>: an assimilation system for estimating emissions of atmospheric methane

Abstract. We describe an assimilation system for atmospheric methane (CH4), CarbonTracker-CH4, and demonstrate the diagnostic value of global or zonally averaged CH4 abundances for evaluating the results. We show that CarbonTracker-CH4 is able to simulate the observed zonal average mole fractions and capture inter-annual variability in emissions quite well at high northern latitudes (53–90° N). In contrast, CarbonTracker-CH4 is less successful in the tropics where there are few observations and therefore misses significant variability and is more influenced by prior flux estimates. CarbonTracker-CH4 estimates of total fluxes at high northern latitudes are about 81 ± 7 Tg CH4 yr−1, about 12 Tg CH4 yr−1 (13%) lower than prior estimates, a result that is consistent with other atmospheric inversions. Emissions from European wetlands are decreased by 30%, a result consistent with previous work by Bergamaschi et al. (2005); however, unlike their results, emissions from wetlands in boreal Eurasia are increased relative to the prior estimate. Although CarbonTracker-CH4 does not estimate an increasing trend in emissions from high northern latitudes for 2000 through 2010, significant inter-annual variability in high northern latitude fluxes is recovered. Exceptionally warm growing season temperatures in the Arctic occurred in 2007, a year that was also anonymously wet. Estimated emissions from natural sources were greater than the decadal average by 4.4 ± 3.8 Tg CH4 yr−1 in 2007. CarbonTracker-CH4 estimates for temperate latitudes are only slightly increased over prior estimates, but about 10 Tg CH4 yr−1 is redistributed from Asia to North America. This difference exceeds the estimated uncertainty for North America (±3.5 Tg CH4 yr−1). We used time invariant prior flux estimates, so for the period from 2000 to 2006, when the growth rate of global atmospheric CH4 was very small, the assimilation does not produce increases in natural or anthropogenic emissions in contrast to bottom-up emission data sets. After 2006, when atmospheric CH4 began its recent increases, CarbonTracker-CH4 allocates some of the increases to anthropogenic emissions at temperate latitudes, and some to tropical wetland emissions. For temperate North America the prior flux increases by about 4 Tg CH4 yr−1 during winter when biogenic emissions are small. Examination of the residuals at some North American observation sites suggests that increased gas and oil exploration may play a role since sites near fossil fuel production are particularly hard for the inversion to fit and the prior flux estimates at these sites are apparently lower and lower over time than what the atmospheric measurements imply. The tropics are not currently well resolved by CarbonTracker-CH4 due to sparse observational coverage and a short assimilation window. However, there is a small uncertainty reduction and posterior emissions are about 18% higher than prior estimates. Most of this increase is allocated to tropical South America rather than being distributed among the global tropics. Our estimates for this source region are about 32 ± 4 Tg CH4 yr−1, in good agreement with the analysis of Melack et al. (2004) who obtained 29 Tg CH4 yr−1 for the most productive region, the Amazon Basin.

Defects, non-abelian t-duality, and the Fourier-Mukai transform of the Ramond-Ramond fields

We construct topological defects generating non-abelian T-duality for isometry groups acting without isotropy. We find that these defects are given by line bundles on the correspondence space with curvature which can be considered as a non-abelian generalization of the curvature of the Poincar\`{e} bundle. We show that the defect equations of motion encode the non-abelian T-duality transformation. The Fourier-Mukai transform of the Ramond-Ramond fields generated by the gauge invariant flux of these defects is studied. We show that it provides elegant and compact way of computation of the transformation of the Ramond-Ramond fields under the non-abelian T-duality.

More stable de Sitter vacua fromS-dual nongeometric fluxes

Stable vacua obtained from isotropic tori compactification might not be fully stable provided the existence of runaway directions in the Kaehler directions of anisotropy. By implementing a genetic algorithm we report the existence of explicit flux configurations leading to stable de Sitter and Anti- de Sitter vacua, consisting on Type IIB compactifications on a 6-dimensional anisotropic torus threaded with standard and S-dual invariant non-geometric fluxes in the presence of orientifold 3-planes. In all dS vacua the masses of the complex structure moduli are heavier than the Hubble scale suggesting that the axio-dilaton and Kaeahler moduli are natural candidates for small-field inflation. In the way, we also report new solutions on isotropic and semi-isotropic tori compactifications. Finally, we observe that, since all our solutions are obtained in the absence of solitonic objects, they are good candidates to be lifted to stable solutions in extended supersymmetric theories.

Defects, super-Poincaré line bundle and fermionic T-duality

Abstract Topological defects are interfaces joining two conformal field theories, for which the energy momentum tensor is continuous across the interface. A class of the topological defects is provided by the interfaces separating two bulk systems each described by its own Lagrangian, where the two descriptions are related by a discrete symmetry. In this paper we elaborate on the cases in which the discrete symmetry is a bosonic or a fermionic T-duality. We review how the equations of motion imposed by the defect encode the general bosonic T-duality transformations for toroidal compactifications. We generalize this analysis in some detail to the case of topological defects allowed in coset CFTs, in particular to those cosets where the gauged group is either an axial or vector U(1). This is discussed in both the operator and Lagrangian approaches. We proceed to construct a defect encoding a fermionic T-duality. We show that the fermionic T-duality is implemented by the Super-Poincaré line bundle. The observation that the exponent of the gauge invariant flux on a defect is a kernel of the Fourier-Mukai transform of the Ramond-Ramond fields, is generalized to a fermionic T-duality. This is done via a fiberwise integration on supermanifolds.

The traffic statics problem in a road network

In this study we define and solve the traffic statics problem in an open diverge-merge network based on a multi-commodity kinematic wave model, whose entropy conditions are given by invariant junction flux functions derived from macroscopic merging and diverging rules. In this problem, we are interested in finding stationary states on all links when origin demands, destination supplies, and route choice proportions are constant. After discussing the properties of four types of stationary states on a road link and presenting stationary entropy conditions at both the merging and diverging junctions, we derive a system of algebraic equations as necessary conditions for all 16 combinations of stationary states on the two intermediate links. Under different network conditions in road capacities, route choice proportions, and merging priorities, we analytically show that the traffic statics problem always admits stationary solutions, which, however, may not be unique. In particular, such stationary solutions exist even under network conditions when an initially empty diverge-merge network can settle in persistent periodic oscillations after a long time. In the future, we will be interested in discussing the stability property of the stationary states and studying the traffic statics problem in general networks. Analytical insights from the simpler traffic statics problems would be helpful for understanding complex traffic dynamics in a road network.

On the relation between reactions and complexes of (bio)chemical reaction networks

Robustness of biochemical systems has become one of the central questions in systems biology although it is notoriously difficult to formally capture its multifaceted nature. Maintenance of normal system function depends not only on the stoichiometry of the underlying interrelated components, but also on the multitude of kinetic parameters. Invariant flux ratios, obtained within flux coupling analysis, as well as invariant complex ratios, derived within chemical reaction network theory, can characterize robust properties of a system at steady state. However, the existing formalisms for the description of these invariants do not provide full characterization as they either only focus on the flux-centric or the concentration-centric view. Here we develop a novel mathematical framework which combines both views and thereby overcomes the limitations of the classical methodologies. Our unified framework will be helpful in analyzing biologically important system properties.

Numerical Simulation of Nucleate Boiling Phenomenon Coupled with Thermal Response of the Solid

The present work describes the response of a heated solid surface during nucleation, growth and departure of a single bubble. Two dimensional, axisymmetric, finite difference schemes are used to solve the governing equations in the liquid, vapor and solid phases. The interface between liquid and vapor phases is tracked by a level set method. An iterative procedure is used at the interface between the solid and fluid phases in order to match temperatures and heat fluxes. Time and space invariant heat fluxes are supplied at the solid base and calculations are carried out for solids with different thermo-physical properties and thicknesses. Near the three-phase contact line, temperatures in the solid are observed to fluctuate significantly over short periods as the bubble base first expands outwards then contracts inwards before departure. The results show that waiting and growth periods can be related directly to wall superheat. The functional relationship between waiting time and wall superheat is found to agree well with the correlations based on experimental data reported in the literature.

Twisted analytic torsion

We review the Reidemeister torsion, Ray-Singer's analytic torsion and the Cheeger-M"uller theorem. We describe the analytic torsion of the de Rham complex twisted by a flux form introduced by the current authors and recall its properties. We define a new twisted analytic torsion for the complex of invariant differential forms on the total space of a principal circle bundle twisted by an invariant flux form. We show that when the dimension is even, such a torsion is invariant under certain deformation of the metric and the flux form. Under T-duality which exchanges the topology of the bundle and the flux form and the radius of the circular fiber with its inverse, the twisted torsions of invariant forms are inverse to each other for any dimension.