Random Phase Approximation Theory Research Articles

Electrical Resistivity Measurements of Surface-Coated Copper Foils.

Due to the direct contact between the probe and sample, the contact of the four-probe method is important for the structural integrity of the sample and the accuracy of electrical resistivity measurements, especially for surface-coated metal foils with multilayered structures. Here, we analyzed the accuracy and stability of four-probe method probing on different sides of copper (Cu) foils covered with graphene (Gr). Theoretical simulations showed similar potential distributions on the probe tip when probing on the Cu and Gr sides. The resistivity of the Gr/Cu foil was 2.31 ± 0.02 μΩ·cm when measured by probing on the Cu side, and 2.30 ± 0.10 μΩ·cm when measured by probing on the Gr side. The major difference in the mean deviation is attributed to surface damage. In addition, the method of probing on the Cu side was sensitive to the resistivity changes of Gr induced by polymers with a dielectric constant range of 2~12, which is consistent with the calculations based on the random phase approximation theory. Our results demonstrated that the probing position on the metal side in the four-probe method can effectively protect the structural integrity of the functional surface-coated layer and maintain the high sensitivity of the measurement, providing guidance for the resistivity measurements of other similarly heterogeneous materials.

Phase behavior of triblock copolymer and homopolymer blends: Effect of copolymer topology

Two distinct linear triblock copolymers with different block sequences, ABA or BAB, are obtained when two identical AB diblock copolymers are jointed at their B or A ends, respectively, resulting in three homologous, AB diblock, ABA, and BAB triblock copolymers with the same chemical composition but different topologies. We demonstrate that the topological effect on the phase behaviors of these copolymers is amplified when A homopolymers are added to the system. Specifically, the phase behaviors of binary blends composed of ABA or BAB linear triblock copolymers and A homopolymers are studied by using the random-phase approximation (RPA) and self-consistent field theory (SCFT). The RPA analysis predicts that the Lifshitz point for the ABA/A blends behaves like a second-order transition but that for the BAB/A blends behaves like a first-order transition. The Lifshitz point of the BAB/A mixtures is found to occur at a much lower homopolymer concentration than that of the ABA/A mixtures, indicating a poorer miscibility of the A homopolymers into the BAB than ABA triblocks, which is also confirmed by SCFT. For sphere-forming triblock copolymers mixed with homopolymers, the poorer miscibility and the more diffused distribution of the A homopolymers in the BAB/A blends result in a phase behavior drastically different from that of the ABA/A and AB/A blends. The ABA/A blends stabilize the Frank-Kasper (FK) phases similar to the AB/A blends, but the stability window of FK phases becomes negligibly small in the corresponding BAB/A blends. Our results demonstrate that the topological effect of block copolymers on the equilibrium phase behaviors can be more prominent in multicomponent systems and thus more attention should be paid to copolymer topologies in the design of polymeric blends. Published by the American Physical Society 2024

Isoscalar giant resonances of <inline-formula><tex-math id="M1">\begin{document}$^{{\bf{18}}}_{{\boldsymbol{\Lambda\Lambda}}}{\bf{O}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M1.png"/></alternatives></inline-formula> in relativistic approach

The interactions between hyperon-nucleon and hyperon-hyperon have been an important topic in strangeness nuclear physics, which play an important role in understanding the properties of hypernuclei and equation of state of strangeness nuclear matter. It is very difficult to perform a direct scattering experiment of the nucleon and hyperon because the short lifetime of the hyperon. Therefore, the hyperon-nucleon interaction and the hyperon-hyperon interaction have been mainly investigated experimentally by <inline-formula><tex-math id="M4">\begin{document}$\gamma$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M4.png"/></alternatives></inline-formula> spectroscopy of single-<inline-formula><tex-math id="M5">\begin{document}$\Lambda$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M5.png"/></alternatives></inline-formula> hypernuclei or double-<inline-formula><tex-math id="M6">\begin{document}$\Lambda$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M6.png"/></alternatives></inline-formula> hypernuclei. There are also many theoretical methods developed to describe the properties of hypernuclei. Most of these models focus mostly on the ground state properties of hypernuclei, and have given exciting results in producing the banding energy, the energy of single-particle levels, deformations, and other properties of hypernuclei. Only a few researches adopting Skyrme energy density functionals is devoted to the study of the collective excitation properties of hypernuclei. In present work, we have extended the relativistic mean field and relativistic random phase approximation theories to study the collective excitation properties of hypernuclei, and use the methods to study the isoscalar collective excited state properties of double <inline-formula><tex-math id="M7">\begin{document}$\Lambda$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M7.png"/></alternatives></inline-formula> hypernuclei. First, the effect of <inline-formula><tex-math id="M8">\begin{document}$\Lambda$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M8.png"/></alternatives></inline-formula> hyperons on the single-particle energy of <sup>16</sup>O and <inline-formula><tex-math id="M9">\begin{document}$^{18}_{\Lambda\Lambda}{\rm{O}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M9.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M9.png"/></alternatives></inline-formula> are discussed in the relativistic mean field theory, the calculations are performed within TM1 parameter set and related hyperon-nucleon interaction, and hyperon-hyperon interaction. We find that it gives a larger attractive effect on the <inline-formula><tex-math id="M10">\begin{document}${{\mathrm{s}}}_{1/2}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M10.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M10.png"/></alternatives></inline-formula> state of proton and neutron, while gives a weaker attractive effect on the state around Fermi surface. The self-consistent relativistic random phase approximation is used to study the collectively excited state properties of hypernucleus <inline-formula><tex-math id="M11">\begin{document}$^{18}_{\Lambda\Lambda}{\rm{O}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M11.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M11.png"/></alternatives></inline-formula>. The isoscalar giant monopole resonance and quadrupole resonance are calculated and analysed in detail, we pay more attention to the effect of the inclusion of <inline-formula><tex-math id="M12">\begin{document}$\Lambda$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M12.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M12.png"/></alternatives></inline-formula> hyperons on the properties of giant resonances. Comparing with the strength distributions of <sup>16</sup>O, changes of response function of <inline-formula><tex-math id="M13">\begin{document}$^{18}_{\Lambda\Lambda}{\rm{O}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M13.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M13.png"/></alternatives></inline-formula> are evidently found both on the isoscalar giant monopole resonance and quadrupole resonance. It is shown that the difference comes mainly from the change of Hartree energy of particle-hole configuration and the contribution of the excitations of <inline-formula><tex-math id="M14">\begin{document}$\Lambda$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M14.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231531_M14.png"/></alternatives></inline-formula> hyperons. We find that the hyperon-hyperon residual interactions have small effect on the monopole resonance function and quadrupole response function in the low-energy region, and have almost no effect on the response functions in the high-energy region.

Microphase versus macrophase separation in the square-well-linear fluid: A theoretical and computational study.

Due to the presence of competing interactions, the square-well-linear fluid can exhibit either liquid-vapor equilibrium (macrophase separation) or clustering (microphase separation). Here we address the issue of determining the boundary between these two regimes, i.e., the Lifshitz point, expressed in terms of a relationship between the parameters of the model. To this aim, we carry out Monte Carlo simulations to compute the structure factor of the fluid, whose behavior at low wave vectors accurately captures the tendency of the fluid to form aggregates or, alternatively, to phase separate. Specifically, for a number of different combinations of attraction and repulsion ranges, we make the system go across the Lifshitz point by increasing the strength of the repulsion. We use simulation results to benchmark the performance of two theories of fluids, namely, the hypernetted chain (HNC) equationand the analytically solvable random phase approximation (RPA); in particular, the RPA theory is applied with two different prescriptions as for the direct correlation function inside the core. Overall, the HNC theory proves to be an appropriate tool to characterize the fluid structure and the low-wave-vector behavior of the structure factor is consistent with the threshold between microphase and macrophase separation established through simulation. The structural predictions of the RPA theory turn out to be less accurate, but this theory offers the advantage of providing an analytical expression of the Lifshitz point. Compared to simulation, both RPA schemes predict a Lifshitz point that falls within the macrophase-separation region of parameters: in the best case, barriers roughly twice higher than predicted are required to attain clustering conditions.

Complex eigenenergy of the giant dipole resonance forO16by the Jost function within the random-phase approximation framework

The Jost function method is extended within the framework of the random phase approximation (RPA) theory to find poles on the complex energy plane that exhibit complex RPA eigenenergies. Poles corresponding to the RPA excited states such as the giant resonance of $^{16}\mathrm{O}$ electric dipole excitations were successfully found on the complex energy plane. Although the giant resonance has been known as a single resonance with large strength and width, it is found that, at least within the RPA framework, the $^{16}\mathrm{O}$ electric dipole giant resonance is formed by multiple poles, each of which is an independent pole with different widths, origins, response properties to residual interactions, and components structures of the density fluctuation.

Phase diagram of the square-lattice Hubbard model with Rashba-type antisymmetric spin-orbit coupling

We clarify the ground-state phase diagram of the half-filled square-lattice Hubbard model with Rashba spin-orbit coupling (SOC) characterized by the spin-split energy bands due to broken inversion symmetry. Although the Rashba metals and insulating magnets have been studied well, the intermediate interaction strength of the system remained elusive due to the lack of appropriate theoretical tools to unbiasedly describe the large-scale magnetic structures. We complementarily apply four different methods (sine-square deformed mean-field theory, random phase approximation, Luttinger-Tisza method, and density matrix embedding theory) and succeed in capturing the incommensurate spin-density-wave (SDW) phases with very long spatial periods which were previously overlooked. The transition to the SDW phases from the metallic phase is driven by an unprecedented instability that nests the two parts of the Fermi surface carrying opposite spins. For large SOC, the spiral, stipe, and vortex phases are obtained, when the four Dirac points exist near the Fermi level and their whole linear dispersions nest by a wavelength $\ensuremath{\pi}$, opening a band gap. These two types of transition provide Fermiology that distinguishes the antisymmetric SOC systems, generating a variety of magnetic phases that start from the relatively weak correlation regime and continue to the strongly interacting limit.

Spurious dipole mode in random-phase approximation and in models based on this approximation

The problems related to the existence of the spurious dipole mode (SDM) in self-consistent nuclear-structure models are considered. A method is formulated that allows one to eliminate the coupling of the SDM with the physical modes in the extended random-phase approximation (ERPA) theories, in particular, in the time blocking approximation (TBA), which is a model of the ERPA type. It is shown that the application of this method in realistic TBA calculations of the $E1$ excitations gives results which are very close to the results of TBA calculations without using this method if the bare external-field $E1$ operators are replaced by effective ones.

Small-Angle X-ray Scattering Analysis on the Estimation of Interaction Parameter of Poly(n-butyl acrylate)-b-poly(methyl methacrylate).

The temperature dependence of the Flory-Huggins interaction parameter χ for poly(n-butyl acrylate)-b-poly(methyl methacrylate) (PBA-b-PMMA) was quantified from small-angle X-ray scattering (SAXS) analysis using random phase approximation (RPA) theory. It was found from the χ estimation (χ=0.0103+14.76/T) that the enthalpic contribution, χH, a measure for temperature susceptibility of χ, is 1.7-4.5 folds smaller for PBA-b-PMMA than for the conventional styrene-diene-based block copolymers, which have been widely used for thermoplastic elastomers. This finding suggests that these fully acrylic components can be a desirable chemical pair for constituting terpolymers applied for thermally stable and mechanically resilient elastomers.

Effects of ground-state correlations on the damping of giant dipole resonances in LS closed-shell nuclei

Abstract The effects of ground-state correlations on the damping of isovector giant dipole resonances in the LS closed-shell nuclei 16O and 40Ca are studied using extended random phase approximation (RPA) approaches derived from the time-dependent density matrix theory. It is pointed out that unconventional two-body amplitudes of one-particle–three-hole and three-particle–one-hole types that are neglected in most extended RPA theories play an important role in the fragmentation of isovector dipole strength.

Iron group nuclei electron capture in super-Chandrasekhar superstrong magnetic white dwarfs

Using the theory of relativistic mean-field effective interactions, the influences of superstrong magnetic fields (SMFs) on electron Fermi energy, binding energy per nucleus and single-particle level structure are discussed in super-Chandrasekhar magnetic white dwarfs. Based on the relativistical SMFs theory model of Potekhin et al., the electron chemical potential is corrected in SMFs, and the electron capture (EC) of iron group nuclei is investigated by using the Shell-Model Monte Carlo method and Random Phase Approximation theory. The EC rates can increase by more than three orders of magnitude due to the increase of the electron Fermi energy and the change of single-particle level structure by SMFs. However, the EC rates can decrease by more than four orders of magnitude due to increase of the nuclei binding energy by SMFs. We compare our results with those of FFNs (Fuller et al.), AUFDs (Aufderheide et al.) and Nabi (Nabi et al.). Our rates are higher by about four orders of magnitude than those of FFN, AUFD and Nabi due to SMFs. Our study may have important reference value for subsequent studies of the instability, mass radius relationship, and thermal and magnetic evolution of super-Chandrasekhar magnetic white dwarfs.

Investigating properties of Cl− and Au− ions using relativistic many-body methods

We investigate the ground state properties of singly charged chlorine (Cl−) and gold (Au−) negative ions by employing four-component relativistic many-body methods. In our approach, we attach an electron to the respective outer orbitals of chlorine (Cl) and gold (Au) atoms to determine the Dirac–Fock (DF) wave functions of the ground state configurations of Cl− and Au−, respectively. As a result, all the single-particle orbitals see the correlation effects due to the appended electron of the negative ion. After obtaining the DF wave functions, lower-order many-body perturbation methods, random-phase approximation, and coupled-cluster (CC) theory in the single and double approximation are applied to obtain the ground state wave functions of both Cl− and Au− ions. Then, we adopt two different approaches to the CC theory—a perturbative approach due to the dipole operator to determine electric dipole polarizability and an electron detachment approach in the Fock-space framework to estimate ionization potential. Our calculations are compared with the available experimental and other theoretical results.

Isoscalar and isovector giant resonances in 44Ca, 54Fe, 64,68Zn and 56,58,60,68Ni

We have studied the uncharacteristic behavior of the measured values of the isoscalar and isovector centroid energies, ECEN, of nuclear giant resonances of multipolarity from L = 0 to L = 3 in 44Ca, 54Fe, 64,68Zn and 56,58,60,68Ni. For this purpose, we carried out calculations of ECEN within the spherical Hartree-Fock (HF)-based random phase approximation (RPA) theory with 33 distinct Skyrme-like effective nucleon-nucleon interactions. We have also determined the Pearson linear correlation coefficients between centroid energies, obtained from the HF-RPA, and the various properties of nuclear matter (NM) of each interaction and determined the sensitivity of ECEN to NM properties. We compared the theoretical values of ECEN obtained from the HF-RPA calculations with experimental data and discuss the results, pointing out significant disagreements between theoretical and experimental values. We note in particular, that we obtain good agreement for the theoretical ECEN of the isovector giant dipole resonance and the available experimental data.

Anisotropic fermionic quasiparticles

We have carried out a comprehensive investigation of the quasiparticle properties of a two-dimensional electron gas, interacting via the long-range Coulomb interaction in the presence of bare mass anisotropy (i.e., with an elliptic noninteracting Fermi surface) by calculating the self-energy, the spectral function, the scattering rate, and the effective mass within the leading-order dynamical self-energy approximation. Our theory is exact in the high-density limit. We find anisotropic features of quasiparticle properties that are not captured by the commonly used isotropic approximation where the anisotropic effective mass is replaced by the isotropic averaged density-of-states mass. Some of these interesting results are as follows: (1) The many-body renormalization of the quasiparticle spectrum becomes highly anisotropic as the quasiparticle energy increases away from the Fermi energy; (2) the interaction-induced inelastic-scattering rate features a strong anisotropy, exhibiting an abrupt jump at different injected energies depending on the momentum direction of the injected electron; (3) the effective-mass enhancement is larger (smaller) for the light (heavy) mass, showing that the anisotropy is reduced by interactions. Our results and analysis show that the unjustified neglect of the mass anisotropy can lead to an incorrect description of quasiparticle properties of the anisotropic system and inaccurate estimates of physical quantities of interest although the use of an equivalent isotropic approximation using the density-of-states effective mass as is commonly and uncritically performed in the literature, works as a reasonable approximation in many situations. In addition to the complete random phase approximation theory for the anisotropic quasiparticles, we also provide a theory using the simpler plasmon-pole approximation, commenting on its validity for anisotropic self-energy calculations. We comment also on the interaction effect on the Fermi-surface topology, finding that the elliptic shape of the bare Fermi surface is preserved with suppressed ellipticity in the interacting system to a high degree of accuracy except in the very strongly interacting limit (and for very high bare mass anisotropy). Our theory provides a complete generalization of the existing isotropic many-body theory of interacting electrons to the corresponding anisotropic systems.

Weakly coupled alternating S=12 chains in the distorted honeycomb lattice compound Na2Cu2TeO6

Spin-1/2 chains with alternating antiferromagnetic (AF) and ferromagnetic (FM) couplings exhibit quantum entanglement like the integer-spin Haldane chains and might be similarly utilized for quantum computations. Such alternating AF-FM chains have been proposed to be realized in the distorted honeycomb-lattice compound Na$_2$Cu$_2$TeO$_6$, but to confirm this picture a comprehensive understanding of the exchange interactions including terms outside of the idealized model is required. Here we employ neutron scattering to study the spin dynamics in Na$_2$Cu$_2$TeO$_6$ and accurately determine the coupling strengths through the random phase approximation and density functional theory (DFT) approaches. We find the AF and FM intrachain couplings are the dominant terms in the spin Hamiltonian, while the interchain couplings are AF but perturbative. This hierarchy in the coupling strengths and the alternating signs of the intrachain couplings can be understood through their different exchange paths. Our results establish Na$_2$Cu$_2$TeO$_6$ as a weakly-coupled alternating AF-FM chain compound and reveal the robustness of the gapped ground state in alternating chains under weak interchain couplings.

Determination of the dipole polarizability of the alkali-metal negative ions

We present electric dipole polarizabilities ($\alpha_d$) of the alkali-metal negative ions, from H$^-$ to Fr$^-$, by employing four-component relativistic many-body methods. Differences in the results are shown by considering Dirac-Coulomb (DC) Hamiltonian, DC Hamiltonian with the Breit interaction, and DC Hamiltonian with the lower-order quantum electrodynamics interactions. At first, these interactions are included self-consistently in the Dirac-Hartree-Fock (DHF) method, and then electron correlation effects are incorporated over the DHF wave functions in the second-order many-body perturbation theory, random phase approximation and coupled-cluster (CC) theory. Roles of electron correlation effects and relativistic corrections are analyzed using the above many-body methods with size of the ions. We finally quote precise values of $\alpha_d$ of the above negative ions by estimating uncertainties to the CC results, and compare them with other calculations wherever available.

The size and affinity effect of counterions on self-assembly of charged block copolymers.

The effect of counterions' size and affinity on the microphase separated morphologies of neutral-charged diblock copolymers is investigated systematically using a random phase approximation (RPA) and self-consistent field theory (SCFT). The phase diagrams as a function of χAB and fA at different counterion sizes and different affinities to neutral blocks are constructed, respectively. Stability limits calculated using the RPA are in good agreement with the disorder-body-centered cubic phase boundaries from SCFT calculations. It was found that increasing the size of counterions causes the phase diagram to shift upward and leftward, which is attributed to electrostatic interactions and the intrinsic volume of counterions. The domain size of the ordered phase shows an unexpected tendency that it decreases with increasing counterions' size. The counterions' distributions in H and G phases demonstrate that it is electrostatic interaction, instead of packing frustration, that plays a leading role in such systems. For finite size counterions, with the increase in affinity between counterions and neutral blocks, the phase diagram shifts upward, indicating the improved compatibility between different blocks. Furthermore, the affinity effect between counterions and neutral blocks can be mapped into an effective Flory parameter χAB ' = χAB + 0.27χBC.

Quantifying the fragility of unprotected quadratic band crossing points

We examine a basic lattice model of interacting fermions that exhibits quadratic band crossing points (QBCPs) in the non-interacting limit. In particular, we consider spinless fermions on the honeycomb lattice with nearest neighbor hopping $t$ and third-nearest neighbor hopping $t''$, which exhibits fine-tuned QBCPs at the corners of the Brillouin zone for ${t'' = t/2}$. In this situation, the density of states remains finite at the Fermi level of the half-filled band and repulsive nearest-neighbor interactions $V$ lead to a charge-density-wave (CDW) instability at infinitesimally small $V$ in the random-phase approximation or mean-field theory. We examine the fragility of the QBCPs against dispersion renormalizations in the ${t\mbox{-}t''\mbox{-}V}$ model using perturbation theory, and find that the $t''$-value needed for the QBCPs increases with $V$ due to the hopping renormalization. However, the instability toward CDW formation always requires a nonzero threshold interaction strength, i.e., one cannot fine-tune $t''$ to recover the QBCPs in the interacting system. These perturbative arguments are supported by quantum Monte Carlo simulations for which we carefully compare the corresponding threshold scales at and beyond the QBCP fine-tuning point. From this analysis, we thus gain a quantitative microscopic understanding of the fragility of the QBCPs in this basic interacting fermion system.

Theoretical and computational methods of protein liquid-liquid phase separation

Liquid-liquid phase separation (LLPS) of proteins is an emerging field in the research of biophysics. Many intrinsically disordered proteins (IDPs) are known to have the ability to assemble via LLPS and to organize into protein-rich and dilute phases both in vivo and in vitro. Such a kind of phase separation of proteins plays an important role in a wide range of cellular processes, such as the formation of membraneless organelles (MLOs), signaling transduction, intracellular organization, chromatin organization, etc. In recent years, there appeared a great number of theoretical analysis, computational simulation and experimental research focusing on the physical principles of LLPS. In this article, the theoretical and computational simulation methods for the LLPS are briefly reviewed. To elucidate the physical principle of LLPS and to understand the phase behaviors of the proteins, biophysicists have introduced the concepts and theories from statistical mechanics and polymer sciences. Flory-Huggins theory and its extensions, such as mean-field model, random phase approximation (RPA) and field theory simulations, can conduce to understanding the phase diagram of the LLPS. To reveal the hidden principles in the sequence-dependent phase behaviors of different biomolecular condensates, different simulation methods including lattice models, off-lattice coarse-grained models, and all-atom simulations are introduced to perform computer simulations. By reducing the conformational space of the proteins, lattice models can capture the key points in LLPS and simplify the computations. In the off-lattice models, a polypeptide can be coarse-grained as connected particles representing repeated short peptide fragments. All-atom simulations can describe the structure of proteins at a higher resolution but consume higher computation-power. Multi-scale simulation may provide the key to understanding LLPS at both high computational efficiency and high accuracy. With these methods, we can elucidate the sequence-dependent phase behaviors of proteins at different resolutions. To sum up, it is necessary to choose the appropriate method to model LLPS processes according to the interactions within the molecules and the specific phase behaviors of the system. The simulations of LLPS can facilitate the comprehensive understanding of the key features which regulate the membraneless compartmentalization in cell biology and shed light on the design of artificial cells and the control of neurodegeneration.

Energy rates due to weak decay rates of vanadium isotopes in stellar environment

The neutrino cooling and gamma heating rates are considered as an important input needed to study the final phases of the evolution of high-mass stars. The weak-interaction mediated processes, namely the $\beta $-decay and electron capture, significantly change the lepton to baryon ratio and accelerate the contraction of the core. The emission of resulting neutrinos/antineutrinos tend to cool the stellar core. On the other hand gamma rays are produced because of electron capture and $\beta $-decay to excited states in daughter nuclei. These gamma rays heat the core and contribute to increase of entropy which may cause convection to occur. In the present work, the weak-interaction heating and cooling rates on a chain of twenty two isotopes of vanadium having mass in the range 43–64 have been estimated using the proton-neutron quasiparticle random phase approximation theory. The rates have been computed for the temperature ranging from ($10^{7}\mbox{--}3\times 10^{10}$) K and for the density range $(10\mbox{--}10^{11})~\mbox{g/cm}^{3}$. Our calculated neutrino energy loss rates have also been compared with the previously reported rates calculated using other theoretical models. At high stellar temperatures, our rates are larger by 1–2 orders of magnitude as compared to previous results.

High-pressure neutron scattering and random-phase approximation analysis of a molten Baroplastic diblock copolymer

Through high-pressure, small-angle neutron scattering (SANS) and a random-phase approximation (RPA) theory based on a molecular model, we investigate the origin of the pressure responsiveness of a phase-segregating deuterated polystyrene-block-poly (2-ethyl hexyl acrylate) (dPS-b-PEHA) copolymer melt for use as a material for low-energy processing. The SANS intensities for the copolymer were measured over a temperature range at applied pressures between 0.1 and ∼83 MPa. The copolymer exhibited an order-disorder transition (ODT) and revealed baroplasticity, where its ODT was suppressed upon pressurization as ΔTODT/ΔP≈ -15.8 K/100 MPa to ease subsequent processing. Theory predicts that a disparity in the self interactions εjj’s (Δεjj=εPS−εPEHA) or a disparity in the compressibilities between blocks precisely yields the observed ΔTODT/ΔP. The effective Flory-Huggins χ is argued to consist of the conventional enthalpic χH and entropic χS coming from Δεjj mediated by the copolymer bulk modulus. Pressure strengthens χH due to densification, whereas the augmented bulk modulus reduces χS. The diminution of χS is shown to be the source of baroplasticity.