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1. Size dependence- and induced transformations- of fractional quantum Hall effects under tilted magnetic fields

   https://doi.org/10.1038/s41598-022-22812-x  

   Wijewardena, U. Kushan; Nanayakkara, Tharanga R.; Kriisa, Annika; Reichl, Christian; Wegscheider, Werner; Mani, Ramesh G. (November 2022, Scientific Reports)

   Abstract Two-dimensional electron systems subjected to high transverse magnetic fields can exhibit Fractional Quantum Hall Effects (FQHE). In the GaAs/AlGaAs 2D electron system, a double degeneracy of Landau levels due to electron-spin, is removed by a small Zeeman spin splitting,$$g \mu _B B$$ $g{\mu }_{B}B$, comparable to the correlation energy. Then, a change of the Zeeman splitting relative to the correlation energy can lead to a re-ordering between spin polarized, partially polarized, and unpolarized many body ground states at a constant filling factor. We show here that tuning the spin energy can produce fractionally quantized Hall effect transitions that include both a change in$$\nu$$ $\nu$for the$$R_{xx}$$ $R_{\mathrm{xx}}$minimum, e.g., from$$\nu = 11/7$$ $\nu =11/7$to$$\nu = 8/5$$ $\nu =8/5$, and a corresponding change in the$$R_{xy}$$ $R_{\mathrm{xy}}$, e.g., from$$R_{xy}/R_{K} = (11/7)^{-1}$$ $R_{\mathrm{xy}}/R_K={(11/7)}^{-1}$to$$R_{xy}/R_{K} = (8/5)^{-1}$$ $R_{\mathrm{xy}}/R_K={(8/5)}^{-1}$, with increasing tilt angle. Further, we exhibit a striking size dependence in the tilt angle interval for the vanishing of the$$\nu = 4/3$$ $\nu =4/3$and$$\nu = 7/5$$ $\nu =7/5$resistance minima, including “avoided crossing” type lineshape characteristics, and observable shifts of$$R_{xy}$$ $R_{\mathrm{xy}}$at the$$R_{xx}$$ $R_{\mathrm{xx}}$minima- the latter occurring for$$\nu = 4/3, 7/5$$ $\nu =4/3,7/5$and the 10/7. The results demonstrate both size dependence and the possibility, not just of competition between different spin polarized states at the same$$\nu$$ $\nu$and$$R_{xy}$$ $R_{\mathrm{xy}}$, but also the tilt- or Zeeman-energy-dependent- crossover between distinct FQHE associated with different Hall resistances. 

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2. Hardness and approximation of submodular minimum linear ordering problems

   https://doi.org/10.1007/s10107-023-02038-z  

   Farhadi, Majid; Gupta, Swati; Sun, Shengding; Tetali, Prasad; Wigal, Michael C (December 2023, Mathematical Programming)

   Abstract The minimum linear ordering problem (MLOP) generalizes well-known combinatorial optimization problems such as minimum linear arrangement and minimum sum set cover. MLOP seeks to minimize an aggregated cost$$f(\cdot )$$ $f(·)$due to an ordering$$\sigma $$ $\sigma$of the items (say [n]), i.e.,$$\min _{\sigma } \sum _{i\in [n]} f(E_{i,\sigma })$$ ${min}_{\sigma }{\sum }_{i\in \left[n\right]}f\left(E_{i,\sigma }\right)$, where$$E_{i,\sigma }$$ $E_{i,\sigma }$is the set of items mapped by$$\sigma $$ $\sigma$to indices [i]. Despite an extensive literature on MLOP variants and approximations for these, it was unclear whether the graphic matroid MLOP was NP-hard. We settle this question through non-trivial reductions from mininimum latency vertex cover and minimum sum vertex cover problems. We further propose a new combinatorial algorithm for approximating monotone submodular MLOP, using the theory of principal partitions. This is in contrast to the rounding algorithm by Iwata et al. (in: APPROX, 2012), using Lovász extension of submodular functions. We show a$$(2-\frac{1+\ell _{f}}{1+|E|})$$ $(2-\frac{1+{\ell }_f}{1+\left|E\right|})$-approximation for monotone submodular MLOP where$$\ell _{f}=\frac{f(E)}{\max _{x\in E}f(\{x\})}$$ ${\ell }_f=\frac{f\left(E\right)}{{max}_{x\in E}f\left(\left\{x\right\}\right)}$satisfies$$1 \le \ell _f \le |E|$$ $1\le {\ell }_f\le \left|E\right|$. Our theory provides new approximation bounds for special cases of the problem, in particular a$$(2-\frac{1+r(E)}{1+|E|})$$ $(2-\frac{1+r\left(E\right)}{1+\left|E\right|})$-approximation for the matroid MLOP, where$$f = r$$ $f=r$is the rank function of a matroid. We further show that minimum latency vertex cover is$$\frac{4}{3}$$ $\frac{4}{3}$-approximable, by which we also lower bound the integrality gap of its natural LP relaxation, which might be of independent interest. 

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3. Modular apparatus for nuclear reactions spectroscopy (MARS): characterization and first application to determine $$^{12}$$C($$^6$$Li,$$^4$$He)$$^{14}\hbox {N}^{g.s}$$ nuclear reaction cross sections

   https://doi.org/10.1140/epjp/s13360-025-06305-0  

   Garrido-Gómez, L; Vegas-Díaz, A; Alvarez, M_A G; Fernández-García, J P; Fernández, B; Ferrer, F J; Lopez-Aires, D (May 2025, The European Physical Journal Plus)

   Abstract This work presents MARS (Modular apparatus for nuclear reactions spectroscopy) and its characterization prior to its first application to measure$$^6$$ $_{}^6$Li+$$^{12}$$ $_{}^{12}$C nuclear reactions. Measurements were performed at the 3 MV tandem accelerator of the CNA (National Accelerator Center), in Seville, Spain. The$$^{6}$$ $_{}^6$Li projectiles were accelerated at energies around the$$^6$$ $_{}^6$Li+$$^{12}$$ $_{}^{12}$C Coulomb barrier ($$V^{\text {cm}}_{B}\sim 3.0$$ $V_B^{\text{cm}}\sim 3.0$MeV - center of mass and$$V^{\text {lab}}_{B}\sim 4.5$$ $V_B^{\text{lab}}\sim 4.5$MeV - laboratory frame). Using a$$^{6}\hbox {Li}^{2+}$$ $_{}^6{\text{Li}}^{2+}$beam, we measured at 13 laboratory energies from 4.00 to 7.75 MeV. Thus, we present the excitation function of$$^{12}$$ $_{}^{12}$C($$^6$$ $_{}^6$Li,$$^4$$ $_{}^4$He)$$^{14}\hbox {N}^{g.s.}$$ $_{}^{14}{\text{N}}^{g.s.}$reaction, at 2 backward angles ($$110.0^\circ $$ $110.0^{\circ }$and$$140.0^\circ $$ $140.0^{\circ }$). The projectile dissociation, leading to this reaction, increases with the bombarding energies around the Coulomb barrier. This dissociation is favored at an optimum energy$$E_{b}^{\text {op}}$$ $E_b^{\text{op}}$$$\ge $$ $\ge$$$V_{B}$$ $V_B$+$$|Q_{bu}|$$ $|Q_{\mathrm{bu}}|$, where$$V_{B}$$ $V_B$is the Coulomb barrier of the system, and$$|Q_{bu}|$$ $|Q_{\mathrm{bu}}|$is the module ofQ-value for the$$^6$$ $_{}^6$Li dissociation into$$^4$$ $_{}^4$He+$$^2$$ $_{}^2$H. This result corroborates a systematic analysis of weakly bound projectiles reacting on several targets [1]. 

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4. Higher arity stability and the functional order property

   https://doi.org/10.1007/s00029-025-01055-4  

   Abd_Aldaim, A; Conant, G; Terry, C (July 2025, Selecta Mathematica)

   Abstract Thek-dimensional functional order property ($$\operatorname {FOP}_k$$ ${FOP}_k$) is a combinatorial property of a$$(k+1)$$ $(k+1)$-partitioned formula. This notion arose in work of Terry and Wolf [59, 60], which identified$$\operatorname {NFOP}_2$$ ${NFOP}_2$as a ternary analogue of stability in the context of two finitary combinatorial problems related to hypergraph regularity and arithmetic regularity. In this paper we show$$\operatorname {NFOP}_k$$ ${NFOP}_k$has equally strong implications in model-theoretic classification theory, where its behavior as a$$(k+1)$$ $(k+1)$-ary version of stability is in close analogy to the behavior ofk-dependence as a$$(k+1)$$ $(k+1)$-ary version of$$\operatorname {NIP}$$ $NIP$. Our results include several new characterizations of$$\operatorname {NFOP}_k$$ ${NFOP}_k$, including a characterization in terms of collapsing indiscernibles, combinatorial recharacterizations, and a characterization in terms of type-counting when$$k=2$$ $k=2$. As a corollary of our collapsing theorem, we show$$\operatorname {NFOP}_k$$ ${NFOP}_k$is closed under Boolean combinations, and that$$\operatorname {FOP}_k$$ ${FOP}_k$can always be witnessed by a formula where all but one variable have length 1. When$$k=2$$ $k=2$, we prove a composition lemma analogous to that of Chernikov and Hempel from the setting of 2-dependence. Using this, we provide a new class of algebraic examples of$$\operatorname {NFOP}_2$$ ${NFOP}_2$theories. Specifically, we show that ifTis the theory of an infinite dimensional vector space over a fieldK, equipped with a bilinear form satisfying certain properties, thenTis$$\operatorname {NFOP}_2$$ ${NFOP}_2$if and only ifKis stable. Along the way we provide a corrected and reorganized proof of Granger’s quantifier elimination and completeness results for these theories. 

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5. Evidence of a liquid–liquid phase transition in H$$_2$$O and D$$_2$$O from path-integral molecular dynamics simulations

   https://doi.org/10.1038/s41598-022-09525-x  

   Eltareb, Ali; Lopez, Gustavo E.; Giovambattista, Nicolas (April 2022, Scientific Reports)

   Abstract We perform path-integral molecular dynamics (PIMD), ring-polymer MD (RPMD), and classical MD simulations of H$$_2$$ ${}_2$O and D$$_2$$ ${}_2$O using the q-TIP4P/F water model over a wide range of temperatures and pressures. The density$$\rho (T)$$ $\rho \left(T\right)$, isothermal compressibility$$\kappa _T(T)$$ ${\kappa }_T\left(T\right)$, and self-diffusion coefficientsD(T) of H$$_2$$ ${}_2$O and D$$_2$$ ${}_2$O are in excellent agreement with available experimental data; the isobaric heat capacity$$C_P(T)$$ $C_P\left(T\right)$obtained from PIMD and MD simulations agree qualitatively well with the experiments. Some of these thermodynamic properties exhibit anomalous maxima upon isobaric cooling, consistent with recent experiments and with the possibility that H$$_2$$ ${}_2$O and D$$_2$$ ${}_2$O exhibit a liquid-liquid critical point (LLCP) at low temperatures and positive pressures. The data from PIMD/MD for H$$_2$$ ${}_2$O and D$$_2$$ ${}_2$O can be fitted remarkably well using the Two-State-Equation-of-State (TSEOS). Using the TSEOS, we estimate that the LLCP for q-TIP4P/F H$$_2$$ ${}_2$O, from PIMD simulations, is located at$$P_c = 167 \pm 9$$ $P_c=167\pm 9$ MPa,$$T_c = 159 \pm 6$$ $T_c=159\pm 6$ K, and$$\rho _c = 1.02 \pm 0.01$$ ${\rho }_c=1.02\pm 0.01$ g/cm$$^3$$ ${}^3$. Isotope substitution effects are important; the LLCP location in q-TIP4P/F D$$_2$$ ${}_2$O is estimated to be$$P_c = 176 \pm 4$$ $P_c=176\pm 4$ MPa,$$T_c = 177 \pm 2$$ $T_c=177\pm 2$ K, and$$\rho _c = 1.13 \pm 0.01$$ ${\rho }_c=1.13\pm 0.01$ g/cm$$^3$$ ${}^3$. Interestingly, for the water model studied, differences in the LLCP location from PIMD and MD simulations suggest that nuclear quantum effects (i.e., atoms delocalization) play an important role in the thermodynamics of water around the LLCP (from the MD simulations of q-TIP4P/F water,$$P_c = 203 \pm 4$$ $P_c=203\pm 4$ MPa,$$T_c = 175 \pm 2$$ $T_c=175\pm 2$ K, and$$\rho _c = 1.03 \pm 0.01$$ ${\rho }_c=1.03\pm 0.01$ g/cm$$^3$$ ${}^3$). Overall, our results strongly support the LLPT scenario to explain water anomalous behavior, independently of the fundamental differences between classical MD and PIMD techniques. The reported values of$$T_c$$ $T_c$for D$$_2$$ ${}_2$O and, particularly, H$$_2$$ ${}_2$O suggest that improved water models are needed for the study of supercooled water. 

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