Overcritical Region Research Articles

Femtosecond laser-induced sub-wavelength plasma inside dielectrics: I. Field enhancement

The creation of high-energy-density (≳106 joules per cm3) over-critical plasmas in a large volume has essential applications in the study of warm dense matter, being present in the hot cores of stars and planets. It was recently shown that femtosecond Bessel beams enable creating over-critical plasmas inside sapphire with sub-wavelength radius and several tens of micrometers in length. Here, the dependence of field structure and absorption mechanism on the plasma density transverse profile are investigated by performing self-consistent Particle-In-Cell (PIC) simulations. Two limiting cases are considered: one is a homogeneous step-like profile that can sustain plasmon formation, and the second is an inhomogeneous Gaussian profile, where resonance absorption occurs. Comparing experimental absorption measures to analytical predictions allows determining the plasma parameters used in PIC simulations. The PIC simulation results are in good agreement with experimental diagnostics of total absorption, near-field fluence distribution, and far-field radiation pattern. We show that in each case, an ambipolar field forms at the plasma surface due to the expansion of the hot electrons and that electron sound waves propagate into the over-critical region.

Simulation of heat transfer in a flow of over-critical nitrogen and oxygen in a horizontal circular tube

In the framework of the k-s turbulence model with enhanced wall treatment, heat transfer in a flow of over-critical nitrogen and oxygen in a horizontal circular tube with heat boundary conditions of the third kind in the pressure range of 20H40 MPa, mass flow rates of 0.03÷0.12 kg/s, and heat transfer coefficients to the environment of 500÷2000 W/(m2K) is simulated. The distributions of the bulk temperature, calculated as the thermodynamic temperature of the average mass enthalpy of the supercritical fluid flow, are obtained. Analysis of the heat transfer coefficient of the flow showed that at pressures less than three times the critical one, a reduced heat transfer mode appears, so the near-critical region is not recommended for use in oxygen and nitrogen gasifiers. In the framework of the multiplicative model for the Nusselt number, insignificant simplices of thermophysical properties are established and correlations for oxygen and nitrogen in the over-critical region are constructed, which agree with the result of the computational experiment with an average relative accuracy of 1^1.5%. On the basis of the one-dimensional heat transfer equation, the adequacy of the obtained correlations is shown. It is established that when using the bulk temperature based on the mass average enthalpy, a separate account of the initial heat transfer section is not required.

Nonlinear integrable dynamics of coupled vibrational and intra-site excitations on a regular one-dimensional lattice

The nonlinear integrable system of coupled vibrational and intra-site excitations on a regular one-dimensional lattice is studied analytically in the framework of specially developed Darboux–Bäcklund dressing technique. The obtained four-component solution to the system demonstrates the pronounced mutual influence between the subsystems in the form of essentially nonlinear superposition of two principally distinct types of traveling waves. The solution is shown to be critical against the value of localization parameter, so that in under-critical region the subsystem of intra-site excitations should be treated as an extended monopole whereas in over-critical region – as an extended dipole.

Essentially Nonperturbative Vacuum Polarization Effects in a Two-Dimensional Dirac-Coulomb System for Z > Zcr: Vacuum Polarization Effects

For a planar Dirac-Coulomb system with a supercritical extended axially symmetric Coulomb source with a charge Z > Zcr,1and radius R0, we consider essentially nonperturbative vacuum polarization effects in the overcritical region. Using results obtained in our preceding paper for the induced charge density \({\rho _{{\rm{VP}}}}(\vec r)\), we thoroughly consider the calculation of the vacuum energy eVPbased on the renormalization, the convergence of the partial expansion for \({\rho _{{\rm{VP}}}}(\vec r)\), and the behavior of the integral induced charge QVPin the overcritical region. In particular, we show that the renormalization using the fermionic loop with two external lines turns out to be a universal technique, which eliminates the divergence of the theory in the purely perturbative and essentially nonperturbative modes for \({\rho _{{\rm{VP}}}}(\vec r)\) and eVP. The most significant result is that for Z ≫ Zcr,1in such a system, the vacuum energy becomes a rapidly decreasing function of the source charge Z reaching large negative values; its behavior is estimated from below (in absolute value) as ∼ −|ηeffZ3|/R0. We also study the dependence of the effect of the decrease in eVPon the cutoff of the Coulomb asymptotics of the external field at different scales R1 gt; R0and R1 ≫ R0.

Essentially Nonperturbative Vacuum Polarization Effects in a Two-Dimensional Dirac–Coulomb System with Z > Zcr: Vacuum Charge Density

For a planar Dirac–Coulomb system with a supercritical axially symmetric Coulomb source with the charge Z > Zcr,1 and radius R0, we consider essentially nonperturbative vacuum-polarization effects. Based on a special combination of analytic methods, computer algebra, and numerical calculations used in our previous papers to study analogous effects in the one-dimensional “hydrogen atom,” we study the behavior of both the vacuum density ρVP(r) and the total induced charge and also the vacuum-polarization energy EVP. We mainly focus on divergences of the theory and the corresponding renormalization, on the convergence of partial series for ρVP(r) and ɛVP, on the integer-valuedness of the total induced charge, and on the behavior of the vacuum energy in the overcritical region. In particular, we show that the renormalization via the fermion loop with two external legs turns out to be a universal method, which removes the divergence of the theory in the purely perturbative and essentially nonperturbative modes for ρVP and ɛVP. The most important result is that for Z ≫ Zcr,1 in such a system, the vacuum energy becomes a rapidly decreasing function of the source charge Z, which reaches large negative values and whose behavior is estimated from below (in absolute value) as ~ −|ηeffZ3|/R0. We also study the dependence of polarization effects on the cutoff of the Coulomb asymptotic form of the external field. We show that screening the asymptotic value significantly changes the structure and properties of the first partial channels with mj = ±1/2,±3/2. We consider the nonperturbative calculation technique and the behavior of the induced density and the integral induced charge QVP in the overcritical region in detail.

Variation of Donor and Acceptor Strength in Analogues of Brooker's Merocyanine and Generalization to Various Classes of Charge Transfer Compounds.

Derivatives of Brooker's merocyanine (BM) have been investigated, which possess different donors and acceptors and therefore vary their donor-acceptor strength SDA. The 00 energies have been extracted from the spectra and compared. Under basic conditions, where the neutral (merocyanine) form is present, the absorption energies for all compounds are similar, whereas there is a large difference for acidic conditions where the cationic (cyanine) form is present. This behavior could be explained by a simple theoretical model involving the dependence of the excitation energy Δ E01 on SDA. This model can be generalized to describe in a consistent way two different well-known classes of neutral chromophores with a certain degree of charge separation, namely merocyanine I (TICT) and merocyanine II (often betainic) compounds. Merocyanines I are characterized by a medium polar aromatic ground state and a zwitterionic quinoid excited state and hence positive solvatochromism, whereas merocyanines II are formally characterized by a zwitterionic aromatic ground state and a less polar quinoid excited state and, accordingly, by negative solvatochromism. On increasing the donor-acceptor strength SDA sufficiently, merocyanines II can, however, move to the so-called overcritical region with the excited state dominated by the zwitterionic valence bond structure. For many of the merocyanine II molecules investigated here, a weakly positive solvatochromic behavior is observed indicating that the ground state contains less of the zwitterionic valence bond wave function than the excited state and that these compounds belong to the overcritical region. The fluorescence spectra have been analyzed in terms of the Franck-Condon model and confirm these conclusions.

LOCAL PARAMETERS OF THE SURFACE ROUGHNESS OF ELECTROCHEMICALLY DEALLOYED Ag-Pd ALLOYS

Local characteristics of surface roughness of the polycrystalline Ag-Pd solid solutions (4 and 8 at. % Pd) which underwent potentiostatic electrochemical dealloying in an acidic nitrate aqueous solution were determined by scanning electron and atomic force microscopy. A qualitative analysis of the SEM and AFM micrographs demonstrated substantial morphological roughening of the surface of Ag-Pd alloys. This results from the formation of hollows and cracks caused by selective leaching of electronegative silver and recrystallization of electropositive palladium into its highly-developed phase. A quantitative analysis of the AFM-data allowed us to determine the numerical values of the main local roughness characteristics of anodically modified alloys. The negative value of the coefficient of surface asymmetry indicates the formation of deep cavities during the dealloying process. The recorded mean roughness generally depends on the AFM-scanning zone, but it stabilizes if the scan zone exceeds several tens of micrometers. The roughness of dealloyed Ag-Pd systems is of micro- and nano-size and increases with anodic potential and electric charge of the electrochemical modification of both studied Ag4Pd and Ag8Pd alloys. This effect can be accounted for by a significant rise in the anodic dissolution rate of silver from the alloys in the overcritical region of polarization, resulting in the formation of deeper surface defects. An increase in the average height of surface irregularities with modification time conforms to the square root law, confirming the non-stationary mass transfer kinetics of the selective dissolution process. Variation of the anodic potential and electric charge makes it possible to find the optimal conditions for the electrochemical synthesis of electrode Ag-Pd materials with given values of arithmetic mean and root-mean-square roughness. The assumption that harmonic sinusoidal function represents the Ag-Pd surface microprofile proved the linear dependence of the roughness factor on dealloying time.

Casimir (vacuum) energy in planar QED with strong coupling

The essentially non-perturbative vacuum polarization effects, caused by an extended external supercritical Coulomb source, are explored for a planar Dirac-Coulomb (DC) system with strong coupling (similar to graphene and graphene-based heterostructures). Taking account of results, obtained in Ref. [1] for the induced charge density ρVP(r→), in the present paper the evaluation of the Casimir (vacuum) energy EVP is presented. The main result is that for a wide range of the system parameters in the overcritical region EVP turns out to be a rapidly decreasing negative function ∼−Z3∕R0 with Z, R0 being the charge and the size of the external source. By an explicit calculation the possibility for complete screening of the electrostatic reflection self-energy of the external source by such polarization effects for Z ≫ Zcr,1 is demonstrated. The dependence of the Casimir energy on the screening of the Coulomb asymptotics of the external source at some R1 > R0 is also explored in detail, and some peculiar effects in the partial channels with the lowest rotational numbers mj = ±1∕2, ±3∕2 in the screened case are also discussed.

Essentially non-perturbative and peculiar polarization effects in planar QED with strong coupling

The essentially non-perturbative polarization effects are considered for a planar supercritical Dirac-Coulomb system with strong coupling (similar to graphene and graphene-based heterostructures) in terms of induced charge density ρVP(r→). The main attention is paid to the renormalization, convergence of the partial expansion and the behavior of ρVP(r→) and the integral induced charge QVP in the overcritical region. The dependence of the induced density on the screening of the Coulomb asymptotics of the external source is also explored in detail. Some peculiar effects in the discrete spectrum with the lowest rotational numbers mj = ±1∕2, ±3∕2 in the screened case are detected and their possible role in the transition through corresponding Zcr is also discussed.

Semidiscrete Integrable Nonlinear Schrӧdinger System with Background-Controlled Intersite Resonant Coupling. Short Summary of Key Properties

The most featured items characterizing the semidiscrete nonlinear Schr¨odinger system with background-controlled intersite resonant coupling are summarized. The system is shown to be integrable in the Lax sense that makes it possible to obtain its soliton solutions in the framework of a properly parametrized dressing procedure based on the Darboux transformation accompanied by the implicit form of B¨acklund transformation. In addition, the system integrability inspires an infinite hierarchy of local conservation laws, some of which were found explicitly in the framework of the generalized recursive approach. The system consists of two basic dynamic subsystems and one concomitant subsystem, and its dynamics is embedded into the Hamiltonian formulation accompanied by the highly nonstandard Poisson structure. The nonzero background level of concomitant fields mediates the appearance of an additional type of the intersite resonant coupling. As a consequence, it establishes the triangular-lattice-ribbon spatial arrangement of location sites for the basic field excitations. At tuning the main background parameter, we are able to switch system’s dynamics between two essentially different regimes separated by the critical point. The physical implications of system’s criticality become evident after a rather sophisticated procedure of canonization of basic field variables. There are two variants to standardize the system equal in their rights. Each variant is realizable in the form of two nonequivalent canonical subsystems. The broken symmetry between canonical subsystems gives rise to the crossover effect in the nature of excited states. Thus, in the under-critical region, the system supports the bright excitations in both subsystems; while, in the over-critical region, one of the subsystems converts into the subsystem of dark excitations.

Estimating the radiative part of QED effects in superheavy nuclear quasimolecules

A method for calculating the electronic levels in the compact superheavy nuclear quasi-molecules, based on solving the two-center Dirac equation using the multipole expansion of two-center potential, is developed. For the internuclear distances up to $d\sim100$~fm such technique reveals a quite fast convergence and allows for computing the electronic levels in such systems with accuracy $\sim 10^{-6} $. The critical distances $R_{cr}$ between the nuclei for $1\sigma_g$ and $1\sigma_u$ electronic levels in the region $Z\simeq 87-100$ are calculated. By means of the same technique the shifts of electronic levels due to the effective interaction $\Delta U_{AMM}$ of the electron's magnetic anomaly with the Coulomb field of the closely spaced heavy nuclei are evaluated as a function of the internuclear distance and the charge of the nuclei, non-perturbatively both in $Z\alpha$ and (partially) in $\alpha/\pi$. It is shown, that the levels shifts near the lower continuum decrease with the enlarging size of the system of Coulomb sources both in the absolute units and in units of $Z^4 \alpha^5 / \pi n^3$. The last result is generalized to the whole self-energy contribution to the level shifts and so to the possible behavior of radiative part of QED-effects with virtual photon exchange near the lower continuum in the overcritical region.

Nonperturbative vacuum polarization effects in two-dimensional supercritical Dirac–Coulomb system I. Vacuum charge density

Based on the original combination of analytical methods, computer algebra tools and numerical calculations, proposed recently in Refs. 1–3, the nonperturbative vacuum polarization effects in the 2+1[Formula: see text]D supercritical Dirac–Coulomb system with [Formula: see text] are explored. Both the vacuum charge density [Formula: see text] and vacuum energy [Formula: see text] are considered. The main result of the work is that in the overcritical region [Formula: see text] turns out to be a rapidly decreasing function [Formula: see text] with [Formula: see text] and [Formula: see text] being the size of the external Coulomb source. Due to a lot of details of calculation the whole work is divided into two parts I and II. In the present part I, we consider the evaluation and behavior of the vacuum density [Formula: see text], which further is used in part II for evaluation of the vacuum energy, with emphasis on the renormalization, convergence of the partial expansion for [Formula: see text] and behavior of the integral induced charge [Formula: see text] in the overcritical region.

Nonperturbative vacuum polarization effects in two-dimensional supercritical Dirac–Coulomb system II. Vacuum energy

Nonperturbative vacuum polarization effects are explored for a supercritical Dirac–Coulomb system with [Formula: see text] in 2+1[Formula: see text]D, based on the original combination of analytical methods, computer algebra and numerical calculations, proposed recently in Refs. 1–3. Both the vacuum charge density [Formula: see text] and vacuum energy [Formula: see text] are considered. Due to a lot of details of calculation the whole work is divided into two parts I and II. Taking account of results, obtained in the part I4 for [Formula: see text], in the present part II, the evaluation of the vacuum energy [Formula: see text] is investigated with emphasis on the renormalization and convergence of the partial expansion for [Formula: see text]. It is shown that the renormalization via fermionic loop turns out to be the universal tool, which removes the divergence of the theory both in the purely perturbative and essentially nonperturbative regimes of the vacuum polarization. The main result of calculation is that for a wide range of the system parameters in the overcritical region [Formula: see text] turns out to be a rapidly decreasing function [Formula: see text] with [Formula: see text] and [Formula: see text] being the size of the external Coulomb source. To the end the similarity in calculations of [Formula: see text] in 2+1 and 3+1[Formula: see text]D is discussed, and qualitative arguments are presented in favor of the possibility for complete screening of the classical electrostatic energy of the Coulomb source by the vacuum polarization effects for [Formula: see text] in 3+1[Formula: see text]D.

Nonperturbative effects of vacuum polarization for a quasi-one-dimensional Dirac–Coulomb system with Z > Z cr

Major nonperturbative properties of the vacuum charge density ρ VP (x) and vacuum-polarization energy ξ VP are considered for an overcritical Coulomb source with Z > Z cr in 1 + 1 D. We demonstrate that, for a broad range of external-field parameters, vacuum energy may significantly deviate from the perturbative quadratic increase and even decrease towards deeply negative values due to vacuum polarization in the overcritical region.

Vacuum energy of one-dimensional supercritical Dirac–Coulomb system

Nonperturbative vacuum polarization effects are explored for a supercritical Coulomb source with [Formula: see text] in 1[Formula: see text]+[Formula: see text]1D. Both the vacuum charge density [Formula: see text] and vacuum energy [Formula: see text] are considered. It is shown that in the overcritical region the behavior of vacuum energy could be significantly different from perturbative quadratic growth up to decrease reaching large negative values.

Distinctive Features Of The Integrable Nonlinear Schrodinger System On A Ribbon Of Triangular Lattice

The dynamics of an integrable nonlinear Schr¨odinger system on a triangular-lattice ribbon is shown to be critical against the value of background parameter regulated by the limiting values of concomitant fields. Namely at the critical point, the number of basic field variables is reduced by half and the Poisson structure of the system becomes degenerate. On the other hand, outside the critical point, the form of Poisson structure turns out to be an essentially nonstandard one, and the meaningful procedure of its standardization leads inevitably to the breaking of the mutual symmetry between the standardized basic subsystems. There are two possible realizations of such an asymmetric standardization, each giving rise to a total suppression of field amplitudes in one of the standardized basic subsystems at the critical value of background parameter. In the undercritical region the standardized basic field amplitudes acquire the meaning of probability amplitudes of some nonequivalent intracell bright excitations, whereas in the overcritical region such an interpretation is proven to be incorrect. A proper analysis shows that the overcritical region could be thought as the region of coexistence between the standardized subsystems of bright and dark excitations.

Symmetry-broken canonizations of the semi-discrete integrable nonlinear Schrödinger system with background-controlled inter-site coupling

The integrable system of nonlinear Schrödinger type consisting of two mutually symmetric basic subsystems and one concomitant subsystem given on a ribbon of triangular lattice is characterized by the highly nonstandard form of Poisson structure. The fact of system criticality against the positive semi-definite background parameter provides us the clue how to organize the nonlinear point transformation ensuring the canonization of field variables. Precisely it allows to introduce two subsets of mutually symmetric intermediate (auxiliary) field variables and to involve one or another of them into a rational procedure of canonization realizable already in terms of two mutually asymmetric subsets of field amplitudes. There are two variants of system asymmetric standardization (namely, the minus-asymmetric and plus-asymmetric ones) emanated from the two-leg structure of underlying space lattice of the primary (noncanonical) nonlinear system. Either of the two asymmetrically standardized nonlinear systems consists of two canonical subsystems which can be referred to as the strong and the weak ones. The strong subsystem is the subsystem of bright nonlinear excitations on the whole admissible interval of the background parameter. In contrast the type of nonlinear excitations in the weak subsystem depends on the chosen domain of the background parameter. Thus in the under-critical region of the background parameter, the weak subsystem behaves as the subsystem of bright excitations while in the over-critical region it turns into the subsystem of dark excitations. Moreover in the very critical point, the field amplitudes of weak subsystem shrink to zero and the canonical system as the whole is reduced to the single strong subsystem. The general results concerning both minus-asymmetric and plus-asymmetric standardizations are confirmed analytically by means of the system multi-component one-soliton solution.

Asymmetric canonicalization of the integrable nonlinear Schrödinger system on a triangular-lattice ribbon

The integrable nonlinear Schrödinger system on a triangular-lattice ribbon characterized by the essentially nonstandard Poisson structure is shown to be standardized to the nonlinear lattice system consisting of two nonequivalent canonical subsystems. In under-critical region of background parameter both of the canonical subsystems should be treated as the subsystems of bright nonlinear excitations. In the over-critical region one of the canonical subsystem should be treated as the subsystem of bright nonlinear excitations while the another as the subsystem of dark nonlinear excitations.

A method to determine the flux limiter via the motion of the M-band emission region in Au hohlraum

AbstractIn this paper, the influence of the electron flux limiter fe on hohlraum plasmas is studied by using the two-dimensional code LARED-H, and a method to experimentally determine fe via the motion of the M-band emission region in Au hohlraum is proposed. From our simulations, the limited free streaming flux may dominates the heat conduction in the regions with steep temperature gradient, including the laser deposition region, the flux-heated overcritical region, and the laser channel boundary between the hot laser plasmas and the surrounding radiation ablated plasmas, while these are important X-ray emission regions. Hence, the choosing of fe may influence the wall plasma expansion and the laser spot motion, and further influence the motion of the emission regions. From our study, the motion of the M-band (>1.5 keV) emission region is sensitive to fe when the limited free streaming flux dominates the heat conduction of the wall plasma expansion region, and so it is possible to determine fe via the motion of the M-band emission region. In this work, the model used in our simulations is taken from the wall and laser spot motion experiments done by Huser et al. (2009).

Quantum criticality in Einstein–Maxwell-dilaton gravity

We investigate the quantum Lifshitz criticality in a general background of Einstein–Maxwell-dilaton gravity. In particular, we demonstrate the existence of critical point with dynamic critical exponent z by tuning a nonminimal coupling to its critical value. We also study the effect of nonminimal coupling and exponent z to the Efimov states and holographic RG flow in the overcritical region. We have found that the nonminimal coupling increases the instability for a probe scalar to condensate and its back reaction is discussed. At last, we give a quantum mechanics treatment to a solvable system with z=2, and comment for generic z>2.